[ { "id": "cap-set-1-lower-2", "constant": "cap-set-1", "group": "cap-set", "bound": "lower", "value": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cap-set/cap-set-1-lower-2.yml" }, { "id": "cap-set-2-lower-4", "constant": "cap-set-2", "group": "cap-set", "bound": "lower", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cap-set/cap-set-2-lower-4.yml" }, { "id": "cap-set-3-lower-9", "constant": "cap-set-3", "group": "cap-set", "bound": "lower", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cap-set/cap-set-3-lower-9.yml" }, { "id": "cap-set-4-lower-20", "constant": "cap-set-4", "group": "cap-set", "bound": "lower", "value": { "latex": "20", "decimal_approx": 20, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "20", "decimal_approx": 20, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cap-set/cap-set-4-lower-20.yml" }, { "id": "cap-set-5-lower-45", "constant": "cap-set-5", "group": "cap-set", "bound": "lower", "value": { "latex": "45", "decimal_approx": 45, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "45", "decimal_approx": 45, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cap-set/cap-set-5-lower-45.yml" }, { "id": "cap-set-6-lower-112", "constant": "cap-set-6", "group": "cap-set", "bound": "lower", "value": { "latex": "112", "decimal_approx": 112, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "112", "decimal_approx": 112, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cap-set/cap-set-6-lower-112.yml" }, { "id": "cap-set-7-lower-236", "constant": "cap-set-7", "group": "cap-set", "bound": "lower", "value": { "latex": "236", "decimal_approx": 236, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "236", "decimal_approx": 236, "alt_display": null }, "comparison": "equal", "source": "edel-bierbrauer-2001", "path": "certificates/cap-set/cap-set-7-lower-236.yml" }, { "id": "cap-set-8-lower-512", "constant": "cap-set-8", "group": "cap-set", "bound": "lower", "value": { "latex": "512", "decimal_approx": 512, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "512", "decimal_approx": 512, "alt_display": null }, "comparison": "equal", "source": "romera-paredes-et-al-2023", "path": "certificates/cap-set/cap-set-8-lower-512.yml" }, { "id": "isosceles-set-1-lower-3", "constant": "isosceles-set-1", "group": "isosceles-set", "bound": "lower", "value": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/isosceles-set/isosceles-set-1-lower-3.yml" }, { "id": "isosceles-set-10-lower-56", "constant": "isosceles-set-10", "group": "isosceles-set", "bound": "lower", "value": { "latex": "56", "decimal_approx": 56, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/isosceles-set/isosceles-set-10-lower-56.yml" }, { "id": "isosceles-set-11-lower-67", "constant": "isosceles-set-11", "group": "isosceles-set", "bound": "lower", "value": { "latex": "67", "decimal_approx": 67, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/isosceles-set/isosceles-set-11-lower-67.yml" }, { "id": "isosceles-set-12-lower-79", "constant": "isosceles-set-12", "group": "isosceles-set", "bound": "lower", "value": { "latex": "79", "decimal_approx": 79, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/isosceles-set/isosceles-set-12-lower-79.yml" }, { "id": "isosceles-set-2-lower-6", "constant": "isosceles-set-2", "group": "isosceles-set", "bound": "lower", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": "erdos-1946", "path": "certificates/isosceles-set/isosceles-set-2-lower-6.yml" }, { "id": "isosceles-set-3-lower-8", "constant": "isosceles-set-3", "group": "isosceles-set", "bound": "lower", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": "kelly-1947", "path": "certificates/isosceles-set/isosceles-set-3-lower-8.yml" }, { "id": "isosceles-set-4-lower-11", "constant": "isosceles-set-4", "group": "isosceles-set", "bound": "lower", "value": { "latex": "11", "decimal_approx": 11, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "11", "decimal_approx": 11, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/isosceles-set/isosceles-set-4-lower-11.yml" }, { "id": "isosceles-set-5-lower-17", "constant": "isosceles-set-5", "group": "isosceles-set", "bound": "lower", "value": { "latex": "17", "decimal_approx": 17, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "17", "decimal_approx": 17, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/isosceles-set/isosceles-set-5-lower-17.yml" }, { "id": "isosceles-set-6-lower-28", "constant": "isosceles-set-6", "group": "isosceles-set", "bound": "lower", "value": { "latex": "28", "decimal_approx": 28, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "28", "decimal_approx": 28, "alt_display": null }, "comparison": "equal", "source": "ionin-2009", "path": "certificates/isosceles-set/isosceles-set-6-lower-28.yml" }, { "id": "isosceles-set-7-lower-30", "constant": "isosceles-set-7", "group": "isosceles-set", "bound": "lower", "value": { "latex": "30", "decimal_approx": 30, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "30", "decimal_approx": 30, "alt_display": null }, "comparison": "equal", "source": "ionin-2009", "path": "certificates/isosceles-set/isosceles-set-7-lower-30.yml" }, { "id": "isosceles-set-8-lower-45", "constant": "isosceles-set-8", "group": "isosceles-set", "bound": "lower", "value": { "latex": "45", "decimal_approx": 45, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "45", "decimal_approx": 45, "alt_display": null }, "comparison": "equal", "source": "lisonek-1997", "path": "certificates/isosceles-set/isosceles-set-8-lower-45.yml" }, { "id": "isosceles-set-9-lower-46", "constant": "isosceles-set-9", "group": "isosceles-set", "bound": "lower", "value": { "latex": "46", "decimal_approx": 46, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/isosceles-set/isosceles-set-9-lower-46.yml" }, { "id": "no-three-in-line-1-lower-1", "constant": "no-three-in-line-1", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/no-three-in-line/no-three-in-line-1-lower-1.yml" }, { "id": "no-three-in-line-10-lower-20", "constant": "no-three-in-line-10", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "20", "decimal_approx": 20, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "20", "decimal_approx": 20, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-10-lower-20.yml" }, { "id": "no-three-in-line-11-lower-22", "constant": "no-three-in-line-11", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "22", "decimal_approx": 22, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "22", "decimal_approx": 22, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-11-lower-22.yml" }, { "id": "no-three-in-line-12-lower-24", "constant": "no-three-in-line-12", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "24", "decimal_approx": 24, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "24", "decimal_approx": 24, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-12-lower-24.yml" }, { "id": "no-three-in-line-13-lower-26", "constant": "no-three-in-line-13", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-13-lower-26.yml" }, { "id": "no-three-in-line-14-lower-28", "constant": "no-three-in-line-14", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "28", "decimal_approx": 28, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "28", "decimal_approx": 28, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-14-lower-28.yml" }, { "id": "no-three-in-line-15-lower-30", "constant": "no-three-in-line-15", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "30", "decimal_approx": 30, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "30", "decimal_approx": 30, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-15-lower-30.yml" }, { "id": "no-three-in-line-16-lower-32", "constant": "no-three-in-line-16", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "32", "decimal_approx": 32, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "32", "decimal_approx": 32, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-16-lower-32.yml" }, { "id": "no-three-in-line-17-lower-34", "constant": "no-three-in-line-17", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "34", "decimal_approx": 34, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "34", "decimal_approx": 34, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-17-lower-34.yml" }, { "id": "no-three-in-line-18-lower-36", "constant": "no-three-in-line-18", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "36", "decimal_approx": 36, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "36", "decimal_approx": 36, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-18-lower-36.yml" }, { "id": "no-three-in-line-19-lower-38", "constant": "no-three-in-line-19", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "38", "decimal_approx": 38, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "38", "decimal_approx": 38, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-19-lower-38.yml" }, { "id": "no-three-in-line-2-lower-4", "constant": "no-three-in-line-2", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-2-lower-4.yml" }, { "id": "no-three-in-line-20-lower-40", "constant": "no-three-in-line-20", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "40", "decimal_approx": 40, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "40", "decimal_approx": 40, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-20-lower-40.yml" }, { "id": "no-three-in-line-21-lower-42", "constant": "no-three-in-line-21", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "42", "decimal_approx": 42, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "42", "decimal_approx": 42, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-21-lower-42.yml" }, { "id": "no-three-in-line-22-lower-44", "constant": "no-three-in-line-22", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "44", "decimal_approx": 44, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "44", "decimal_approx": 44, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-22-lower-44.yml" }, { "id": "no-three-in-line-23-lower-46", "constant": "no-three-in-line-23", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "46", "decimal_approx": 46, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "46", "decimal_approx": 46, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-23-lower-46.yml" }, { "id": "no-three-in-line-24-lower-48", "constant": "no-three-in-line-24", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "48", "decimal_approx": 48, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "48", "decimal_approx": 48, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-24-lower-48.yml" }, { "id": "no-three-in-line-25-lower-50", "constant": "no-three-in-line-25", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "50", "decimal_approx": 50, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "50", "decimal_approx": 50, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-25-lower-50.yml" }, { "id": "no-three-in-line-26-lower-52", "constant": "no-three-in-line-26", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "52", "decimal_approx": 52, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "52", "decimal_approx": 52, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-26-lower-52.yml" }, { "id": "no-three-in-line-27-lower-54", "constant": "no-three-in-line-27", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "54", "decimal_approx": 54, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "54", "decimal_approx": 54, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-27-lower-54.yml" }, { "id": "no-three-in-line-28-lower-56", "constant": "no-three-in-line-28", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "56", "decimal_approx": 56, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "56", "decimal_approx": 56, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-28-lower-56.yml" }, { "id": "no-three-in-line-29-lower-58", "constant": "no-three-in-line-29", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "58", "decimal_approx": 58, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "58", "decimal_approx": 58, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-29-lower-58.yml" }, { "id": "no-three-in-line-3-lower-6", "constant": "no-three-in-line-3", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-3-lower-6.yml" }, { "id": "no-three-in-line-30-lower-60", "constant": "no-three-in-line-30", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "60", "decimal_approx": 60, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "60", "decimal_approx": 60, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-30-lower-60.yml" }, { "id": "no-three-in-line-31-lower-62", "constant": "no-three-in-line-31", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "62", "decimal_approx": 62, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "62", "decimal_approx": 62, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-31-lower-62.yml" }, { "id": "no-three-in-line-32-lower-64", "constant": "no-three-in-line-32", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "64", "decimal_approx": 64, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "64", "decimal_approx": 64, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-32-lower-64.yml" }, { "id": "no-three-in-line-33-lower-66", "constant": "no-three-in-line-33", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "66", "decimal_approx": 66, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "66", "decimal_approx": 66, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-33-lower-66.yml" }, { "id": "no-three-in-line-34-lower-68", "constant": "no-three-in-line-34", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "68", "decimal_approx": 68, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "68", "decimal_approx": 68, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-34-lower-68.yml" }, { "id": "no-three-in-line-35-lower-70", "constant": "no-three-in-line-35", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "70", "decimal_approx": 70, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "70", "decimal_approx": 70, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-35-lower-70.yml" }, { "id": "no-three-in-line-36-lower-72", "constant": "no-three-in-line-36", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "72", "decimal_approx": 72, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "72", "decimal_approx": 72, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-36-lower-72.yml" }, { "id": "no-three-in-line-37-lower-74", "constant": "no-three-in-line-37", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "74", "decimal_approx": 74, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "74", "decimal_approx": 74, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-37-lower-74.yml" }, { "id": "no-three-in-line-38-lower-76", "constant": "no-three-in-line-38", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "76", "decimal_approx": 76, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "76", "decimal_approx": 76, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-38-lower-76.yml" }, { "id": "no-three-in-line-39-lower-78", "constant": "no-three-in-line-39", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "78", "decimal_approx": 78, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "78", "decimal_approx": 78, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-39-lower-78.yml" }, { "id": "no-three-in-line-4-lower-8", "constant": "no-three-in-line-4", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-4-lower-8.yml" }, { "id": "no-three-in-line-40-lower-80", "constant": "no-three-in-line-40", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "80", "decimal_approx": 80, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "80", "decimal_approx": 80, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-40-lower-80.yml" }, { "id": "no-three-in-line-41-lower-82", "constant": "no-three-in-line-41", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "82", "decimal_approx": 82, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "82", "decimal_approx": 82, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-41-lower-82.yml" }, { "id": "no-three-in-line-42-lower-84", "constant": "no-three-in-line-42", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "84", "decimal_approx": 84, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "84", "decimal_approx": 84, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-42-lower-84.yml" }, { "id": "no-three-in-line-43-lower-86", "constant": "no-three-in-line-43", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "86", "decimal_approx": 86, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "86", "decimal_approx": 86, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-43-lower-86.yml" }, { "id": "no-three-in-line-44-lower-88", "constant": "no-three-in-line-44", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "88", "decimal_approx": 88, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "88", "decimal_approx": 88, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-44-lower-88.yml" }, { "id": "no-three-in-line-45-lower-90", "constant": "no-three-in-line-45", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "90", "decimal_approx": 90, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "90", "decimal_approx": 90, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-45-lower-90.yml" }, { "id": "no-three-in-line-46-lower-92", "constant": "no-three-in-line-46", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "92", "decimal_approx": 92, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "92", "decimal_approx": 92, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-46-lower-92.yml" }, { "id": "no-three-in-line-47-lower-94", "constant": "no-three-in-line-47", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "94", "decimal_approx": 94, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "94", "decimal_approx": 94, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-47-lower-94.yml" }, { "id": "no-three-in-line-48-lower-96", "constant": "no-three-in-line-48", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "96", "decimal_approx": 96, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "96", "decimal_approx": 96, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-48-lower-96.yml" }, { "id": "no-three-in-line-49-lower-98", "constant": "no-three-in-line-49", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "98", "decimal_approx": 98, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "98", "decimal_approx": 98, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-49-lower-98.yml" }, { "id": "no-three-in-line-5-lower-10", "constant": "no-three-in-line-5", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-5-lower-10.yml" }, { "id": "no-three-in-line-50-lower-100", "constant": "no-three-in-line-50", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "100", "decimal_approx": 100, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "100", "decimal_approx": 100, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-50-lower-100.yml" }, { "id": "no-three-in-line-51-lower-102", "constant": "no-three-in-line-51", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "102", "decimal_approx": 102, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "102", "decimal_approx": 102, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-51-lower-102.yml" }, { "id": "no-three-in-line-52-lower-104", "constant": "no-three-in-line-52", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "104", "decimal_approx": 104, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "104", "decimal_approx": 104, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-52-lower-104.yml" }, { "id": "no-three-in-line-53-lower-106", "constant": "no-three-in-line-53", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "106", "decimal_approx": 106, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "106", "decimal_approx": 106, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-53-lower-106.yml" }, { "id": "no-three-in-line-54-lower-108", "constant": "no-three-in-line-54", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "108", "decimal_approx": 108, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "108", "decimal_approx": 108, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-54-lower-108.yml" }, { "id": "no-three-in-line-55-lower-110", "constant": "no-three-in-line-55", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "110", "decimal_approx": 110, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "110", "decimal_approx": 110, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-55-lower-110.yml" }, { "id": "no-three-in-line-56-lower-112", "constant": "no-three-in-line-56", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "112", "decimal_approx": 112, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "112", "decimal_approx": 112, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-56-lower-112.yml" }, { "id": "no-three-in-line-57-lower-114", "constant": "no-three-in-line-57", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "114", "decimal_approx": 114, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "114", "decimal_approx": 114, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-57-lower-114.yml" }, { "id": "no-three-in-line-58-lower-116", "constant": "no-three-in-line-58", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "116", "decimal_approx": 116, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "116", "decimal_approx": 116, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-58-lower-116.yml" }, { "id": "no-three-in-line-59-lower-118", "constant": "no-three-in-line-59", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "118", "decimal_approx": 118, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "118", "decimal_approx": 118, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-59-lower-118.yml" }, { "id": "no-three-in-line-6-lower-12", "constant": "no-three-in-line-6", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "12", "decimal_approx": 12, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "12", "decimal_approx": 12, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-6-lower-12.yml" }, { "id": "no-three-in-line-60-lower-120", "constant": "no-three-in-line-60", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "120", "decimal_approx": 120, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "120", "decimal_approx": 120, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-60-lower-120.yml" }, { "id": "no-three-in-line-61-lower-122", "constant": "no-three-in-line-61", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "122", "decimal_approx": 122, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "122", "decimal_approx": 122, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-61-lower-122.yml" }, { "id": "no-three-in-line-62-lower-124", "constant": "no-three-in-line-62", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "124", "decimal_approx": 124, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "124", "decimal_approx": 124, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-62-lower-124.yml" }, { "id": "no-three-in-line-63-lower-126", "constant": "no-three-in-line-63", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "126", "decimal_approx": 126, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "126", "decimal_approx": 126, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-63-lower-126.yml" }, { "id": "no-three-in-line-64-lower-128", "constant": "no-three-in-line-64", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "128", "decimal_approx": 128, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "128", "decimal_approx": 128, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026", "path": "certificates/no-three-in-line/no-three-in-line-64-lower-128.yml" }, { "id": "no-three-in-line-65-lower-130", "constant": "no-three-in-line-65", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "130", "decimal_approx": 130, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "130", "decimal_approx": 130, "alt_display": null }, "comparison": "equal", "source": "heule-2026-06-18", "path": "certificates/no-three-in-line/no-three-in-line-65-lower-130.yml" }, { "id": "no-three-in-line-66-lower-132", "constant": "no-three-in-line-66", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "132", "decimal_approx": 132, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "132", "decimal_approx": 132, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026-03-09", "path": "certificates/no-three-in-line/no-three-in-line-66-lower-132.yml" }, { "id": "no-three-in-line-67-lower-134", "constant": "no-three-in-line-67", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "134", "decimal_approx": 134, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "134", "decimal_approx": 134, "alt_display": null }, "comparison": "equal", "source": "heule-2026-06-21", "path": "certificates/no-three-in-line/no-three-in-line-67-lower-134.yml" }, { "id": "no-three-in-line-68-lower-136", "constant": "no-three-in-line-68", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "136", "decimal_approx": 136, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "136", "decimal_approx": 136, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026-03-23", "path": "certificates/no-three-in-line/no-three-in-line-68-lower-136.yml" }, { "id": "no-three-in-line-69-lower-138", "constant": "no-three-in-line-69", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "138", "decimal_approx": 138, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "138", "decimal_approx": 138, "alt_display": null }, "comparison": "equal", "source": "heule-2026-06-21", "path": "certificates/no-three-in-line/no-three-in-line-69-lower-138.yml" }, { "id": "no-three-in-line-7-lower-14", "constant": "no-three-in-line-7", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-7-lower-14.yml" }, { "id": "no-three-in-line-70-lower-140", "constant": "no-three-in-line-70", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "140", "decimal_approx": 140, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "140", "decimal_approx": 140, "alt_display": null }, "comparison": "equal", "source": "heule-2026-06-17", "path": "certificates/no-three-in-line/no-three-in-line-70-lower-140.yml" }, { "id": "no-three-in-line-71-lower-142", "constant": "no-three-in-line-71", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "142", "decimal_approx": 142, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "142", "decimal_approx": 142, "alt_display": null }, "comparison": "equal", "source": "heule-2026-08-17", "path": "certificates/no-three-in-line/no-three-in-line-71-lower-142.yml" }, { "id": "no-three-in-line-72-lower-144", "constant": "no-three-in-line-72", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "144", "decimal_approx": 144, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "144", "decimal_approx": 144, "alt_display": null }, "comparison": "equal", "source": "heule-2026-06-25", "path": "certificates/no-three-in-line/no-three-in-line-72-lower-144.yml" }, { "id": "no-three-in-line-73-lower-146", "constant": "no-three-in-line-73", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "146", "decimal_approx": 146, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "146", "decimal_approx": 146, "alt_display": null }, "comparison": "equal", "source": "heule-2026-08-19", "path": "certificates/no-three-in-line/no-three-in-line-73-lower-146.yml" }, { "id": "no-three-in-line-74-lower-148", "constant": "no-three-in-line-74", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "148", "decimal_approx": 148, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "148", "decimal_approx": 148, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026-07-20", "path": "certificates/no-three-in-line/no-three-in-line-74-lower-148.yml" }, { "id": "no-three-in-line-75-lower-148", "constant": "no-three-in-line-75", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "148", "decimal_approx": 148, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/no-three-in-line/no-three-in-line-75-lower-148.yml" }, { "id": "no-three-in-line-76-lower-152", "constant": "no-three-in-line-76", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "152", "decimal_approx": 152, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "152", "decimal_approx": 152, "alt_display": null }, "comparison": "equal", "source": "heule-2026-08-10", "path": "certificates/no-three-in-line/no-three-in-line-76-lower-152.yml" }, { "id": "no-three-in-line-77-lower-152", "constant": "no-three-in-line-77", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "152", "decimal_approx": 152, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/no-three-in-line/no-three-in-line-77-lower-152.yml" }, { "id": "no-three-in-line-78-lower-156", "constant": "no-three-in-line-78", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "156", "decimal_approx": 156, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "156", "decimal_approx": 156, "alt_display": null }, "comparison": "equal", "source": "prellberg-2026-10-28", "path": "certificates/no-three-in-line/no-three-in-line-78-lower-156.yml" }, { "id": "no-three-in-line-8-lower-16", "constant": "no-three-in-line-8", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "16", "decimal_approx": 16, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "16", "decimal_approx": 16, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-8-lower-16.yml" }, { "id": "no-three-in-line-9-lower-18", "constant": "no-three-in-line-9", "group": "no-three-in-line", "bound": "lower", "value": { "latex": "18", "decimal_approx": 18, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-05", "current": true, "literature": { "latex": "18", "decimal_approx": 18, "alt_display": null }, "comparison": "equal", "source": "flammenkamp-no3in", "path": "certificates/no-three-in-line/no-three-in-line-9-lower-18.yml" }, { "id": "affine-line-arrangements-1-lower-1", "constant": "affine-line-arrangements-1", "group": "affine-line-arrangements", "bound": "lower", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements/affine-line-arrangements-1-lower-1.yml" }, { "id": "affine-line-arrangements-2-lower-2", "constant": "affine-line-arrangements-2", "group": "affine-line-arrangements", "bound": "lower", "value": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements/affine-line-arrangements-2-lower-2.yml" }, { "id": "affine-line-arrangements-3-lower-4", "constant": "affine-line-arrangements-3", "group": "affine-line-arrangements", "bound": "lower", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements/affine-line-arrangements-3-lower-4.yml" }, { "id": "affine-line-arrangements-4-lower-9", "constant": "affine-line-arrangements-4", "group": "affine-line-arrangements", "bound": "lower", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements/affine-line-arrangements-4-lower-9.yml" }, { "id": "affine-line-arrangements-5-lower-47", "constant": "affine-line-arrangements-5", "group": "affine-line-arrangements", "bound": "lower", "value": { "latex": "47", "decimal_approx": 47, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "47", "decimal_approx": 47, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements/affine-line-arrangements-5-lower-47.yml" }, { "id": "affine-line-arrangements-6-lower-791", "constant": "affine-line-arrangements-6", "group": "affine-line-arrangements", "bound": "lower", "value": { "latex": "791", "decimal_approx": 791, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "791", "decimal_approx": 791, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements/affine-line-arrangements-6-lower-791.yml" }, { "id": "affine-line-arrangements-general-position-1-lower-1", "constant": "affine-line-arrangements-general-position-1", "group": "affine-line-arrangements-general-position", "bound": "lower", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-1-lower-1.yml" }, { "id": "affine-line-arrangements-general-position-2-lower-1", "constant": "affine-line-arrangements-general-position-2", "group": "affine-line-arrangements-general-position", "bound": "lower", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-2-lower-1.yml" }, { "id": "affine-line-arrangements-general-position-3-lower-1", "constant": "affine-line-arrangements-general-position-3", "group": "affine-line-arrangements-general-position", "bound": "lower", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-3-lower-1.yml" }, { "id": "affine-line-arrangements-general-position-4-lower-1", "constant": "affine-line-arrangements-general-position-4", "group": "affine-line-arrangements-general-position", "bound": "lower", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-4-lower-1.yml" }, { "id": "affine-line-arrangements-general-position-5-lower-6", "constant": "affine-line-arrangements-general-position-5", "group": "affine-line-arrangements-general-position", "bound": "lower", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-5-lower-6.yml" }, { "id": "affine-line-arrangements-general-position-6-lower-43", "constant": "affine-line-arrangements-general-position-6", "group": "affine-line-arrangements-general-position", "bound": "lower", "value": { "latex": "43", "decimal_approx": 43, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "43", "decimal_approx": 43, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-6-lower-43.yml" }, { "id": "affine-line-arrangements-general-position-7-lower-922", "constant": "affine-line-arrangements-general-position-7", "group": "affine-line-arrangements-general-position", "bound": "lower", "value": { "latex": "922", "decimal_approx": 922, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "922", "decimal_approx": 922, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-7-lower-922.yml" }, { "id": "coil-in-the-box-10-lower-374", "constant": "coil-in-the-box-10", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "374", "decimal_approx": 374, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "374", "decimal_approx": 374, "alt_display": null }, "comparison": "equal", "source": "orland-et-al-2026", "path": "certificates/coil-in-the-box/coil-in-the-box-10-lower-374.yml" }, { "id": "coil-in-the-box-11-lower-740", "constant": "coil-in-the-box-11", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "740", "decimal_approx": 740, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "740", "decimal_approx": 740, "alt_display": null }, "comparison": "equal", "source": "echols-2026-07-23", "path": "certificates/coil-in-the-box/coil-in-the-box-11-lower-740.yml" }, { "id": "coil-in-the-box-12-lower-1468", "constant": "coil-in-the-box-12", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "1468", "decimal_approx": 1468, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "1468", "decimal_approx": 1468, "alt_display": null }, "comparison": "equal", "source": "echols-2026-07-22", "path": "certificates/coil-in-the-box/coil-in-the-box-12-lower-1468.yml" }, { "id": "coil-in-the-box-13-lower-2930", "constant": "coil-in-the-box-13", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "2930", "decimal_approx": 2930, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "2930", "decimal_approx": 2930, "alt_display": null }, "comparison": "equal", "source": "echols-2026-08-29", "path": "certificates/coil-in-the-box/coil-in-the-box-13-lower-2930.yml" }, { "id": "coil-in-the-box-2-lower-4", "constant": "coil-in-the-box-2", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/coil-in-the-box/coil-in-the-box-2-lower-4.yml" }, { "id": "coil-in-the-box-3-lower-6", "constant": "coil-in-the-box-3", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/coil-in-the-box/coil-in-the-box-3-lower-6.yml" }, { "id": "coil-in-the-box-4-lower-8", "constant": "coil-in-the-box-4", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/coil-in-the-box/coil-in-the-box-4-lower-8.yml" }, { "id": "coil-in-the-box-5-lower-14", "constant": "coil-in-the-box-5", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/coil-in-the-box/coil-in-the-box-5-lower-14.yml" }, { "id": "coil-in-the-box-6-lower-26", "constant": "coil-in-the-box-6", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/coil-in-the-box/coil-in-the-box-6-lower-26.yml" }, { "id": "coil-in-the-box-7-lower-48", "constant": "coil-in-the-box-7", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "48", "decimal_approx": 48, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "48", "decimal_approx": 48, "alt_display": null }, "comparison": "equal", "source": "kochut-1996", "path": "certificates/coil-in-the-box/coil-in-the-box-7-lower-48.yml" }, { "id": "coil-in-the-box-8-lower-96", "constant": "coil-in-the-box-8", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "96", "decimal_approx": 96, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "96", "decimal_approx": 96, "alt_display": null }, "comparison": "equal", "source": "ostergard-pettersson-2014-coil", "path": "certificates/coil-in-the-box/coil-in-the-box-8-lower-96.yml" }, { "id": "coil-in-the-box-9-lower-192", "constant": "coil-in-the-box-9", "group": "coil-in-the-box", "bound": "lower", "value": { "latex": "192", "decimal_approx": 192, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "192", "decimal_approx": 192, "alt_display": null }, "comparison": "equal", "source": "orland-et-al-2026", "path": "certificates/coil-in-the-box/coil-in-the-box-9-lower-192.yml" }, { "id": "schur-8-lower-5372", "constant": "schur-8", "group": "schur", "bound": "lower", "value": { "latex": "5372", "decimal_approx": 5372, "alt_display": null }, "kind": "lean", "submitted_by": "darkhipo", "date": "2026-11-04", "current": true, "literature": { "latex": "5372", "decimal_approx": 5372, "alt_display": null }, "comparison": "equal", "source": "chen-zhu-long-2026", "path": "certificates/schur/schur-8-lower-5372.yml" }, { "id": "snake-in-the-box-1-lower-1", "constant": "snake-in-the-box-1", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/snake-in-the-box/snake-in-the-box-1-lower-1.yml" }, { "id": "snake-in-the-box-10-lower-379", "constant": "snake-in-the-box-10", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "379", "decimal_approx": 379, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "379", "decimal_approx": 379, "alt_display": null }, "comparison": "equal", "source": "orland-et-al-2026", "path": "certificates/snake-in-the-box/snake-in-the-box-10-lower-379.yml" }, { "id": "snake-in-the-box-11-lower-750", "constant": "snake-in-the-box-11", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "750", "decimal_approx": 750, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "750", "decimal_approx": 750, "alt_display": null }, "comparison": "equal", "source": "echols-2026-08-29", "path": "certificates/snake-in-the-box/snake-in-the-box-11-lower-750.yml" }, { "id": "snake-in-the-box-12-lower-1480", "constant": "snake-in-the-box-12", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "1480", "decimal_approx": 1480, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "1480", "decimal_approx": 1480, "alt_display": null }, "comparison": "equal", "source": "itty-2026", "path": "certificates/snake-in-the-box/snake-in-the-box-12-lower-1480.yml" }, { "id": "snake-in-the-box-13-lower-2946", "constant": "snake-in-the-box-13", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "2946", "decimal_approx": 2946, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "2946", "decimal_approx": 2946, "alt_display": null }, "comparison": "equal", "source": "toner-2026", "path": "certificates/snake-in-the-box/snake-in-the-box-13-lower-2946.yml" }, { "id": "snake-in-the-box-2-lower-2", "constant": "snake-in-the-box-2", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/snake-in-the-box/snake-in-the-box-2-lower-2.yml" }, { "id": "snake-in-the-box-3-lower-4", "constant": "snake-in-the-box-3", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/snake-in-the-box/snake-in-the-box-3-lower-4.yml" }, { "id": "snake-in-the-box-4-lower-7", "constant": "snake-in-the-box-4", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/snake-in-the-box/snake-in-the-box-4-lower-7.yml" }, { "id": "snake-in-the-box-5-lower-13", "constant": "snake-in-the-box-5", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "13", "decimal_approx": 13, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "13", "decimal_approx": 13, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/snake-in-the-box/snake-in-the-box-5-lower-13.yml" }, { "id": "snake-in-the-box-6-lower-26", "constant": "snake-in-the-box-6", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/snake-in-the-box/snake-in-the-box-6-lower-26.yml" }, { "id": "snake-in-the-box-7-lower-50", "constant": "snake-in-the-box-7", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "50", "decimal_approx": 50, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "50", "decimal_approx": 50, "alt_display": null }, "comparison": "equal", "source": "potter-et-al-1994", "path": "certificates/snake-in-the-box/snake-in-the-box-7-lower-50.yml" }, { "id": "snake-in-the-box-8-lower-98", "constant": "snake-in-the-box-8", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "98", "decimal_approx": 98, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "98", "decimal_approx": 98, "alt_display": null }, "comparison": "equal", "source": "carlson-hougen-2010", "path": "certificates/snake-in-the-box/snake-in-the-box-8-lower-98.yml" }, { "id": "snake-in-the-box-9-lower-191", "constant": "snake-in-the-box-9", "group": "snake-in-the-box", "bound": "lower", "value": { "latex": "191", "decimal_approx": 191, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-04", "current": true, "literature": { "latex": "191", "decimal_approx": 191, "alt_display": null }, "comparison": "equal", "source": "orland-et-al-2026", "path": "certificates/snake-in-the-box/snake-in-the-box-9-lower-191.yml" }, { "id": "golomb-ruler-1-upper-0", "constant": "golomb-ruler-1", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "0", "decimal_approx": 0, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "0", "decimal_approx": 0, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/golomb-ruler/golomb-ruler-1-upper-0.yml" }, { "id": "golomb-ruler-10-upper-55", "constant": "golomb-ruler-10", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "55", "decimal_approx": 55, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "55", "decimal_approx": 55, "alt_display": null }, "comparison": "equal", "source": "robinson-bernstein-1967", "path": "certificates/golomb-ruler/golomb-ruler-10-upper-55.yml" }, { "id": "golomb-ruler-11-upper-72", "constant": "golomb-ruler-11", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "72", "decimal_approx": 72, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "72", "decimal_approx": 72, "alt_display": null }, "comparison": "equal", "source": "robinson-bernstein-1967", "path": "certificates/golomb-ruler/golomb-ruler-11-upper-72.yml" }, { "id": "golomb-ruler-12-upper-85", "constant": "golomb-ruler-12", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "85", "decimal_approx": 85, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "85", "decimal_approx": 85, "alt_display": null }, "comparison": "equal", "source": "robinson-bernstein-1967", "path": "certificates/golomb-ruler/golomb-ruler-12-upper-85.yml" }, { "id": "golomb-ruler-13-upper-106", "constant": "golomb-ruler-13", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "106", "decimal_approx": 106, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "106", "decimal_approx": 106, "alt_display": null }, "comparison": "equal", "source": "robinson-1983", "path": "certificates/golomb-ruler/golomb-ruler-13-upper-106.yml" }, { "id": "golomb-ruler-14-upper-127", "constant": "golomb-ruler-14", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "127", "decimal_approx": 127, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "127", "decimal_approx": 127, "alt_display": null }, "comparison": "equal", "source": "robinson-bernstein-1967", "path": "certificates/golomb-ruler/golomb-ruler-14-upper-127.yml" }, { "id": "golomb-ruler-15-upper-151", "constant": "golomb-ruler-15", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "151", "decimal_approx": 151, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "151", "decimal_approx": 151, "alt_display": null }, "comparison": "equal", "source": "shearer-1990", "path": "certificates/golomb-ruler/golomb-ruler-15-upper-151.yml" }, { "id": "golomb-ruler-16-upper-177", "constant": "golomb-ruler-16", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "177", "decimal_approx": 177, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "177", "decimal_approx": 177, "alt_display": null }, "comparison": "equal", "source": "shearer-1990", "path": "certificates/golomb-ruler/golomb-ruler-16-upper-177.yml" }, { "id": "golomb-ruler-17-upper-199", "constant": "golomb-ruler-17", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "199", "decimal_approx": 199, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "199", "decimal_approx": 199, "alt_display": null }, "comparison": "equal", "source": "atkinson-hassenklover-1984", "path": "certificates/golomb-ruler/golomb-ruler-17-upper-199.yml" }, { "id": "golomb-ruler-18-upper-216", "constant": "golomb-ruler-18", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "216", "decimal_approx": 216, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "216", "decimal_approx": 216, "alt_display": null }, "comparison": "equal", "source": "robinson-bernstein-1967", "path": "certificates/golomb-ruler/golomb-ruler-18-upper-216.yml" }, { "id": "golomb-ruler-19-upper-246", "constant": "golomb-ruler-19", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "246", "decimal_approx": 246, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "246", "decimal_approx": 246, "alt_display": null }, "comparison": "equal", "source": "robinson-bernstein-1967", "path": "certificates/golomb-ruler/golomb-ruler-19-upper-246.yml" }, { "id": "golomb-ruler-2-upper-1", "constant": "golomb-ruler-2", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/golomb-ruler/golomb-ruler-2-upper-1.yml" }, { "id": "golomb-ruler-20-upper-283", "constant": "golomb-ruler-20", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "283", "decimal_approx": 283, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "283", "decimal_approx": 283, "alt_display": null }, "comparison": "equal", "source": "robinson-bernstein-1967", "path": "certificates/golomb-ruler/golomb-ruler-20-upper-283.yml" }, { "id": "golomb-ruler-21-upper-333", "constant": "golomb-ruler-21", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "333", "decimal_approx": 333, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "333", "decimal_approx": 333, "alt_display": null }, "comparison": "equal", "source": "robinson-bernstein-1967", "path": "certificates/golomb-ruler/golomb-ruler-21-upper-333.yml" }, { "id": "golomb-ruler-22-upper-356", "constant": "golomb-ruler-22", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "356", "decimal_approx": 356, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "356", "decimal_approx": 356, "alt_display": null }, "comparison": "equal", "source": "atkinson-hassenklover-1984", "path": "certificates/golomb-ruler/golomb-ruler-22-upper-356.yml" }, { "id": "golomb-ruler-23-upper-372", "constant": "golomb-ruler-23", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "372", "decimal_approx": 372, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "372", "decimal_approx": 372, "alt_display": null }, "comparison": "equal", "source": "robinson-bernstein-1967", "path": "certificates/golomb-ruler/golomb-ruler-23-upper-372.yml" }, { "id": "golomb-ruler-24-upper-425", "constant": "golomb-ruler-24", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "425", "decimal_approx": 425, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "425", "decimal_approx": 425, "alt_display": null }, "comparison": "equal", "source": "robinson-bernstein-1967", "path": "certificates/golomb-ruler/golomb-ruler-24-upper-425.yml" }, { "id": "golomb-ruler-25-upper-480", "constant": "golomb-ruler-25", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "480", "decimal_approx": 480, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "480", "decimal_approx": 480, "alt_display": null }, "comparison": "equal", "source": "atkinson-hassenklover-1984", "path": "certificates/golomb-ruler/golomb-ruler-25-upper-480.yml" }, { "id": "golomb-ruler-26-upper-492", "constant": "golomb-ruler-26", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "492", "decimal_approx": 492, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "492", "decimal_approx": 492, "alt_display": null }, "comparison": "equal", "source": "atkinson-hassenklover-1984", "path": "certificates/golomb-ruler/golomb-ruler-26-upper-492.yml" }, { "id": "golomb-ruler-27-upper-553", "constant": "golomb-ruler-27", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "553", "decimal_approx": 553, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "553", "decimal_approx": 553, "alt_display": null }, "comparison": "equal", "source": "atkinson-hassenklover-1984", "path": "certificates/golomb-ruler/golomb-ruler-27-upper-553.yml" }, { "id": "golomb-ruler-28-upper-585", "constant": "golomb-ruler-28", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "585", "decimal_approx": 585, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "585", "decimal_approx": 585, "alt_display": null }, "comparison": "equal", "source": "atkinson-hassenklover-1984", "path": "certificates/golomb-ruler/golomb-ruler-28-upper-585.yml" }, { "id": "golomb-ruler-29-upper-623", "constant": "golomb-ruler-29", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "623", "decimal_approx": 623, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "623", "decimal_approx": 623, "alt_display": null }, "comparison": "equal", "source": "atkinson-hassenklover-1984", "path": "certificates/golomb-ruler/golomb-ruler-29-upper-623.yml" }, { "id": "golomb-ruler-3-upper-3", "constant": "golomb-ruler-3", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/golomb-ruler/golomb-ruler-3-upper-3.yml" }, { "id": "golomb-ruler-30-upper-680", "constant": "golomb-ruler-30", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "680", "decimal_approx": 680, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "680", "decimal_approx": 680, "alt_display": null }, "comparison": "equal", "source": "atkinson-hassenklover-1984", "path": "certificates/golomb-ruler/golomb-ruler-30-upper-680.yml" }, { "id": "golomb-ruler-4-upper-6", "constant": "golomb-ruler-4", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/golomb-ruler/golomb-ruler-4-upper-6.yml" }, { "id": "golomb-ruler-5-upper-11", "constant": "golomb-ruler-5", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "11", "decimal_approx": 11, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "11", "decimal_approx": 11, "alt_display": null }, "comparison": "equal", "source": "babcock-1953", "path": "certificates/golomb-ruler/golomb-ruler-5-upper-11.yml" }, { "id": "golomb-ruler-6-upper-17", "constant": "golomb-ruler-6", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "17", "decimal_approx": 17, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "17", "decimal_approx": 17, "alt_display": null }, "comparison": "equal", "source": "babcock-1953", "path": "certificates/golomb-ruler/golomb-ruler-6-upper-17.yml" }, { "id": "golomb-ruler-7-upper-25", "constant": "golomb-ruler-7", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "25", "decimal_approx": 25, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "25", "decimal_approx": 25, "alt_display": null }, "comparison": "equal", "source": "babcock-1953", "path": "certificates/golomb-ruler/golomb-ruler-7-upper-25.yml" }, { "id": "golomb-ruler-8-upper-34", "constant": "golomb-ruler-8", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "34", "decimal_approx": 34, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "34", "decimal_approx": 34, "alt_display": null }, "comparison": "equal", "source": "babcock-1953", "path": "certificates/golomb-ruler/golomb-ruler-8-upper-34.yml" }, { "id": "golomb-ruler-9-upper-44", "constant": "golomb-ruler-9", "group": "golomb-ruler", "bound": "upper", "value": { "latex": "44", "decimal_approx": 44, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "44", "decimal_approx": 44, "alt_display": null }, "comparison": "equal", "source": "mixon-1972", "path": "certificates/golomb-ruler/golomb-ruler-9-upper-44.yml" }, { "id": "schur-1-lower-1", "constant": "schur-1", "group": "schur", "bound": "lower", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/schur/schur-1-lower-1.yml" }, { "id": "schur-2-lower-4", "constant": "schur-2", "group": "schur", "bound": "lower", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/schur/schur-2-lower-4.yml" }, { "id": "schur-3-lower-13", "constant": "schur-3", "group": "schur", "bound": "lower", "value": { "latex": "13", "decimal_approx": 13, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "13", "decimal_approx": 13, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/schur/schur-3-lower-13.yml" }, { "id": "schur-4-lower-44", "constant": "schur-4", "group": "schur", "bound": "lower", "value": { "latex": "44", "decimal_approx": 44, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "44", "decimal_approx": 44, "alt_display": null }, "comparison": "equal", "source": "golomb-baumert-1965", "path": "certificates/schur/schur-4-lower-44.yml" }, { "id": "schur-5-lower-160", "constant": "schur-5", "group": "schur", "bound": "lower", "value": { "latex": "160", "decimal_approx": 160, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "160", "decimal_approx": 160, "alt_display": null }, "comparison": "equal", "source": "exoo-1994", "path": "certificates/schur/schur-5-lower-160.yml" }, { "id": "schur-6-lower-537", "constant": "schur-6", "group": "schur", "bound": "lower", "value": { "latex": "537", "decimal_approx": 537, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "537", "decimal_approx": 537, "alt_display": null }, "comparison": "equal", "source": "chen-zhu-long-2026", "path": "certificates/schur/schur-6-lower-537.yml" }, { "id": "schur-7-lower-1696", "constant": "schur-7", "group": "schur", "bound": "lower", "value": { "latex": "1696", "decimal_approx": 1696, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "1696", "decimal_approx": 1696, "alt_display": null }, "comparison": "equal", "source": "rowley-2021", "path": "certificates/schur/schur-7-lower-1696.yml" }, { "id": "van-der-waerden-2-11-lower-193942", "constant": "van-der-waerden-2-11", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "193942", "decimal_approx": 193942, "alt_display": "193,942" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "193942", "decimal_approx": 193942, "alt_display": "193,942" }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-2-11-lower-193942.yml" }, { "id": "van-der-waerden-2-5-lower-178", "constant": "van-der-waerden-2-5", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "178", "decimal_approx": 178, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "178", "decimal_approx": 178, "alt_display": null }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-2-5-lower-178.yml" }, { "id": "van-der-waerden-2-6-lower-1132", "constant": "van-der-waerden-2-6", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "1132", "decimal_approx": 1132, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "1132", "decimal_approx": 1132, "alt_display": null }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-2-6-lower-1132.yml" }, { "id": "van-der-waerden-2-8-lower-11496", "constant": "van-der-waerden-2-8", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "11496", "decimal_approx": 11496, "alt_display": "11,496" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "11496", "decimal_approx": 11496, "alt_display": "11,496" }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-2-8-lower-11496.yml" }, { "id": "van-der-waerden-2-9-lower-41266", "constant": "van-der-waerden-2-9", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "41266", "decimal_approx": 41266, "alt_display": "41,266" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "41266", "decimal_approx": 41266, "alt_display": "41,266" }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-2-9-lower-41266.yml" }, { "id": "van-der-waerden-4-5-lower-17706", "constant": "van-der-waerden-4-5", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "17706", "decimal_approx": 17706, "alt_display": "17,706" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "17706", "decimal_approx": 17706, "alt_display": "17,706" }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-4-5-lower-17706.yml" }, { "id": "weak-schur-1-lower-2", "constant": "weak-schur-1", "group": "weak-schur", "bound": "lower", "value": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/weak-schur/weak-schur-1-lower-2.yml" }, { "id": "weak-schur-2-lower-8", "constant": "weak-schur-2", "group": "weak-schur", "bound": "lower", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/weak-schur/weak-schur-2-lower-8.yml" }, { "id": "weak-schur-3-lower-23", "constant": "weak-schur-3", "group": "weak-schur", "bound": "lower", "value": { "latex": "23", "decimal_approx": 23, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "23", "decimal_approx": 23, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/weak-schur/weak-schur-3-lower-23.yml" }, { "id": "weak-schur-4-lower-66", "constant": "weak-schur-4", "group": "weak-schur", "bound": "lower", "value": { "latex": "66", "decimal_approx": 66, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "66", "decimal_approx": 66, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/weak-schur/weak-schur-4-lower-66.yml" }, { "id": "weak-schur-5-lower-207", "constant": "weak-schur-5", "group": "weak-schur", "bound": "lower", "value": { "latex": "207", "decimal_approx": 207, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "207", "decimal_approx": 207, "alt_display": null }, "comparison": "equal", "source": "rowley-2025", "path": "certificates/weak-schur/weak-schur-5-lower-207.yml" }, { "id": "weak-schur-6-lower-650", "constant": "weak-schur-6", "group": "weak-schur", "bound": "lower", "value": { "latex": "650", "decimal_approx": 650, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-03", "current": true, "literature": { "latex": "650", "decimal_approx": 650, "alt_display": null }, "comparison": "equal", "source": "rodrigo-2026", "path": "certificates/weak-schur/weak-schur-6-lower-650.yml" }, { "id": "degree-diameter-10-3-lower-366", "constant": "degree-diameter-10-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "366", "decimal_approx": 366, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "650", "decimal_approx": 650, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-10-3-lower-366.yml" }, { "id": "degree-diameter-11-2-lower-98", "constant": "degree-diameter-11-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "98", "decimal_approx": 98, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "106", "decimal_approx": 106, "alt_display": null }, "comparison": "weaker", "source": "mmsgraphs", "path": "certificates/degree-diameter/degree-diameter-11-2-lower-98.yml" }, { "id": "degree-diameter-11-3-lower-420", "constant": "degree-diameter-11-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "420", "decimal_approx": 420, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "715", "decimal_approx": 715, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-11-3-lower-420.yml" }, { "id": "degree-diameter-12-3-lower-558", "constant": "degree-diameter-12-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "558", "decimal_approx": 558, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "810", "decimal_approx": 810, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-12-3-lower-558.yml" }, { "id": "degree-diameter-13-2-lower-162", "constant": "degree-diameter-13-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "162", "decimal_approx": 162, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "162", "decimal_approx": 162, "alt_display": null }, "comparison": "equal", "source": "mmsgraphs", "path": "certificates/degree-diameter/degree-diameter-13-2-lower-162.yml" }, { "id": "degree-diameter-13-3-lower-630", "constant": "degree-diameter-13-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "630", "decimal_approx": 630, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "972", "decimal_approx": 972, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-13-3-lower-630.yml" }, { "id": "degree-diameter-14-3-lower-791", "constant": "degree-diameter-14-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "791", "decimal_approx": 791, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "1201", "decimal_approx": 1201, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-14-3-lower-791.yml" }, { "id": "degree-diameter-15-2-lower-183", "constant": "degree-diameter-15-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "183", "decimal_approx": 183, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "190", "decimal_approx": 190, "alt_display": null }, "comparison": "weaker", "source": "brown-1966", "path": "certificates/degree-diameter/degree-diameter-15-2-lower-183.yml" }, { "id": "degree-diameter-15-3-lower-812", "constant": "degree-diameter-15-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "812", "decimal_approx": 812, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "1620", "decimal_approx": 1620, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-15-3-lower-812.yml" }, { "id": "degree-diameter-16-2-lower-183", "constant": "degree-diameter-16-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "183", "decimal_approx": 183, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "216", "decimal_approx": 216, "alt_display": null }, "comparison": "weaker", "source": "brown-1966", "path": "certificates/degree-diameter/degree-diameter-16-2-lower-183.yml" }, { "id": "degree-diameter-16-3-lower-1055", "constant": "degree-diameter-16-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "1055", "decimal_approx": 1055, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "1920", "decimal_approx": 1920, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-16-3-lower-1055.yml" }, { "id": "degree-diameter-17-2-lower-274", "constant": "degree-diameter-17-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "274", "decimal_approx": 274, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "274", "decimal_approx": 274, "alt_display": null }, "comparison": "equal", "source": "brown-1966", "path": "certificates/degree-diameter/degree-diameter-17-2-lower-274.yml" }, { "id": "degree-diameter-19-2-lower-338", "constant": "degree-diameter-19-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "338", "decimal_approx": 338, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "338", "decimal_approx": 338, "alt_display": null }, "comparison": "equal", "source": "mmsgraphs", "path": "certificates/degree-diameter/degree-diameter-19-2-lower-338.yml" }, { "id": "degree-diameter-3-10-lower-820", "constant": "degree-diameter-3-10", "group": "degree-diameter", "bound": "lower", "value": { "latex": "820", "decimal_approx": 820, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "1250", "decimal_approx": 1250, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-3-10-lower-820.yml" }, { "id": "degree-diameter-3-3-lower-20", "constant": "degree-diameter-3-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "20", "decimal_approx": 20, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "20", "decimal_approx": 20, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/degree-diameter/degree-diameter-3-3-lower-20.yml" }, { "id": "degree-diameter-3-4-lower-38", "constant": "degree-diameter-3-4", "group": "degree-diameter", "bound": "lower", "value": { "latex": "38", "decimal_approx": 38, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "38", "decimal_approx": 38, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/degree-diameter/degree-diameter-3-4-lower-38.yml" }, { "id": "degree-diameter-3-5-lower-64", "constant": "degree-diameter-3-5", "group": "degree-diameter", "bound": "lower", "value": { "latex": "64", "decimal_approx": 64, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "70", "decimal_approx": 70, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-3-5-lower-64.yml" }, { "id": "degree-diameter-3-6-lower-64", "constant": "degree-diameter-3-6", "group": "degree-diameter", "bound": "lower", "value": { "latex": "64", "decimal_approx": 64, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "132", "decimal_approx": 132, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-3-6-lower-64.yml" }, { "id": "degree-diameter-3-7-lower-162", "constant": "degree-diameter-3-7", "group": "degree-diameter", "bound": "lower", "value": { "latex": "162", "decimal_approx": 162, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "200", "decimal_approx": 200, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-3-7-lower-162.yml" }, { "id": "degree-diameter-3-8-lower-272", "constant": "degree-diameter-3-8", "group": "degree-diameter", "bound": "lower", "value": { "latex": "272", "decimal_approx": 272, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "360", "decimal_approx": 360, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-3-8-lower-272.yml" }, { "id": "degree-diameter-3-9-lower-506", "constant": "degree-diameter-3-9", "group": "degree-diameter", "bound": "lower", "value": { "latex": "506", "decimal_approx": 506, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "600", "decimal_approx": 600, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-3-9-lower-506.yml" }, { "id": "degree-diameter-4-2-lower-15", "constant": "degree-diameter-4-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "15", "decimal_approx": 15, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "15", "decimal_approx": 15, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/degree-diameter/degree-diameter-4-2-lower-15.yml" }, { "id": "degree-diameter-4-3-lower-41", "constant": "degree-diameter-4-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "41", "decimal_approx": 41, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "41", "decimal_approx": 41, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/degree-diameter/degree-diameter-4-3-lower-41.yml" }, { "id": "degree-diameter-4-4-lower-84", "constant": "degree-diameter-4-4", "group": "degree-diameter", "bound": "lower", "value": { "latex": "84", "decimal_approx": 84, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "104", "decimal_approx": 104, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-4-4-lower-84.yml" }, { "id": "degree-diameter-4-5-lower-205", "constant": "degree-diameter-4-5", "group": "degree-diameter", "bound": "lower", "value": { "latex": "205", "decimal_approx": 205, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "364", "decimal_approx": 364, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-4-5-lower-205.yml" }, { "id": "degree-diameter-4-6-lower-513", "constant": "degree-diameter-4-6", "group": "degree-diameter", "bound": "lower", "value": { "latex": "513", "decimal_approx": 513, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "760", "decimal_approx": 760, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-4-6-lower-513.yml" }, { "id": "degree-diameter-4-7-lower-1155", "constant": "degree-diameter-4-7", "group": "degree-diameter", "bound": "lower", "value": { "latex": "1155", "decimal_approx": 1155, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "1344", "decimal_approx": 1344, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-4-7-lower-1155.yml" }, { "id": "degree-diameter-5-2-lower-24", "constant": "degree-diameter-5-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "24", "decimal_approx": 24, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "24", "decimal_approx": 24, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/degree-diameter/degree-diameter-5-2-lower-24.yml" }, { "id": "degree-diameter-5-3-lower-54", "constant": "degree-diameter-5-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "54", "decimal_approx": 54, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "72", "decimal_approx": 72, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-5-3-lower-54.yml" }, { "id": "degree-diameter-5-4-lower-210", "constant": "degree-diameter-5-4", "group": "degree-diameter", "bound": "lower", "value": { "latex": "210", "decimal_approx": 210, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "252", "decimal_approx": 252, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-5-4-lower-210.yml" }, { "id": "degree-diameter-5-5-lower-506", "constant": "degree-diameter-5-5", "group": "degree-diameter", "bound": "lower", "value": { "latex": "506", "decimal_approx": 506, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "650", "decimal_approx": 650, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-5-5-lower-506.yml" }, { "id": "degree-diameter-6-2-lower-32", "constant": "degree-diameter-6-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "32", "decimal_approx": 32, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "32", "decimal_approx": 32, "alt_display": null }, "comparison": "equal", "source": "mmsgraphs", "path": "certificates/degree-diameter/degree-diameter-6-2-lower-32.yml" }, { "id": "degree-diameter-6-3-lower-90", "constant": "degree-diameter-6-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "90", "decimal_approx": 90, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "120", "decimal_approx": 120, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-6-3-lower-90.yml" }, { "id": "degree-diameter-6-4-lower-355", "constant": "degree-diameter-6-4", "group": "degree-diameter", "bound": "lower", "value": { "latex": "355", "decimal_approx": 355, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "441", "decimal_approx": 441, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-6-4-lower-355.yml" }, { "id": "degree-diameter-6-5-lower-1395", "constant": "degree-diameter-6-5", "group": "degree-diameter", "bound": "lower", "value": { "latex": "1395", "decimal_approx": 1395, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "1518", "decimal_approx": 1518, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-6-5-lower-1395.yml" }, { "id": "degree-diameter-7-3-lower-140", "constant": "degree-diameter-7-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "140", "decimal_approx": 140, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "170", "decimal_approx": 170, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-7-3-lower-140.yml" }, { "id": "degree-diameter-7-4-lower-602", "constant": "degree-diameter-7-4", "group": "degree-diameter", "bound": "lower", "value": { "latex": "602", "decimal_approx": 602, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "684", "decimal_approx": 684, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-7-4-lower-602.yml" }, { "id": "degree-diameter-8-3-lower-253", "constant": "degree-diameter-8-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "253", "decimal_approx": 253, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "253", "decimal_approx": 253, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/degree-diameter/degree-diameter-8-3-lower-253.yml" }, { "id": "degree-diameter-8-4-lower-1029", "constant": "degree-diameter-8-4", "group": "degree-diameter", "bound": "lower", "value": { "latex": "1029", "decimal_approx": 1029, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "1100", "decimal_approx": 1100, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-8-4-lower-1029.yml" }, { "id": "degree-diameter-9-2-lower-74", "constant": "degree-diameter-9-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "74", "decimal_approx": 74, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "74", "decimal_approx": 74, "alt_display": null }, "comparison": "equal", "source": "brown-1966", "path": "certificates/degree-diameter/degree-diameter-9-2-lower-74.yml" }, { "id": "degree-diameter-9-3-lower-256", "constant": "degree-diameter-9-3", "group": "degree-diameter", "bound": "lower", "value": { "latex": "256", "decimal_approx": 256, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "585", "decimal_approx": 585, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-9-3-lower-256.yml" }, { "id": "degree-diameter-9-4-lower-1254", "constant": "degree-diameter-9-4", "group": "degree-diameter", "bound": "lower", "value": { "latex": "1254", "decimal_approx": 1254, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "1768", "decimal_approx": 1768, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/degree-diameter/degree-diameter-9-4-lower-1254.yml" }, { "id": "ramsey-3-10-lower-39", "constant": "ramsey-3-10", "group": "ramsey", "bound": "lower", "value": { "latex": "39", "decimal_approx": 39, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "40", "decimal_approx": 40, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-3-10-lower-39.yml" }, { "id": "ramsey-3-11-lower-46", "constant": "ramsey-3-11", "group": "ramsey", "bound": "lower", "value": { "latex": "46", "decimal_approx": 46, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "47", "decimal_approx": 47, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-3-11-lower-46.yml" }, { "id": "ramsey-3-12-lower-49", "constant": "ramsey-3-12", "group": "ramsey", "bound": "lower", "value": { "latex": "49", "decimal_approx": 49, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "53", "decimal_approx": 53, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-3-12-lower-49.yml" }, { "id": "ramsey-3-13-lower-58", "constant": "ramsey-3-13", "group": "ramsey", "bound": "lower", "value": { "latex": "58", "decimal_approx": 58, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "61", "decimal_approx": 61, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-3-13-lower-58.yml" }, { "id": "ramsey-3-14-lower-64", "constant": "ramsey-3-14", "group": "ramsey", "bound": "lower", "value": { "latex": "64", "decimal_approx": 64, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "67", "decimal_approx": 67, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-3-14-lower-64.yml" }, { "id": "ramsey-3-15-lower-72", "constant": "ramsey-3-15", "group": "ramsey", "bound": "lower", "value": { "latex": "72", "decimal_approx": 72, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "74", "decimal_approx": 74, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-3-15-lower-72.yml" }, { "id": "ramsey-3-6-lower-18", "constant": "ramsey-3-6", "group": "ramsey", "bound": "lower", "value": { "latex": "18", "decimal_approx": 18, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "18", "decimal_approx": 18, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/ramsey/ramsey-3-6-lower-18.yml" }, { "id": "ramsey-3-7-lower-23", "constant": "ramsey-3-7", "group": "ramsey", "bound": "lower", "value": { "latex": "23", "decimal_approx": 23, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "23", "decimal_approx": 23, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/ramsey/ramsey-3-7-lower-23.yml" }, { "id": "ramsey-3-8-lower-28", "constant": "ramsey-3-8", "group": "ramsey", "bound": "lower", "value": { "latex": "28", "decimal_approx": 28, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "28", "decimal_approx": 28, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/ramsey/ramsey-3-8-lower-28.yml" }, { "id": "ramsey-3-9-lower-36", "constant": "ramsey-3-9", "group": "ramsey", "bound": "lower", "value": { "latex": "36", "decimal_approx": 36, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "36", "decimal_approx": 36, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/ramsey/ramsey-3-9-lower-36.yml" }, { "id": "ramsey-4-5-lower-25", "constant": "ramsey-4-5", "group": "ramsey", "bound": "lower", "value": { "latex": "25", "decimal_approx": 25, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "25", "decimal_approx": 25, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/ramsey/ramsey-4-5-lower-25.yml" }, { "id": "ramsey-4-6-lower-34", "constant": "ramsey-4-6", "group": "ramsey", "bound": "lower", "value": { "latex": "34", "decimal_approx": 34, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "36", "decimal_approx": 36, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-4-6-lower-34.yml" }, { "id": "ramsey-4-7-lower-47", "constant": "ramsey-4-7", "group": "ramsey", "bound": "lower", "value": { "latex": "47", "decimal_approx": 47, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "49", "decimal_approx": 49, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-4-7-lower-47.yml" }, { "id": "ramsey-4-8-lower-52", "constant": "ramsey-4-8", "group": "ramsey", "bound": "lower", "value": { "latex": "52", "decimal_approx": 52, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "59", "decimal_approx": 59, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-4-8-lower-52.yml" }, { "id": "ramsey-4-9-lower-69", "constant": "ramsey-4-9", "group": "ramsey", "bound": "lower", "value": { "latex": "69", "decimal_approx": 69, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "73", "decimal_approx": 73, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-4-9-lower-69.yml" }, { "id": "ramsey-5-5-lower-42", "constant": "ramsey-5-5", "group": "ramsey", "bound": "lower", "value": { "latex": "42", "decimal_approx": 42, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "43", "decimal_approx": 43, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-5-5-lower-42.yml" }, { "id": "ramsey-5-6-lower-54", "constant": "ramsey-5-6", "group": "ramsey", "bound": "lower", "value": { "latex": "54", "decimal_approx": 54, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "59", "decimal_approx": 59, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-5-6-lower-54.yml" }, { "id": "ramsey-5-7-lower-71", "constant": "ramsey-5-7", "group": "ramsey", "bound": "lower", "value": { "latex": "71", "decimal_approx": 71, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "80", "decimal_approx": 80, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-5-7-lower-71.yml" }, { "id": "ramsey-7-7-lower-205", "constant": "ramsey-7-7", "group": "ramsey", "bound": "lower", "value": { "latex": "205", "decimal_approx": 205, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "205", "decimal_approx": 205, "alt_display": null }, "comparison": "equal", "source": "mathon-1987", "path": "certificates/ramsey/ramsey-7-7-lower-205.yml" }, { "id": "ramsey-8-8-lower-282", "constant": "ramsey-8-8", "group": "ramsey", "bound": "lower", "value": { "latex": "282", "decimal_approx": 282, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-02", "current": true, "literature": { "latex": "282", "decimal_approx": 282, "alt_display": null }, "comparison": "equal", "source": "burling-reyner-1972", "path": "certificates/ramsey/ramsey-8-8-lower-282.yml" }, { "id": "circle-in-equilateral-1-lower-2sqrt3", "constant": "circle-in-equilateral-1", "group": "circle-in-equilateral", "bound": "lower", "value": { "latex": "2\\sqrt{3}", "decimal_approx": 3.464102, "alt_display": "\u22483.464102" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "2\\sqrt{3}", "decimal_approx": 3.464102, "alt_display": "\u22483.464102" }, "comparison": "equal", "source": null, "path": "certificates/circle-in-equilateral/circle-in-equilateral-1-lower-2sqrt3.yml" }, { "id": "circle-in-equilateral-1-upper-2sqrt3", "constant": "circle-in-equilateral-1", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "2\\sqrt{3}", "decimal_approx": 3.464102, "alt_display": "\u22483.464102" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "2\\sqrt{3}", "decimal_approx": 3.464102, "alt_display": "\u22483.464102" }, "comparison": "equal", "source": null, "path": "certificates/circle-in-equilateral/circle-in-equilateral-1-upper-2sqrt3.yml" }, { "id": "circle-in-equilateral-10-lower-6-2sqrt3", "constant": "circle-in-equilateral-10", "group": "circle-in-equilateral", "bound": "lower", "value": { "latex": "6+2\\sqrt{3}", "decimal_approx": 9.464102, "alt_display": "\u22489.464102" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "6+2\\sqrt{3}", "decimal_approx": 9.464102, "alt_display": "\u22489.464102" }, "comparison": "equal", "source": null, "path": "certificates/circle-in-equilateral/circle-in-equilateral-10-lower-6-2sqrt3.yml" }, { "id": "circle-in-equilateral-10-upper-6-2sqrt3", "constant": "circle-in-equilateral-10", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "6+2\\sqrt{3}", "decimal_approx": 9.464102, "alt_display": "\u22489.464102" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "6+2\\sqrt{3}", "decimal_approx": 9.464102, "alt_display": "\u22489.464102" }, "comparison": "equal", "source": "oler-groemer-1961", "path": "certificates/circle-in-equilateral/circle-in-equilateral-10-upper-6-2sqrt3.yml" }, { "id": "circle-in-equilateral-11-upper-4-2sqrt3-4sqrt6over3", "constant": "circle-in-equilateral-11", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "4+2\\sqrt{3}+\\frac{4\\sqrt{6}}{3}", "decimal_approx": 10.73009, "alt_display": "\u224810.73009" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "4+2\\sqrt{3}+\\frac{4\\sqrt{6}}{3}", "decimal_approx": 10.73009, "alt_display": "\u224810.73009" }, "comparison": "equal", "source": "melissen-1994a", "path": "certificates/circle-in-equilateral/circle-in-equilateral-11-upper-4-2sqrt3-4sqrt6over3.yml" }, { "id": "circle-in-equilateral-12-upper-4-4sqrt3", "constant": "circle-in-equilateral-12", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "4+4\\sqrt{3}", "decimal_approx": 10.9282, "alt_display": "\u224810.9282" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "4+4\\sqrt{3}", "decimal_approx": 10.9282, "alt_display": "\u224810.9282" }, "comparison": "equal", "source": "melissen-1994b", "path": "certificates/circle-in-equilateral/circle-in-equilateral-12-upper-4-4sqrt3.yml" }, { "id": "circle-in-equilateral-13-upper-4-10sqrt3over3-2sqrt6over3", "constant": "circle-in-equilateral-13", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "4+\\frac{10\\sqrt{3}}{3}+\\frac{2\\sqrt{6}}{3}", "decimal_approx": 11.4065, "alt_display": "\u224811.4065" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "4+\\frac{2\\sqrt{6}}{3} + \\frac{10\\sqrt{3}}{3}", "decimal_approx": 11.4065, "alt_display": "\u224811.4065" }, "comparison": "equal", "source": "melissen-1993", "path": "certificates/circle-in-equilateral/circle-in-equilateral-13-upper-4-10sqrt3over3-2sqrt6over3.yml" }, { "id": "circle-in-equilateral-14-upper-8-2sqrt3", "constant": "circle-in-equilateral-14", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "8+2\\sqrt{3}", "decimal_approx": 11.4641, "alt_display": "\u224811.4641" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "8+2\\sqrt{3}", "decimal_approx": 11.4641, "alt_display": "\u224811.4641" }, "comparison": "equal", "source": "oler-groemer-1961", "path": "certificates/circle-in-equilateral/circle-in-equilateral-14-upper-8-2sqrt3.yml" }, { "id": "circle-in-equilateral-15-upper-8-2sqrt3", "constant": "circle-in-equilateral-15", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "8+2\\sqrt{3}", "decimal_approx": 11.4641, "alt_display": "\u224811.4641" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "8+2\\sqrt{3}", "decimal_approx": 11.4641, "alt_display": "\u224811.4641" }, "comparison": "equal", "source": "oler-groemer-1961", "path": "certificates/circle-in-equilateral/circle-in-equilateral-15-upper-8-2sqrt3.yml" }, { "id": "circle-in-equilateral-2-lower-2-2sqrt3", "constant": "circle-in-equilateral-2", "group": "circle-in-equilateral", "bound": "lower", "value": { "latex": "2+2\\sqrt{3}", "decimal_approx": 5.464102, "alt_display": "\u22485.464102" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "2+2\\sqrt{3}", "decimal_approx": 5.464102, "alt_display": "\u22485.464102" }, "comparison": "equal", "source": null, "path": "certificates/circle-in-equilateral/circle-in-equilateral-2-lower-2-2sqrt3.yml" }, { "id": "circle-in-equilateral-2-upper-2-2sqrt3", "constant": "circle-in-equilateral-2", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "2+2\\sqrt{3}", "decimal_approx": 5.464102, "alt_display": "\u22485.464102" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "2+2\\sqrt{3}", "decimal_approx": 5.464102, "alt_display": "\u22485.464102" }, "comparison": "equal", "source": null, "path": "certificates/circle-in-equilateral/circle-in-equilateral-2-upper-2-2sqrt3.yml" }, { "id": "circle-in-equilateral-3-lower-2-2sqrt3", "constant": "circle-in-equilateral-3", "group": "circle-in-equilateral", "bound": "lower", "value": { "latex": "2+2\\sqrt{3}", "decimal_approx": 5.464102, "alt_display": "\u22485.464102" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "2+2\\sqrt{3}", "decimal_approx": 5.464102, "alt_display": "\u22485.464102" }, "comparison": "equal", "source": null, "path": "certificates/circle-in-equilateral/circle-in-equilateral-3-lower-2-2sqrt3.yml" }, { "id": "circle-in-equilateral-3-upper-2-2sqrt3", "constant": "circle-in-equilateral-3", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "2+2\\sqrt{3}", "decimal_approx": 5.464102, "alt_display": "\u22485.464102" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "2+2\\sqrt{3}", "decimal_approx": 5.464102, "alt_display": "\u22485.464102" }, "comparison": "equal", "source": null, "path": "certificates/circle-in-equilateral/circle-in-equilateral-3-upper-2-2sqrt3.yml" }, { "id": "circle-in-equilateral-4-lower-4sqrt3", "constant": "circle-in-equilateral-4", "group": "circle-in-equilateral", "bound": "lower", "value": { "latex": "4\\sqrt{3}", "decimal_approx": 6.928203, "alt_display": "\u22486.928203" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "4\\sqrt{3}", "decimal_approx": 6.928203, "alt_display": "\u22486.928203" }, "comparison": "equal", "source": null, "path": "certificates/circle-in-equilateral/circle-in-equilateral-4-lower-4sqrt3.yml" }, { "id": "circle-in-equilateral-4-upper-4sqrt3", "constant": "circle-in-equilateral-4", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "4\\sqrt{3}", "decimal_approx": 6.928203, "alt_display": "\u22486.928203" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "4\\sqrt{3}", "decimal_approx": 6.928203, "alt_display": "\u22486.928203" }, "comparison": "equal", "source": "milano-1987", "path": "certificates/circle-in-equilateral/circle-in-equilateral-4-upper-4sqrt3.yml" }, { "id": "circle-in-equilateral-5-lower-4-2sqrt3", "constant": "circle-in-equilateral-5", "group": "circle-in-equilateral", "bound": "lower", "value": { "latex": "4+2\\sqrt{3}", "decimal_approx": 7.464102, "alt_display": "\u22487.464102" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "4+2\\sqrt{3}", "decimal_approx": 7.464102, "alt_display": "\u22487.464102" }, "comparison": "equal", "source": null, "path": "certificates/circle-in-equilateral/circle-in-equilateral-5-lower-4-2sqrt3.yml" }, { "id": "circle-in-equilateral-5-upper-4-2sqrt3", "constant": "circle-in-equilateral-5", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "4+2\\sqrt{3}", "decimal_approx": 7.464102, "alt_display": "\u22487.464102" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "4+2\\sqrt{3}", "decimal_approx": 7.464102, "alt_display": "\u22487.464102" }, "comparison": "equal", "source": "oler-groemer-1961", "path": "certificates/circle-in-equilateral/circle-in-equilateral-5-upper-4-2sqrt3.yml" }, { "id": "circle-in-equilateral-6-lower-4-2sqrt3", "constant": "circle-in-equilateral-6", "group": "circle-in-equilateral", "bound": "lower", "value": { "latex": "4+2\\sqrt{3}", "decimal_approx": 7.464102, "alt_display": "\u22487.464102" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "4+2\\sqrt{3}", "decimal_approx": 7.464102, "alt_display": "\u22487.464102" }, "comparison": "equal", "source": null, "path": "certificates/circle-in-equilateral/circle-in-equilateral-6-lower-4-2sqrt3.yml" }, { "id": "circle-in-equilateral-6-upper-4-2sqrt3", "constant": "circle-in-equilateral-6", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "4+2\\sqrt{3}", "decimal_approx": 7.464102, "alt_display": "\u22487.464102" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "4+2\\sqrt{3}", "decimal_approx": 7.464102, "alt_display": "\u22487.464102" }, "comparison": "equal", "source": "oler-groemer-1961", "path": "certificates/circle-in-equilateral/circle-in-equilateral-6-upper-4-2sqrt3.yml" }, { "id": "circle-in-equilateral-7-upper-2-4sqrt3", "constant": "circle-in-equilateral-7", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "2+4\\sqrt{3}", "decimal_approx": 8.928203, "alt_display": "\u22488.928203" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "2+4\\sqrt{3}", "decimal_approx": 8.928203, "alt_display": "\u22488.928203" }, "comparison": "equal", "source": "melissen-1993", "path": "certificates/circle-in-equilateral/circle-in-equilateral-7-upper-2-4sqrt3.yml" }, { "id": "circle-in-equilateral-8-upper-2-2sqrt3-2sqrt33over3", "constant": "circle-in-equilateral-8", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "2+2\\sqrt{3}+\\frac{2\\sqrt{33}}{3}", "decimal_approx": 9.29381, "alt_display": "\u22489.29381" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "2+2\\sqrt{3}+\\frac{2\\sqrt{33}}{3}", "decimal_approx": 9.29381, "alt_display": "\u22489.29381" }, "comparison": "equal", "source": "melissen-1993", "path": "certificates/circle-in-equilateral/circle-in-equilateral-8-upper-2-2sqrt3-2sqrt33over3.yml" }, { "id": "circle-in-equilateral-9-upper-6-2sqrt3", "constant": "circle-in-equilateral-9", "group": "circle-in-equilateral", "bound": "upper", "value": { "latex": "6+2\\sqrt{3}", "decimal_approx": 9.464102, "alt_display": "\u22489.464102" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-11-01", "current": true, "literature": { "latex": "6+2\\sqrt{3}", "decimal_approx": 9.464102, "alt_display": "\u22489.464102" }, "comparison": "equal", "source": "melissen-1993", "path": "certificates/circle-in-equilateral/circle-in-equilateral-9-upper-6-2sqrt3.yml" }, { "id": "van-der-waerden-2-10-lower-103475", "constant": "van-der-waerden-2-10", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "103475", "decimal_approx": 103475, "alt_display": "103,475" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-31", "current": true, "literature": { "latex": "103475", "decimal_approx": 103475, "alt_display": "103,475" }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-2-10-lower-103475.yml" }, { "id": "van-der-waerden-2-7-lower-3704", "constant": "van-der-waerden-2-7", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "3704", "decimal_approx": 3704, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-31", "current": true, "literature": { "latex": "3704", "decimal_approx": 3704, "alt_display": null }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-2-7-lower-3704.yml" }, { "id": "van-der-waerden-3-4-lower-293", "constant": "van-der-waerden-3-4", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "293", "decimal_approx": 293, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-31", "current": true, "literature": { "latex": "293", "decimal_approx": 293, "alt_display": null }, "comparison": "equal", "source": "rabung-1979", "path": "certificates/van-der-waerden/van-der-waerden-3-4-lower-293.yml" }, { "id": "van-der-waerden-3-8-lower-238401", "constant": "van-der-waerden-3-8", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "238401", "decimal_approx": 238401, "alt_display": "238,401" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-31", "current": true, "literature": { "latex": "238401", "decimal_approx": 238401, "alt_display": "238,401" }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-3-8-lower-238401.yml" }, { "id": "van-der-waerden-4-3-lower-76", "constant": "van-der-waerden-4-3", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "76", "decimal_approx": 76, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-31", "current": true, "literature": { "latex": "76", "decimal_approx": 76, "alt_display": null }, "comparison": "equal", "source": "rabung-1979", "path": "certificates/van-der-waerden/van-der-waerden-4-3-lower-76.yml" }, { "id": "van-der-waerden-4-4-lower-1049", "constant": "van-der-waerden-4-4", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "1049", "decimal_approx": 1049, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-31", "current": true, "literature": { "latex": "1049", "decimal_approx": 1049, "alt_display": null }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-4-4-lower-1049.yml" }, { "id": "van-der-waerden-5-4-lower-2255", "constant": "van-der-waerden-5-4", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "2255", "decimal_approx": 2255, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-31", "current": true, "literature": { "latex": "2255", "decimal_approx": 2255, "alt_display": null }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-5-4-lower-2255.yml" }, { "id": "van-der-waerden-6-4-lower-9779", "constant": "van-der-waerden-6-4", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "9779", "decimal_approx": 9779, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-31", "current": true, "literature": { "latex": "9779", "decimal_approx": 9779, "alt_display": null }, "comparison": "equal", "source": "rabung-lotts-2012", "path": "certificates/van-der-waerden/van-der-waerden-6-4-lower-9779.yml" }, { "id": "kissing-number-1-lower-2", "constant": "kissing-number-1", "group": "kissing-number", "bound": "lower", "value": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-1-lower-2.yml" }, { "id": "kissing-number-10-lower-336", "constant": "kissing-number-10", "group": "kissing-number", "bound": "lower", "value": { "latex": "336", "decimal_approx": 336, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "510", "decimal_approx": 510, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-10-lower-336.yml" }, { "id": "kissing-number-11-lower-438", "constant": "kissing-number-11", "group": "kissing-number", "bound": "lower", "value": { "latex": "438", "decimal_approx": 438, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "604", "decimal_approx": 604, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-11-lower-438.yml" }, { "id": "kissing-number-12-lower-756", "constant": "kissing-number-12", "group": "kissing-number", "bound": "lower", "value": { "latex": "756", "decimal_approx": 756, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "841", "decimal_approx": 841, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-12-lower-756.yml" }, { "id": "kissing-number-13-lower-906", "constant": "kissing-number-13", "group": "kissing-number", "bound": "lower", "value": { "latex": "906", "decimal_approx": 906, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "1154", "decimal_approx": 1154, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-13-lower-906.yml" }, { "id": "kissing-number-14-lower-1422", "constant": "kissing-number-14", "group": "kissing-number", "bound": "lower", "value": { "latex": "1422", "decimal_approx": 1422, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "1932", "decimal_approx": 1932, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-14-lower-1422.yml" }, { "id": "kissing-number-15-lower-2340", "constant": "kissing-number-15", "group": "kissing-number", "bound": "lower", "value": { "latex": "2340", "decimal_approx": 2340, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2564", "decimal_approx": 2564, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-15-lower-2340.yml" }, { "id": "kissing-number-16-lower-4320", "constant": "kissing-number-16", "group": "kissing-number", "bound": "lower", "value": { "latex": "4320", "decimal_approx": 4320, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4320", "decimal_approx": 4320, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-16-lower-4320.yml" }, { "id": "kissing-number-17-lower-5346", "constant": "kissing-number-17", "group": "kissing-number", "bound": "lower", "value": { "latex": "5346", "decimal_approx": 5346, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5730", "decimal_approx": 5730, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-17-lower-5346.yml" }, { "id": "kissing-number-18-lower-7398", "constant": "kissing-number-18", "group": "kissing-number", "bound": "lower", "value": { "latex": "7398", "decimal_approx": 7398, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8358", "decimal_approx": 8358, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-18-lower-7398.yml" }, { "id": "kissing-number-19-lower-10668", "constant": "kissing-number-19", "group": "kissing-number", "bound": "lower", "value": { "latex": "10668", "decimal_approx": 10668, "alt_display": "10,668" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "12460", "decimal_approx": 12460, "alt_display": "12,460" }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-19-lower-10668.yml" }, { "id": "kissing-number-2-lower-6", "constant": "kissing-number-2", "group": "kissing-number", "bound": "lower", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-2-lower-6.yml" }, { "id": "kissing-number-20-lower-17400", "constant": "kissing-number-20", "group": "kissing-number", "bound": "lower", "value": { "latex": "17400", "decimal_approx": 17400, "alt_display": "17,400" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "19448", "decimal_approx": 19448, "alt_display": "19,448" }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-20-lower-17400.yml" }, { "id": "kissing-number-21-lower-27720", "constant": "kissing-number-21", "group": "kissing-number", "bound": "lower", "value": { "latex": "27720", "decimal_approx": 27720, "alt_display": "27,720" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "31560", "decimal_approx": 31560, "alt_display": "31,560" }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-21-lower-27720.yml" }, { "id": "kissing-number-22-lower-49896", "constant": "kissing-number-22", "group": "kissing-number", "bound": "lower", "value": { "latex": "49896", "decimal_approx": 49896, "alt_display": "49,896" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "49896", "decimal_approx": 49896, "alt_display": "49,896" }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-22-lower-49896.yml" }, { "id": "kissing-number-23-lower-93150", "constant": "kissing-number-23", "group": "kissing-number", "bound": "lower", "value": { "latex": "93150", "decimal_approx": 93150, "alt_display": "93,150" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "93150", "decimal_approx": 93150, "alt_display": "93,150" }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-23-lower-93150.yml" }, { "id": "kissing-number-24-lower-196560", "constant": "kissing-number-24", "group": "kissing-number", "bound": "lower", "value": { "latex": "196560", "decimal_approx": 196560, "alt_display": "196,560" }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "196560", "decimal_approx": 196560, "alt_display": "196,560" }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-24-lower-196560.yml" }, { "id": "kissing-number-3-lower-12", "constant": "kissing-number-3", "group": "kissing-number", "bound": "lower", "value": { "latex": "12", "decimal_approx": 12, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "12", "decimal_approx": 12, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-3-lower-12.yml" }, { "id": "kissing-number-4-lower-24", "constant": "kissing-number-4", "group": "kissing-number", "bound": "lower", "value": { "latex": "24", "decimal_approx": 24, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "24", "decimal_approx": 24, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-4-lower-24.yml" }, { "id": "kissing-number-5-lower-40", "constant": "kissing-number-5", "group": "kissing-number", "bound": "lower", "value": { "latex": "40", "decimal_approx": 40, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "40", "decimal_approx": 40, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-5-lower-40.yml" }, { "id": "kissing-number-6-lower-72", "constant": "kissing-number-6", "group": "kissing-number", "bound": "lower", "value": { "latex": "72", "decimal_approx": 72, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "72", "decimal_approx": 72, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-6-lower-72.yml" }, { "id": "kissing-number-7-lower-126", "constant": "kissing-number-7", "group": "kissing-number", "bound": "lower", "value": { "latex": "126", "decimal_approx": 126, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "126", "decimal_approx": 126, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-7-lower-126.yml" }, { "id": "kissing-number-8-lower-240", "constant": "kissing-number-8", "group": "kissing-number", "bound": "lower", "value": { "latex": "240", "decimal_approx": 240, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "240", "decimal_approx": 240, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/kissing-number/kissing-number-8-lower-240.yml" }, { "id": "kissing-number-9-lower-272", "constant": "kissing-number-9", "group": "kissing-number", "bound": "lower", "value": { "latex": "272", "decimal_approx": 272, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "306", "decimal_approx": 306, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/kissing-number/kissing-number-9-lower-272.yml" }, { "id": "square-packing-in-square-1-lower-1", "constant": "square-packing-in-square-1", "group": "square-packing", "bound": "lower", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-1-lower-1.yml" }, { "id": "square-packing-in-square-1-upper-1", "constant": "square-packing-in-square-1", "group": "square-packing", "bound": "upper", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-1-upper-1.yml" }, { "id": "square-packing-in-square-10-lower-sqrt10", "constant": "square-packing-in-square-10", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{10}", "decimal_approx": 3.162278, "alt_display": "\u22483.162278" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3 + \\frac{1}{\\sqrt{2}}", "decimal_approx": 3.707107, "alt_display": "\u22483.707107" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-10-lower-sqrt10.yml" }, { "id": "square-packing-in-square-10-upper-4", "constant": "square-packing-in-square-10", "group": "square-packing", "bound": "upper", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3 + \\frac{1}{\\sqrt{2}}", "decimal_approx": 3.707107, "alt_display": "\u22483.707107" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-10-upper-4.yml" }, { "id": "square-packing-in-square-100-lower-10", "constant": "square-packing-in-square-100", "group": "square-packing", "bound": "lower", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-100-lower-10.yml" }, { "id": "square-packing-in-square-100-upper-10", "constant": "square-packing-in-square-100", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-100-upper-10.yml" }, { "id": "square-packing-in-square-11-lower-sqrt11", "constant": "square-packing-in-square-11", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{11}", "decimal_approx": 3.316625, "alt_display": "\u22483.316625" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2 + \\frac{4}{\\sqrt{5}}", "decimal_approx": 3.788854, "alt_display": "\u22483.788854" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-11-lower-sqrt11.yml" }, { "id": "square-packing-in-square-11-upper-4", "constant": "square-packing-in-square-11", "group": "square-packing", "bound": "upper", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}3.8771", "decimal_approx": 3.8771, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-11-upper-4.yml" }, { "id": "square-packing-in-square-12-lower-sqrt12", "constant": "square-packing-in-square-12", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{12}", "decimal_approx": 3.464102, "alt_display": "\u22483.464102" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2 + \\frac{4}{\\sqrt{5}}", "decimal_approx": 3.788854, "alt_display": "\u22483.788854" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-12-lower-sqrt12.yml" }, { "id": "square-packing-in-square-12-upper-4", "constant": "square-packing-in-square-12", "group": "square-packing", "bound": "upper", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-12-upper-4.yml" }, { "id": "square-packing-in-square-13-lower-sqrt13", "constant": "square-packing-in-square-13", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{13}", "decimal_approx": 3.605551, "alt_display": "\u22483.605551" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-13-lower-sqrt13.yml" }, { "id": "square-packing-in-square-13-upper-4", "constant": "square-packing-in-square-13", "group": "square-packing", "bound": "upper", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-13-upper-4.yml" }, { "id": "square-packing-in-square-14-lower-sqrt14", "constant": "square-packing-in-square-14", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{14}", "decimal_approx": 3.741657, "alt_display": "\u22483.741657" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-14-lower-sqrt14.yml" }, { "id": "square-packing-in-square-14-upper-4", "constant": "square-packing-in-square-14", "group": "square-packing", "bound": "upper", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-14-upper-4.yml" }, { "id": "square-packing-in-square-15-lower-sqrt15", "constant": "square-packing-in-square-15", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{15}", "decimal_approx": 3.872983, "alt_display": "\u22483.872983" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-15-lower-sqrt15.yml" }, { "id": "square-packing-in-square-15-upper-4", "constant": "square-packing-in-square-15", "group": "square-packing", "bound": "upper", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-15-upper-4.yml" }, { "id": "square-packing-in-square-16-lower-4", "constant": "square-packing-in-square-16", "group": "square-packing", "bound": "lower", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-16-lower-4.yml" }, { "id": "square-packing-in-square-16-upper-4", "constant": "square-packing-in-square-16", "group": "square-packing", "bound": "upper", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-16-upper-4.yml" }, { "id": "square-packing-in-square-17-lower-sqrt17", "constant": "square-packing-in-square-17", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{17}", "decimal_approx": 4.123106, "alt_display": "\u22484.123106" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "\\frac{40\\sqrt{2}+19}{17}", "decimal_approx": 4.445208, "alt_display": "\u22484.445208" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-17-lower-sqrt17.yml" }, { "id": "square-packing-in-square-17-upper-5", "constant": "square-packing-in-square-17", "group": "square-packing", "bound": "upper", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}4.6755", "decimal_approx": 4.6755, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-17-upper-5.yml" }, { "id": "square-packing-in-square-18-lower-sqrt18", "constant": "square-packing-in-square-18", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{18}", "decimal_approx": 4.242641, "alt_display": "\u22484.242641" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "\\frac{40\\sqrt{2}+19}{17}", "decimal_approx": 4.445208, "alt_display": "\u22484.445208" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-18-lower-sqrt18.yml" }, { "id": "square-packing-in-square-18-upper-5", "constant": "square-packing-in-square-18", "group": "square-packing", "bound": "upper", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "\\frac{7+\\sqrt{7}}{2}", "decimal_approx": 4.822876, "alt_display": "\u22484.822876" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-18-upper-5.yml" }, { "id": "square-packing-in-square-19-lower-sqrt19", "constant": "square-packing-in-square-19", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{19}", "decimal_approx": 4.358899, "alt_display": "\u22484.358899" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6\\sqrt{2}-4", "decimal_approx": 4.485281, "alt_display": "\u22484.485281" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-19-lower-sqrt19.yml" }, { "id": "square-packing-in-square-19-upper-5", "constant": "square-packing-in-square-19", "group": "square-packing", "bound": "upper", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3+\\frac{4\\sqrt{2}}{3}", "decimal_approx": 4.885618, "alt_display": "\u22484.885618" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-19-upper-5.yml" }, { "id": "square-packing-in-square-2-lower-sqrt2", "constant": "square-packing-in-square-2", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{2}", "decimal_approx": 1.414214, "alt_display": "\u22481.414214" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-2-lower-sqrt2.yml" }, { "id": "square-packing-in-square-2-upper-2", "constant": "square-packing-in-square-2", "group": "square-packing", "bound": "upper", "value": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-2-upper-2.yml" }, { "id": "square-packing-in-square-20-lower-sqrt20", "constant": "square-packing-in-square-20", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{20}", "decimal_approx": 4.472136, "alt_display": "\u22484.472136" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6\\sqrt{2}-4", "decimal_approx": 4.485281, "alt_display": "\u22484.485281" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-20-lower-sqrt20.yml" }, { "id": "square-packing-in-square-20-upper-5", "constant": "square-packing-in-square-20", "group": "square-packing", "bound": "upper", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-20-upper-5.yml" }, { "id": "square-packing-in-square-21-lower-sqrt21", "constant": "square-packing-in-square-21", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{21}", "decimal_approx": 4.582576, "alt_display": "\u22484.582576" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4.7438", "decimal_approx": 4.7438, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-21-lower-sqrt21.yml" }, { "id": "square-packing-in-square-21-upper-5", "constant": "square-packing-in-square-21", "group": "square-packing", "bound": "upper", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-21-upper-5.yml" }, { "id": "square-packing-in-square-22-lower-sqrt22", "constant": "square-packing-in-square-22", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{22}", "decimal_approx": 4.690416, "alt_display": "\u22484.690416" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-22-lower-sqrt22.yml" }, { "id": "square-packing-in-square-22-upper-5", "constant": "square-packing-in-square-22", "group": "square-packing", "bound": "upper", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-22-upper-5.yml" }, { "id": "square-packing-in-square-23-lower-sqrt23", "constant": "square-packing-in-square-23", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{23}", "decimal_approx": 4.795832, "alt_display": "\u22484.795832" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-23-lower-sqrt23.yml" }, { "id": "square-packing-in-square-23-upper-5", "constant": "square-packing-in-square-23", "group": "square-packing", "bound": "upper", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-23-upper-5.yml" }, { "id": "square-packing-in-square-24-lower-sqrt24", "constant": "square-packing-in-square-24", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{24}", "decimal_approx": 4.898979, "alt_display": "\u22484.898979" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-24-lower-sqrt24.yml" }, { "id": "square-packing-in-square-24-upper-5", "constant": "square-packing-in-square-24", "group": "square-packing", "bound": "upper", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-24-upper-5.yml" }, { "id": "square-packing-in-square-25-lower-5", "constant": "square-packing-in-square-25", "group": "square-packing", "bound": "lower", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-25-lower-5.yml" }, { "id": "square-packing-in-square-25-upper-5", "constant": "square-packing-in-square-25", "group": "square-packing", "bound": "upper", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-25-upper-5.yml" }, { "id": "square-packing-in-square-26-lower-sqrt26", "constant": "square-packing-in-square-26", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{26}", "decimal_approx": 5.09902, "alt_display": "\u22485.09902" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{27+2\\sqrt{10}}{13}", "decimal_approx": 5.391854, "alt_display": "\u22485.391854" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-26-lower-sqrt26.yml" }, { "id": "square-packing-in-square-26-upper-6", "constant": "square-packing-in-square-26", "group": "square-packing", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "\\frac{7}{2}+\\frac{3\\sqrt{2}}{2}", "decimal_approx": 5.62132, "alt_display": "\u22485.62132" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-26-upper-6.yml" }, { "id": "square-packing-in-square-27-lower-sqrt27", "constant": "square-packing-in-square-27", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{27}", "decimal_approx": 5.196152, "alt_display": "\u22485.196152" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{27+2\\sqrt{10}}{13}", "decimal_approx": 5.391854, "alt_display": "\u22485.391854" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-27-lower-sqrt27.yml" }, { "id": "square-packing-in-square-27-upper-6", "constant": "square-packing-in-square-27", "group": "square-packing", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5+\\frac{1}{\\sqrt{2}}", "decimal_approx": 5.707107, "alt_display": "\u22485.707107" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-27-upper-6.yml" }, { "id": "square-packing-in-square-28-lower-sqrt28", "constant": "square-packing-in-square-28", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{28}", "decimal_approx": 5.291503, "alt_display": "\u22485.291503" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{6}{\\sqrt{5}}", "decimal_approx": 5.511709, "alt_display": "\u22485.511709" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-28-lower-sqrt28.yml" }, { "id": "square-packing-in-square-28-upper-6", "constant": "square-packing-in-square-28", "group": "square-packing", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}5.8244", "decimal_approx": 5.8244, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-28-upper-6.yml" }, { "id": "square-packing-in-square-29-lower-sqrt29", "constant": "square-packing-in-square-29", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{29}", "decimal_approx": 5.385165, "alt_display": "\u22485.385165" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{6}{\\sqrt{5}}", "decimal_approx": 5.511709, "alt_display": "\u22485.511709" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-29-lower-sqrt29.yml" }, { "id": "square-packing-in-square-29-upper-6", "constant": "square-packing-in-square-29", "group": "square-packing", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}5.9338", "decimal_approx": 5.9338, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-29-upper-6.yml" }, { "id": "square-packing-in-square-3-lower-sqrt3", "constant": "square-packing-in-square-3", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{3}", "decimal_approx": 1.732051, "alt_display": "\u22481.732051" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-3-lower-sqrt3.yml" }, { "id": "square-packing-in-square-3-upper-2", "constant": "square-packing-in-square-3", "group": "square-packing", "bound": "upper", "value": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-3-upper-2.yml" }, { "id": "square-packing-in-square-30-lower-sqrt30", "constant": "square-packing-in-square-30", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{30}", "decimal_approx": 5.477226, "alt_display": "\u22485.477226" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{6}{\\sqrt{5}}", "decimal_approx": 5.511709, "alt_display": "\u22485.511709" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-30-lower-sqrt30.yml" }, { "id": "square-packing-in-square-30-upper-6", "constant": "square-packing-in-square-30", "group": "square-packing", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-30-upper-6.yml" }, { "id": "square-packing-in-square-31-lower-sqrt31", "constant": "square-packing-in-square-31", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{31}", "decimal_approx": 5.567764, "alt_display": "\u22485.567764" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5.6415", "decimal_approx": 5.6415, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-31-lower-sqrt31.yml" }, { "id": "square-packing-in-square-31-upper-6", "constant": "square-packing-in-square-31", "group": "square-packing", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-31-upper-6.yml" }, { "id": "square-packing-in-square-32-lower-sqrt32", "constant": "square-packing-in-square-32", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{32}", "decimal_approx": 5.656854, "alt_display": "\u22485.656854" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-32-lower-sqrt32.yml" }, { "id": "square-packing-in-square-32-upper-6", "constant": "square-packing-in-square-32", "group": "square-packing", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-32-upper-6.yml" }, { "id": "square-packing-in-square-33-lower-sqrt33", "constant": "square-packing-in-square-33", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{33}", "decimal_approx": 5.744563, "alt_display": "\u22485.744563" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-33-lower-sqrt33.yml" }, { "id": "square-packing-in-square-33-upper-6", "constant": "square-packing-in-square-33", "group": "square-packing", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-33-upper-6.yml" }, { "id": "square-packing-in-square-34-lower-sqrt34", "constant": "square-packing-in-square-34", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{34}", "decimal_approx": 5.830952, "alt_display": "\u22485.830952" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-34-lower-sqrt34.yml" }, { "id": "square-packing-in-square-34-upper-6", "constant": "square-packing-in-square-34", "group": "square-packing", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-34-upper-6.yml" }, { "id": "square-packing-in-square-35-lower-sqrt35", "constant": "square-packing-in-square-35", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{35}", "decimal_approx": 5.91608, "alt_display": "\u22485.91608" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-35-lower-sqrt35.yml" }, { "id": "square-packing-in-square-35-upper-6", "constant": "square-packing-in-square-35", "group": "square-packing", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-35-upper-6.yml" }, { "id": "square-packing-in-square-36-lower-6", "constant": "square-packing-in-square-36", "group": "square-packing", "bound": "lower", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-36-lower-6.yml" }, { "id": "square-packing-in-square-36-upper-6", "constant": "square-packing-in-square-36", "group": "square-packing", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-36-upper-6.yml" }, { "id": "square-packing-in-square-37-lower-sqrt37", "constant": "square-packing-in-square-37", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{37}", "decimal_approx": 6.082763, "alt_display": "\u22486.082763" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{113+10\\sqrt{3}}{37}", "decimal_approx": 6.350603, "alt_display": "\u22486.350603" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-37-lower-sqrt37.yml" }, { "id": "square-packing-in-square-37-upper-7", "constant": "square-packing-in-square-37", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}6.5986", "decimal_approx": 6.5986, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-37-upper-7.yml" }, { "id": "square-packing-in-square-38-lower-sqrt38", "constant": "square-packing-in-square-38", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{38}", "decimal_approx": 6.164414, "alt_display": "\u22486.164414" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{113+10\\sqrt{3}}{37}", "decimal_approx": 6.350603, "alt_display": "\u22486.350603" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-38-lower-sqrt38.yml" }, { "id": "square-packing-in-square-38-upper-7", "constant": "square-packing-in-square-38", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6+\\frac{1}{\\sqrt{2}}", "decimal_approx": 6.707107, "alt_display": "\u22486.707107" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-38-upper-7.yml" }, { "id": "square-packing-in-square-39-lower-sqrt39", "constant": "square-packing-in-square-39", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{39}", "decimal_approx": 6.244998, "alt_display": "\u22486.244998" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{113+10\\sqrt{3}}{37}", "decimal_approx": 6.350603, "alt_display": "\u22486.350603" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-39-lower-sqrt39.yml" }, { "id": "square-packing-in-square-39-upper-7", "constant": "square-packing-in-square-39", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}6.8107", "decimal_approx": 6.8107, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-39-upper-7.yml" }, { "id": "square-packing-in-square-4-lower-2", "constant": "square-packing-in-square-4", "group": "square-packing", "bound": "lower", "value": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-4-lower-2.yml" }, { "id": "square-packing-in-square-4-upper-2", "constant": "square-packing-in-square-4", "group": "square-packing", "bound": "upper", "value": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2", "decimal_approx": 2, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-4-upper-2.yml" }, { "id": "square-packing-in-square-40-lower-sqrt40", "constant": "square-packing-in-square-40", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{40}", "decimal_approx": 6.324555, "alt_display": "\u22486.324555" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{8}{\\sqrt{5}}", "decimal_approx": 6.406136, "alt_display": "\u22486.406136" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-40-lower-sqrt40.yml" }, { "id": "square-packing-in-square-40-upper-7", "constant": "square-packing-in-square-40", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "4+2\\sqrt{2}", "decimal_approx": 6.828427, "alt_display": "\u22486.828427" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-40-upper-7.yml" }, { "id": "square-packing-in-square-41-lower-sqrt41", "constant": "square-packing-in-square-41", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{41}", "decimal_approx": 6.403124, "alt_display": "\u22486.403124" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{8}{\\sqrt{5}}", "decimal_approx": 6.406136, "alt_display": "\u22486.406136" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-41-lower-sqrt41.yml" }, { "id": "square-packing-in-square-41-upper-7", "constant": "square-packing-in-square-41", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}6.9267", "decimal_approx": 6.9267, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-41-upper-7.yml" }, { "id": "square-packing-in-square-42-lower-sqrt42", "constant": "square-packing-in-square-42", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{42}", "decimal_approx": 6.480741, "alt_display": "\u22486.480741" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-42-lower-sqrt42.yml" }, { "id": "square-packing-in-square-42-upper-7", "constant": "square-packing-in-square-42", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-42-upper-7.yml" }, { "id": "square-packing-in-square-43-lower-sqrt43", "constant": "square-packing-in-square-43", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{43}", "decimal_approx": 6.557439, "alt_display": "\u22486.557439" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-43-lower-sqrt43.yml" }, { "id": "square-packing-in-square-43-upper-7", "constant": "square-packing-in-square-43", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-43-upper-7.yml" }, { "id": "square-packing-in-square-44-lower-sqrt44", "constant": "square-packing-in-square-44", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{44}", "decimal_approx": 6.63325, "alt_display": "\u22486.63325" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-44-lower-sqrt44.yml" }, { "id": "square-packing-in-square-44-upper-7", "constant": "square-packing-in-square-44", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-44-upper-7.yml" }, { "id": "square-packing-in-square-45-lower-sqrt45", "constant": "square-packing-in-square-45", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{45}", "decimal_approx": 6.708204, "alt_display": "\u22486.708204" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-45-lower-sqrt45.yml" }, { "id": "square-packing-in-square-45-upper-7", "constant": "square-packing-in-square-45", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-45-upper-7.yml" }, { "id": "square-packing-in-square-46-lower-sqrt46", "constant": "square-packing-in-square-46", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{46}", "decimal_approx": 6.78233, "alt_display": "\u22486.78233" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-46-lower-sqrt46.yml" }, { "id": "square-packing-in-square-46-upper-7", "constant": "square-packing-in-square-46", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-46-upper-7.yml" }, { "id": "square-packing-in-square-47-lower-sqrt47", "constant": "square-packing-in-square-47", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{47}", "decimal_approx": 6.855655, "alt_display": "\u22486.855655" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-47-lower-sqrt47.yml" }, { "id": "square-packing-in-square-47-upper-7", "constant": "square-packing-in-square-47", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-47-upper-7.yml" }, { "id": "square-packing-in-square-48-lower-sqrt48", "constant": "square-packing-in-square-48", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{48}", "decimal_approx": 6.928203, "alt_display": "\u22486.928203" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-48-lower-sqrt48.yml" }, { "id": "square-packing-in-square-48-upper-7", "constant": "square-packing-in-square-48", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-48-upper-7.yml" }, { "id": "square-packing-in-square-49-lower-7", "constant": "square-packing-in-square-49", "group": "square-packing", "bound": "lower", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-49-lower-7.yml" }, { "id": "square-packing-in-square-49-upper-7", "constant": "square-packing-in-square-49", "group": "square-packing", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-49-upper-7.yml" }, { "id": "square-packing-in-square-5-lower-sqrt5", "constant": "square-packing-in-square-5", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{5}", "decimal_approx": 2.236068, "alt_display": "\u22482.236068" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2 + \\frac{1}{\\sqrt{2}}", "decimal_approx": 2.707107, "alt_display": "\u22482.707107" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-5-lower-sqrt5.yml" }, { "id": "square-packing-in-square-5-upper-3", "constant": "square-packing-in-square-5", "group": "square-packing", "bound": "upper", "value": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2 + \\frac{1}{\\sqrt{2}}", "decimal_approx": 2.707107, "alt_display": "\u22482.707107" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-5-upper-3.yml" }, { "id": "square-packing-in-square-50-lower-sqrt50", "constant": "square-packing-in-square-50", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{50}", "decimal_approx": 7.071068, "alt_display": "\u22487.071068" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{101+3\\sqrt{14}}{25}", "decimal_approx": 7.317426, "alt_display": "\u22487.317426" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-50-lower-sqrt50.yml" }, { "id": "square-packing-in-square-50-upper-8", "constant": "square-packing-in-square-50", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7+\\frac{4}{7}", "decimal_approx": 7.571429, "alt_display": "\u22487.571429" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-50-upper-8.yml" }, { "id": "square-packing-in-square-51-lower-sqrt51", "constant": "square-packing-in-square-51", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{51}", "decimal_approx": 7.141428, "alt_display": "\u22487.141428" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{101+3\\sqrt{14}}{25}", "decimal_approx": 7.317426, "alt_display": "\u22487.317426" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-51-lower-sqrt51.yml" }, { "id": "square-packing-in-square-51-upper-8", "constant": "square-packing-in-square-51", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}7.7008", "decimal_approx": 7.7008, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-51-upper-8.yml" }, { "id": "square-packing-in-square-52-lower-sqrt52", "constant": "square-packing-in-square-52", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{52}", "decimal_approx": 7.211103, "alt_display": "\u22487.211103" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{101+3\\sqrt{14}}{25}", "decimal_approx": 7.317426, "alt_display": "\u22487.317426" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-52-lower-sqrt52.yml" }, { "id": "square-packing-in-square-52-upper-8", "constant": "square-packing-in-square-52", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7+\\frac{1}{\\sqrt{2}}", "decimal_approx": 7.707107, "alt_display": "\u22487.707107" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-52-upper-8.yml" }, { "id": "square-packing-in-square-53-lower-sqrt53", "constant": "square-packing-in-square-53", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{53}", "decimal_approx": 7.28011, "alt_display": "\u22487.28011" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{101+3\\sqrt{14}}{25}", "decimal_approx": 7.317426, "alt_display": "\u22487.317426" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-53-lower-sqrt53.yml" }, { "id": "square-packing-in-square-53-upper-8", "constant": "square-packing-in-square-53", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "\\frac{13}{2}+\\frac{\\sqrt{7}}{2}", "decimal_approx": 7.822876, "alt_display": "\u22487.822876" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-53-upper-8.yml" }, { "id": "square-packing-in-square-54-lower-sqrt54", "constant": "square-packing-in-square-54", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{54}", "decimal_approx": 7.348469, "alt_display": "\u22487.348469" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-54-lower-sqrt54.yml" }, { "id": "square-packing-in-square-54-upper-8", "constant": "square-packing-in-square-54", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "7-\\frac{\\sqrt{2}}{2}+\\sqrt{1+\\sqrt{2}}", "decimal_approx": 7.846667, "alt_display": "\u22487.846667" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-54-upper-8.yml" }, { "id": "square-packing-in-square-55-lower-sqrt55", "constant": "square-packing-in-square-55", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{55}", "decimal_approx": 7.416198, "alt_display": "\u22487.416198" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-55-lower-sqrt55.yml" }, { "id": "square-packing-in-square-55-upper-8", "constant": "square-packing-in-square-55", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}7.9458", "decimal_approx": 7.9458, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-55-upper-8.yml" }, { "id": "square-packing-in-square-56-lower-sqrt56", "constant": "square-packing-in-square-56", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{56}", "decimal_approx": 7.483315, "alt_display": "\u22487.483315" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-56-lower-sqrt56.yml" }, { "id": "square-packing-in-square-56-upper-8", "constant": "square-packing-in-square-56", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-56-upper-8.yml" }, { "id": "square-packing-in-square-57-lower-sqrt57", "constant": "square-packing-in-square-57", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{57}", "decimal_approx": 7.549834, "alt_display": "\u22487.549834" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-57-lower-sqrt57.yml" }, { "id": "square-packing-in-square-57-upper-8", "constant": "square-packing-in-square-57", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-57-upper-8.yml" }, { "id": "square-packing-in-square-58-lower-sqrt58", "constant": "square-packing-in-square-58", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{58}", "decimal_approx": 7.615773, "alt_display": "\u22487.615773" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-58-lower-sqrt58.yml" }, { "id": "square-packing-in-square-58-upper-8", "constant": "square-packing-in-square-58", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-58-upper-8.yml" }, { "id": "square-packing-in-square-59-lower-sqrt59", "constant": "square-packing-in-square-59", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{59}", "decimal_approx": 7.681146, "alt_display": "\u22487.681146" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-59-lower-sqrt59.yml" }, { "id": "square-packing-in-square-59-upper-8", "constant": "square-packing-in-square-59", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-59-upper-8.yml" }, { "id": "square-packing-in-square-6-lower-sqrt6", "constant": "square-packing-in-square-6", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{6}", "decimal_approx": 2.44949, "alt_display": "\u22482.44949" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-6-lower-sqrt6.yml" }, { "id": "square-packing-in-square-6-upper-3", "constant": "square-packing-in-square-6", "group": "square-packing", "bound": "upper", "value": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-6-upper-3.yml" }, { "id": "square-packing-in-square-60-lower-sqrt60", "constant": "square-packing-in-square-60", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{60}", "decimal_approx": 7.745967, "alt_display": "\u22487.745967" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-60-lower-sqrt60.yml" }, { "id": "square-packing-in-square-60-upper-8", "constant": "square-packing-in-square-60", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-60-upper-8.yml" }, { "id": "square-packing-in-square-61-lower-sqrt61", "constant": "square-packing-in-square-61", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{61}", "decimal_approx": 7.81025, "alt_display": "\u22487.81025" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-61-lower-sqrt61.yml" }, { "id": "square-packing-in-square-61-upper-8", "constant": "square-packing-in-square-61", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-61-upper-8.yml" }, { "id": "square-packing-in-square-62-lower-sqrt62", "constant": "square-packing-in-square-62", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{62}", "decimal_approx": 7.874008, "alt_display": "\u22487.874008" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-62-lower-sqrt62.yml" }, { "id": "square-packing-in-square-62-upper-8", "constant": "square-packing-in-square-62", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-62-upper-8.yml" }, { "id": "square-packing-in-square-63-lower-sqrt63", "constant": "square-packing-in-square-63", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{63}", "decimal_approx": 7.937254, "alt_display": "\u22487.937254" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-63-lower-sqrt63.yml" }, { "id": "square-packing-in-square-63-upper-8", "constant": "square-packing-in-square-63", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-63-upper-8.yml" }, { "id": "square-packing-in-square-64-lower-8", "constant": "square-packing-in-square-64", "group": "square-packing", "bound": "lower", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-64-lower-8.yml" }, { "id": "square-packing-in-square-64-upper-8", "constant": "square-packing-in-square-64", "group": "square-packing", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-64-upper-8.yml" }, { "id": "square-packing-in-square-65-lower-sqrt65", "constant": "square-packing-in-square-65", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{65}", "decimal_approx": 8.062258, "alt_display": "\u22488.062258" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{71}{13}", "decimal_approx": 8.289966, "alt_display": "\u22488.289966" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-65-lower-sqrt65.yml" }, { "id": "square-packing-in-square-65-upper-9", "constant": "square-packing-in-square-65", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5+\\frac{5}{\\sqrt{2}}", "decimal_approx": 8.535534, "alt_display": "\u22488.535534" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-65-upper-9.yml" }, { "id": "square-packing-in-square-66-lower-sqrt66", "constant": "square-packing-in-square-66", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{66}", "decimal_approx": 8.124038, "alt_display": "\u22488.124038" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{71}{13}", "decimal_approx": 8.289966, "alt_display": "\u22488.289966" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-66-lower-sqrt66.yml" }, { "id": "square-packing-in-square-66-upper-9", "constant": "square-packing-in-square-66", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3+4\\sqrt{2}", "decimal_approx": 8.656854, "alt_display": "\u22488.656854" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-66-upper-9.yml" }, { "id": "square-packing-in-square-67-lower-sqrt67", "constant": "square-packing-in-square-67", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{67}", "decimal_approx": 8.185353, "alt_display": "\u22488.185353" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{71}{13}", "decimal_approx": 8.289966, "alt_display": "\u22488.289966" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-67-lower-sqrt67.yml" }, { "id": "square-packing-in-square-67-upper-9", "constant": "square-packing-in-square-67", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "8+\\frac{1}{\\sqrt{2}}", "decimal_approx": 8.707107, "alt_display": "\u22488.707107" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-67-upper-9.yml" }, { "id": "square-packing-in-square-68-lower-sqrt68", "constant": "square-packing-in-square-68", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{68}", "decimal_approx": 8.246211, "alt_display": "\u22488.246211" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "2\\sqrt{2}+\\frac{71}{13}", "decimal_approx": 8.289966, "alt_display": "\u22488.289966" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-68-lower-sqrt68.yml" }, { "id": "square-packing-in-square-68-upper-9", "constant": "square-packing-in-square-68", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}8.7988", "decimal_approx": 8.7988, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-68-upper-9.yml" }, { "id": "square-packing-in-square-69-lower-sqrt69", "constant": "square-packing-in-square-69", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{69}", "decimal_approx": 8.306624, "alt_display": "\u22488.306624" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-69-lower-sqrt69.yml" }, { "id": "square-packing-in-square-69-upper-9", "constant": "square-packing-in-square-69", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}8.8272", "decimal_approx": 8.8272, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-69-upper-9.yml" }, { "id": "square-packing-in-square-7-lower-sqrt7", "constant": "square-packing-in-square-7", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{7}", "decimal_approx": 2.645751, "alt_display": "\u22482.645751" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-7-lower-sqrt7.yml" }, { "id": "square-packing-in-square-7-upper-3", "constant": "square-packing-in-square-7", "group": "square-packing", "bound": "upper", "value": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-7-upper-3.yml" }, { "id": "square-packing-in-square-70-lower-sqrt70", "constant": "square-packing-in-square-70", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{70}", "decimal_approx": 8.3666, "alt_display": "\u22488.3666" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-70-lower-sqrt70.yml" }, { "id": "square-packing-in-square-70-upper-9", "constant": "square-packing-in-square-70", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}8.8817", "decimal_approx": 8.8817, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-70-upper-9.yml" }, { "id": "square-packing-in-square-71-lower-sqrt71", "constant": "square-packing-in-square-71", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{71}", "decimal_approx": 8.42615, "alt_display": "\u22488.42615" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-71-lower-sqrt71.yml" }, { "id": "square-packing-in-square-71-upper-9", "constant": "square-packing-in-square-71", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}8.9441", "decimal_approx": 8.9441, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-71-upper-9.yml" }, { "id": "square-packing-in-square-72-lower-sqrt72", "constant": "square-packing-in-square-72", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{72}", "decimal_approx": 8.485281, "alt_display": "\u22488.485281" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-72-lower-sqrt72.yml" }, { "id": "square-packing-in-square-72-upper-9", "constant": "square-packing-in-square-72", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-72-upper-9.yml" }, { "id": "square-packing-in-square-73-lower-sqrt73", "constant": "square-packing-in-square-73", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{73}", "decimal_approx": 8.544004, "alt_display": "\u22488.544004" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-73-lower-sqrt73.yml" }, { "id": "square-packing-in-square-73-upper-9", "constant": "square-packing-in-square-73", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-73-upper-9.yml" }, { "id": "square-packing-in-square-74-lower-sqrt74", "constant": "square-packing-in-square-74", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{74}", "decimal_approx": 8.602325, "alt_display": "\u22488.602325" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-74-lower-sqrt74.yml" }, { "id": "square-packing-in-square-74-upper-9", "constant": "square-packing-in-square-74", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-74-upper-9.yml" }, { "id": "square-packing-in-square-75-lower-sqrt75", "constant": "square-packing-in-square-75", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{75}", "decimal_approx": 8.660254, "alt_display": "\u22488.660254" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-75-lower-sqrt75.yml" }, { "id": "square-packing-in-square-75-upper-9", "constant": "square-packing-in-square-75", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-75-upper-9.yml" }, { "id": "square-packing-in-square-76-lower-sqrt76", "constant": "square-packing-in-square-76", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{76}", "decimal_approx": 8.717798, "alt_display": "\u22488.717798" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-76-lower-sqrt76.yml" }, { "id": "square-packing-in-square-76-upper-9", "constant": "square-packing-in-square-76", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-76-upper-9.yml" }, { "id": "square-packing-in-square-77-lower-sqrt77", "constant": "square-packing-in-square-77", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{77}", "decimal_approx": 8.774964, "alt_display": "\u22488.774964" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-77-lower-sqrt77.yml" }, { "id": "square-packing-in-square-77-upper-9", "constant": "square-packing-in-square-77", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-77-upper-9.yml" }, { "id": "square-packing-in-square-78-lower-sqrt78", "constant": "square-packing-in-square-78", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{78}", "decimal_approx": 8.831761, "alt_display": "\u22488.831761" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-78-lower-sqrt78.yml" }, { "id": "square-packing-in-square-78-upper-9", "constant": "square-packing-in-square-78", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-78-upper-9.yml" }, { "id": "square-packing-in-square-79-lower-sqrt79", "constant": "square-packing-in-square-79", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{79}", "decimal_approx": 8.888194, "alt_display": "\u22488.888194" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-79-lower-sqrt79.yml" }, { "id": "square-packing-in-square-79-upper-9", "constant": "square-packing-in-square-79", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-79-upper-9.yml" }, { "id": "square-packing-in-square-8-lower-sqrt8", "constant": "square-packing-in-square-8", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{8}", "decimal_approx": 2.828427, "alt_display": "\u22482.828427" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-8-lower-sqrt8.yml" }, { "id": "square-packing-in-square-8-upper-3", "constant": "square-packing-in-square-8", "group": "square-packing", "bound": "upper", "value": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-8-upper-3.yml" }, { "id": "square-packing-in-square-80-lower-sqrt80", "constant": "square-packing-in-square-80", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{80}", "decimal_approx": 8.944272, "alt_display": "\u22488.944272" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-80-lower-sqrt80.yml" }, { "id": "square-packing-in-square-80-upper-9", "constant": "square-packing-in-square-80", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-80-upper-9.yml" }, { "id": "square-packing-in-square-81-lower-9", "constant": "square-packing-in-square-81", "group": "square-packing", "bound": "lower", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-81-lower-9.yml" }, { "id": "square-packing-in-square-81-upper-9", "constant": "square-packing-in-square-81", "group": "square-packing", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-81-upper-9.yml" }, { "id": "square-packing-in-square-82-lower-sqrt82", "constant": "square-packing-in-square-82", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{82}", "decimal_approx": 9.055385, "alt_display": "\u22489.055385" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}9.2667", "decimal_approx": 9.2667, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-82-lower-sqrt82.yml" }, { "id": "square-packing-in-square-82-upper-10", "constant": "square-packing-in-square-82", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "6+\\frac{5}{\\sqrt{2}}", "decimal_approx": 9.535534, "alt_display": "\u22489.535534" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-82-upper-10.yml" }, { "id": "square-packing-in-square-83-lower-sqrt83", "constant": "square-packing-in-square-83", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{83}", "decimal_approx": 9.110434, "alt_display": "\u22489.110434" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}9.2667", "decimal_approx": 9.2667, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-83-lower-sqrt83.yml" }, { "id": "square-packing-in-square-83-upper-10", "constant": "square-packing-in-square-83", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}9.6348", "decimal_approx": 9.6348, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-83-upper-10.yml" }, { "id": "square-packing-in-square-84-lower-sqrt84", "constant": "square-packing-in-square-84", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{84}", "decimal_approx": 9.165151, "alt_display": "\u22489.165151" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}9.2667", "decimal_approx": 9.2667, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-84-lower-sqrt84.yml" }, { "id": "square-packing-in-square-84-upper-10", "constant": "square-packing-in-square-84", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "9+\\frac{1}{\\sqrt{2}}", "decimal_approx": 9.707107, "alt_display": "\u22489.707107" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-84-upper-10.yml" }, { "id": "square-packing-in-square-85-lower-sqrt85", "constant": "square-packing-in-square-85", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{85}", "decimal_approx": 9.219544, "alt_display": "\u22489.219544" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}9.2667", "decimal_approx": 9.2667, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-85-lower-sqrt85.yml" }, { "id": "square-packing-in-square-85-upper-10", "constant": "square-packing-in-square-85", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "\\frac{11}{2}+3\\sqrt{2}", "decimal_approx": 9.742641, "alt_display": "\u22489.742641" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-85-upper-10.yml" }, { "id": "square-packing-in-square-86-lower-sqrt86", "constant": "square-packing-in-square-86", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{86}", "decimal_approx": 9.273618, "alt_display": "\u22489.273618" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-86-lower-sqrt86.yml" }, { "id": "square-packing-in-square-86-upper-10", "constant": "square-packing-in-square-86", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "\\frac{17+\\sqrt{7}}{2}", "decimal_approx": 9.822876, "alt_display": "\u22489.822876" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-86-upper-10.yml" }, { "id": "square-packing-in-square-87-lower-sqrt87", "constant": "square-packing-in-square-87", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{87}", "decimal_approx": 9.327379, "alt_display": "\u22489.327379" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-87-lower-sqrt87.yml" }, { "id": "square-packing-in-square-87-upper-10", "constant": "square-packing-in-square-87", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}9.8388", "decimal_approx": 9.8388, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-87-upper-10.yml" }, { "id": "square-packing-in-square-88-lower-sqrt88", "constant": "square-packing-in-square-88", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{88}", "decimal_approx": 9.380832, "alt_display": "\u22489.380832" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-88-lower-sqrt88.yml" }, { "id": "square-packing-in-square-88-upper-10", "constant": "square-packing-in-square-88", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "{\\approx}9.8882", "decimal_approx": 9.8882, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-88-upper-10.yml" }, { "id": "square-packing-in-square-89-lower-sqrt89", "constant": "square-packing-in-square-89", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{89}", "decimal_approx": 9.433981, "alt_display": "\u22489.433981" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-89-lower-sqrt89.yml" }, { "id": "square-packing-in-square-89-upper-10", "constant": "square-packing-in-square-89", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "5+\\frac{7}{\\sqrt{2}}", "decimal_approx": 9.949747, "alt_display": "\u22489.949747" }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-89-upper-10.yml" }, { "id": "square-packing-in-square-9-lower-3", "constant": "square-packing-in-square-9", "group": "square-packing", "bound": "lower", "value": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-9-lower-3.yml" }, { "id": "square-packing-in-square-9-upper-3", "constant": "square-packing-in-square-9", "group": "square-packing", "bound": "upper", "value": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-9-upper-3.yml" }, { "id": "square-packing-in-square-90-lower-sqrt90", "constant": "square-packing-in-square-90", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{90}", "decimal_approx": 9.486833, "alt_display": "\u22489.486833" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-90-lower-sqrt90.yml" }, { "id": "square-packing-in-square-90-upper-10", "constant": "square-packing-in-square-90", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-90-upper-10.yml" }, { "id": "square-packing-in-square-91-lower-sqrt91", "constant": "square-packing-in-square-91", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{91}", "decimal_approx": 9.539392, "alt_display": "\u22489.539392" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-91-lower-sqrt91.yml" }, { "id": "square-packing-in-square-91-upper-10", "constant": "square-packing-in-square-91", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-91-upper-10.yml" }, { "id": "square-packing-in-square-92-lower-sqrt92", "constant": "square-packing-in-square-92", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{92}", "decimal_approx": 9.591663, "alt_display": "\u22489.591663" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-92-lower-sqrt92.yml" }, { "id": "square-packing-in-square-92-upper-10", "constant": "square-packing-in-square-92", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-92-upper-10.yml" }, { "id": "square-packing-in-square-93-lower-sqrt93", "constant": "square-packing-in-square-93", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{93}", "decimal_approx": 9.643651, "alt_display": "\u22489.643651" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-93-lower-sqrt93.yml" }, { "id": "square-packing-in-square-93-upper-10", "constant": "square-packing-in-square-93", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-93-upper-10.yml" }, { "id": "square-packing-in-square-94-lower-sqrt94", "constant": "square-packing-in-square-94", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{94}", "decimal_approx": 9.69536, "alt_display": "\u22489.69536" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-94-lower-sqrt94.yml" }, { "id": "square-packing-in-square-94-upper-10", "constant": "square-packing-in-square-94", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-94-upper-10.yml" }, { "id": "square-packing-in-square-95-lower-sqrt95", "constant": "square-packing-in-square-95", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{95}", "decimal_approx": 9.746794, "alt_display": "\u22489.746794" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-95-lower-sqrt95.yml" }, { "id": "square-packing-in-square-95-upper-10", "constant": "square-packing-in-square-95", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-95-upper-10.yml" }, { "id": "square-packing-in-square-96-lower-sqrt96", "constant": "square-packing-in-square-96", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{96}", "decimal_approx": 9.797959, "alt_display": "\u22489.797959" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-96-lower-sqrt96.yml" }, { "id": "square-packing-in-square-96-upper-10", "constant": "square-packing-in-square-96", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-96-upper-10.yml" }, { "id": "square-packing-in-square-97-lower-sqrt97", "constant": "square-packing-in-square-97", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{97}", "decimal_approx": 9.848858, "alt_display": "\u22489.848858" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/square-packing/square-packing-in-square-97-lower-sqrt97.yml" }, { "id": "square-packing-in-square-97-upper-10", "constant": "square-packing-in-square-97", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-97-upper-10.yml" }, { "id": "square-packing-in-square-98-lower-sqrt98", "constant": "square-packing-in-square-98", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{98}", "decimal_approx": 9.899495, "alt_display": "\u22489.899495" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-98-lower-sqrt98.yml" }, { "id": "square-packing-in-square-98-upper-10", "constant": "square-packing-in-square-98", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-98-upper-10.yml" }, { "id": "square-packing-in-square-99-lower-sqrt99", "constant": "square-packing-in-square-99", "group": "square-packing", "bound": "lower", "value": { "latex": "\\sqrt{99}", "decimal_approx": 9.949874, "alt_display": "\u22489.949874" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/square-packing/square-packing-in-square-99-lower-sqrt99.yml" }, { "id": "square-packing-in-square-99-upper-10", "constant": "square-packing-in-square-99", "group": "square-packing", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-30", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/square-packing/square-packing-in-square-99-upper-10.yml" }, { "id": "cage-10-10-lower-14762", "constant": "cage-10-10", "group": "cage", "bound": "lower", "value": { "latex": "14762", "decimal_approx": 14762, "alt_display": "14,762" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-10-lower-14762.yml" }, { "id": "cage-10-11-lower-73811", "constant": "cage-10-11", "group": "cage", "bound": "lower", "value": { "latex": "73811", "decimal_approx": 73811, "alt_display": "73,811" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-11-lower-73811.yml" }, { "id": "cage-10-12-lower-132860", "constant": "cage-10-12", "group": "cage", "bound": "lower", "value": { "latex": "132860", "decimal_approx": 132860, "alt_display": "132,860" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-12-lower-132860.yml" }, { "id": "cage-10-13-lower-664301", "constant": "cage-10-13", "group": "cage", "bound": "lower", "value": { "latex": "664301", "decimal_approx": 664301, "alt_display": "664,301" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-13-lower-664301.yml" }, { "id": "cage-10-14-lower-1195742", "constant": "cage-10-14", "group": "cage", "bound": "lower", "value": { "latex": "1195742", "decimal_approx": 1195742, "alt_display": "1,195,742" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-14-lower-1195742.yml" }, { "id": "cage-10-15-lower-5978711", "constant": "cage-10-15", "group": "cage", "bound": "lower", "value": { "latex": "5978711", "decimal_approx": 5978711, "alt_display": "5,978,711" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-15-lower-5978711.yml" }, { "id": "cage-10-16-lower-10761680", "constant": "cage-10-16", "group": "cage", "bound": "lower", "value": { "latex": "10761680", "decimal_approx": 10761680, "alt_display": "10,761,680" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-16-lower-10761680.yml" }, { "id": "cage-10-3-lower-11", "constant": "cage-10-3", "group": "cage", "bound": "lower", "value": { "latex": "11", "decimal_approx": 11, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-3-lower-11.yml" }, { "id": "cage-10-4-lower-20", "constant": "cage-10-4", "group": "cage", "bound": "lower", "value": { "latex": "20", "decimal_approx": 20, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-4-lower-20.yml" }, { "id": "cage-10-5-lower-101", "constant": "cage-10-5", "group": "cage", "bound": "lower", "value": { "latex": "101", "decimal_approx": 101, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "103", "decimal_approx": 103, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-10-5-lower-101.yml" }, { "id": "cage-10-6-lower-182", "constant": "cage-10-6", "group": "cage", "bound": "lower", "value": { "latex": "182", "decimal_approx": 182, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "182", "decimal_approx": 182, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-10-6-lower-182.yml" }, { "id": "cage-10-7-lower-911", "constant": "cage-10-7", "group": "cage", "bound": "lower", "value": { "latex": "911", "decimal_approx": 911, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-7-lower-911.yml" }, { "id": "cage-10-8-lower-1640", "constant": "cage-10-8", "group": "cage", "bound": "lower", "value": { "latex": "1640", "decimal_approx": 1640, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-8-lower-1640.yml" }, { "id": "cage-10-9-lower-8201", "constant": "cage-10-9", "group": "cage", "bound": "lower", "value": { "latex": "8201", "decimal_approx": 8201, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-9-lower-8201.yml" }, { "id": "cage-11-10-lower-22222", "constant": "cage-11-10", "group": "cage", "bound": "lower", "value": { "latex": "22222", "decimal_approx": 22222, "alt_display": "22,222" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-10-lower-22222.yml" }, { "id": "cage-11-11-lower-122222", "constant": "cage-11-11", "group": "cage", "bound": "lower", "value": { "latex": "122222", "decimal_approx": 122222, "alt_display": "122,222" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-11-lower-122222.yml" }, { "id": "cage-11-12-lower-222222", "constant": "cage-11-12", "group": "cage", "bound": "lower", "value": { "latex": "222222", "decimal_approx": 222222, "alt_display": "222,222" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-12-lower-222222.yml" }, { "id": "cage-11-13-lower-1222222", "constant": "cage-11-13", "group": "cage", "bound": "lower", "value": { "latex": "1222222", "decimal_approx": 1222222, "alt_display": "1,222,222" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-13-lower-1222222.yml" }, { "id": "cage-11-14-lower-2222222", "constant": "cage-11-14", "group": "cage", "bound": "lower", "value": { "latex": "2222222", "decimal_approx": 2222222, "alt_display": "2,222,222" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-14-lower-2222222.yml" }, { "id": "cage-11-15-lower-12222222", "constant": "cage-11-15", "group": "cage", "bound": "lower", "value": { "latex": "12222222", "decimal_approx": 12222222, "alt_display": "12,222,222" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-15-lower-12222222.yml" }, { "id": "cage-11-16-lower-22222222", "constant": "cage-11-16", "group": "cage", "bound": "lower", "value": { "latex": "22222222", "decimal_approx": 22222222, "alt_display": "22,222,222" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-16-lower-22222222.yml" }, { "id": "cage-11-3-lower-12", "constant": "cage-11-3", "group": "cage", "bound": "lower", "value": { "latex": "12", "decimal_approx": 12, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-3-lower-12.yml" }, { "id": "cage-11-4-lower-22", "constant": "cage-11-4", "group": "cage", "bound": "lower", "value": { "latex": "22", "decimal_approx": 22, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-4-lower-22.yml" }, { "id": "cage-11-5-lower-122", "constant": "cage-11-5", "group": "cage", "bound": "lower", "value": { "latex": "122", "decimal_approx": 122, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "124", "decimal_approx": 124, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-11-5-lower-122.yml" }, { "id": "cage-11-6-lower-222", "constant": "cage-11-6", "group": "cage", "bound": "lower", "value": { "latex": "222", "decimal_approx": 222, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "224", "decimal_approx": 224, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-11-6-lower-222.yml" }, { "id": "cage-11-7-lower-1222", "constant": "cage-11-7", "group": "cage", "bound": "lower", "value": { "latex": "1222", "decimal_approx": 1222, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-7-lower-1222.yml" }, { "id": "cage-11-8-lower-2222", "constant": "cage-11-8", "group": "cage", "bound": "lower", "value": { "latex": "2222", "decimal_approx": 2222, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-8-lower-2222.yml" }, { "id": "cage-11-9-lower-12222", "constant": "cage-11-9", "group": "cage", "bound": "lower", "value": { "latex": "12222", "decimal_approx": 12222, "alt_display": "12,222" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-9-lower-12222.yml" }, { "id": "cage-12-10-lower-32210", "constant": "cage-12-10", "group": "cage", "bound": "lower", "value": { "latex": "32210", "decimal_approx": 32210, "alt_display": "32,210" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-10-lower-32210.yml" }, { "id": "cage-12-11-lower-193261", "constant": "cage-12-11", "group": "cage", "bound": "lower", "value": { "latex": "193261", "decimal_approx": 193261, "alt_display": "193,261" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-11-lower-193261.yml" }, { "id": "cage-12-12-lower-354312", "constant": "cage-12-12", "group": "cage", "bound": "lower", "value": { "latex": "354312", "decimal_approx": 354312, "alt_display": "354,312" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-12-lower-354312.yml" }, { "id": "cage-12-13-lower-2125873", "constant": "cage-12-13", "group": "cage", "bound": "lower", "value": { "latex": "2125873", "decimal_approx": 2125873, "alt_display": "2,125,873" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-13-lower-2125873.yml" }, { "id": "cage-12-14-lower-3897434", "constant": "cage-12-14", "group": "cage", "bound": "lower", "value": { "latex": "3897434", "decimal_approx": 3897434, "alt_display": "3,897,434" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-14-lower-3897434.yml" }, { "id": "cage-12-15-lower-23384605", "constant": "cage-12-15", "group": "cage", "bound": "lower", "value": { "latex": "23384605", "decimal_approx": 23384605, "alt_display": "23,384,605" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-15-lower-23384605.yml" }, { "id": "cage-12-16-lower-42871776", "constant": "cage-12-16", "group": "cage", "bound": "lower", "value": { "latex": "42871776", "decimal_approx": 42871776, "alt_display": "42,871,776" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-16-lower-42871776.yml" }, { "id": "cage-12-3-lower-13", "constant": "cage-12-3", "group": "cage", "bound": "lower", "value": { "latex": "13", "decimal_approx": 13, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-3-lower-13.yml" }, { "id": "cage-12-4-lower-24", "constant": "cage-12-4", "group": "cage", "bound": "lower", "value": { "latex": "24", "decimal_approx": 24, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-4-lower-24.yml" }, { "id": "cage-12-5-lower-145", "constant": "cage-12-5", "group": "cage", "bound": "lower", "value": { "latex": "145", "decimal_approx": 145, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "147", "decimal_approx": 147, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-12-5-lower-145.yml" }, { "id": "cage-12-6-lower-266", "constant": "cage-12-6", "group": "cage", "bound": "lower", "value": { "latex": "266", "decimal_approx": 266, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "266", "decimal_approx": 266, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-12-6-lower-266.yml" }, { "id": "cage-12-7-lower-1597", "constant": "cage-12-7", "group": "cage", "bound": "lower", "value": { "latex": "1597", "decimal_approx": 1597, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-7-lower-1597.yml" }, { "id": "cage-12-8-lower-2928", "constant": "cage-12-8", "group": "cage", "bound": "lower", "value": { "latex": "2928", "decimal_approx": 2928, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-8-lower-2928.yml" }, { "id": "cage-12-9-lower-17569", "constant": "cage-12-9", "group": "cage", "bound": "lower", "value": { "latex": "17569", "decimal_approx": 17569, "alt_display": "17,569" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-9-lower-17569.yml" }, { "id": "cage-13-10-lower-45242", "constant": "cage-13-10", "group": "cage", "bound": "lower", "value": { "latex": "45242", "decimal_approx": 45242, "alt_display": "45,242" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-10-lower-45242.yml" }, { "id": "cage-13-11-lower-294074", "constant": "cage-13-11", "group": "cage", "bound": "lower", "value": { "latex": "294074", "decimal_approx": 294074, "alt_display": "294,074" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-11-lower-294074.yml" }, { "id": "cage-13-12-lower-542906", "constant": "cage-13-12", "group": "cage", "bound": "lower", "value": { "latex": "542906", "decimal_approx": 542906, "alt_display": "542,906" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-12-lower-542906.yml" }, { "id": "cage-13-13-lower-3528890", "constant": "cage-13-13", "group": "cage", "bound": "lower", "value": { "latex": "3528890", "decimal_approx": 3528890, "alt_display": "3,528,890" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-13-lower-3528890.yml" }, { "id": "cage-13-14-lower-6514874", "constant": "cage-13-14", "group": "cage", "bound": "lower", "value": { "latex": "6514874", "decimal_approx": 6514874, "alt_display": "6,514,874" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-14-lower-6514874.yml" }, { "id": "cage-13-15-lower-42346682", "constant": "cage-13-15", "group": "cage", "bound": "lower", "value": { "latex": "42346682", "decimal_approx": 42346682, "alt_display": "42,346,682" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-15-lower-42346682.yml" }, { "id": "cage-13-16-lower-78178490", "constant": "cage-13-16", "group": "cage", "bound": "lower", "value": { "latex": "78178490", "decimal_approx": 78178490, "alt_display": "78,178,490" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-16-lower-78178490.yml" }, { "id": "cage-13-3-lower-14", "constant": "cage-13-3", "group": "cage", "bound": "lower", "value": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-3-lower-14.yml" }, { "id": "cage-13-4-lower-26", "constant": "cage-13-4", "group": "cage", "bound": "lower", "value": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-4-lower-26.yml" }, { "id": "cage-13-5-lower-170", "constant": "cage-13-5", "group": "cage", "bound": "lower", "value": { "latex": "170", "decimal_approx": 170, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "174", "decimal_approx": 174, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-13-5-lower-170.yml" }, { "id": "cage-13-6-lower-314", "constant": "cage-13-6", "group": "cage", "bound": "lower", "value": { "latex": "314", "decimal_approx": 314, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "314", "decimal_approx": 314, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-13-6-lower-314.yml" }, { "id": "cage-13-7-lower-2042", "constant": "cage-13-7", "group": "cage", "bound": "lower", "value": { "latex": "2042", "decimal_approx": 2042, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-7-lower-2042.yml" }, { "id": "cage-13-8-lower-3770", "constant": "cage-13-8", "group": "cage", "bound": "lower", "value": { "latex": "3770", "decimal_approx": 3770, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-8-lower-3770.yml" }, { "id": "cage-13-9-lower-24506", "constant": "cage-13-9", "group": "cage", "bound": "lower", "value": { "latex": "24506", "decimal_approx": 24506, "alt_display": "24,506" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-9-lower-24506.yml" }, { "id": "cage-14-10-lower-61882", "constant": "cage-14-10", "group": "cage", "bound": "lower", "value": { "latex": "61882", "decimal_approx": 61882, "alt_display": "61,882" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-10-lower-61882.yml" }, { "id": "cage-14-11-lower-433175", "constant": "cage-14-11", "group": "cage", "bound": "lower", "value": { "latex": "433175", "decimal_approx": 433175, "alt_display": "433,175" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-11-lower-433175.yml" }, { "id": "cage-14-12-lower-804468", "constant": "cage-14-12", "group": "cage", "bound": "lower", "value": { "latex": "804468", "decimal_approx": 804468, "alt_display": "804,468" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-12-lower-804468.yml" }, { "id": "cage-14-13-lower-5631277", "constant": "cage-14-13", "group": "cage", "bound": "lower", "value": { "latex": "5631277", "decimal_approx": 5631277, "alt_display": "5,631,277" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-13-lower-5631277.yml" }, { "id": "cage-14-14-lower-10458086", "constant": "cage-14-14", "group": "cage", "bound": "lower", "value": { "latex": "10458086", "decimal_approx": 10458086, "alt_display": "10,458,086" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-14-lower-10458086.yml" }, { "id": "cage-14-15-lower-73206603", "constant": "cage-14-15", "group": "cage", "bound": "lower", "value": { "latex": "73206603", "decimal_approx": 73206603, "alt_display": "73,206,603" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-15-lower-73206603.yml" }, { "id": "cage-14-16-lower-135955120", "constant": "cage-14-16", "group": "cage", "bound": "lower", "value": { "latex": "135955120", "decimal_approx": 135955120, "alt_display": "135,955,120" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-16-lower-135955120.yml" }, { "id": "cage-14-3-lower-15", "constant": "cage-14-3", "group": "cage", "bound": "lower", "value": { "latex": "15", "decimal_approx": 15, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-3-lower-15.yml" }, { "id": "cage-14-4-lower-28", "constant": "cage-14-4", "group": "cage", "bound": "lower", "value": { "latex": "28", "decimal_approx": 28, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-4-lower-28.yml" }, { "id": "cage-14-5-lower-197", "constant": "cage-14-5", "group": "cage", "bound": "lower", "value": { "latex": "197", "decimal_approx": 197, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "199", "decimal_approx": 199, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-14-5-lower-197.yml" }, { "id": "cage-14-6-lower-366", "constant": "cage-14-6", "group": "cage", "bound": "lower", "value": { "latex": "366", "decimal_approx": 366, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "366", "decimal_approx": 366, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-14-6-lower-366.yml" }, { "id": "cage-14-7-lower-2563", "constant": "cage-14-7", "group": "cage", "bound": "lower", "value": { "latex": "2563", "decimal_approx": 2563, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-7-lower-2563.yml" }, { "id": "cage-14-8-lower-4760", "constant": "cage-14-8", "group": "cage", "bound": "lower", "value": { "latex": "4760", "decimal_approx": 4760, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-8-lower-4760.yml" }, { "id": "cage-14-9-lower-33321", "constant": "cage-14-9", "group": "cage", "bound": "lower", "value": { "latex": "33321", "decimal_approx": 33321, "alt_display": "33,321" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-9-lower-33321.yml" }, { "id": "cage-15-10-lower-82742", "constant": "cage-15-10", "group": "cage", "bound": "lower", "value": { "latex": "82742", "decimal_approx": 82742, "alt_display": "82,742" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-10-lower-82742.yml" }, { "id": "cage-15-11-lower-620566", "constant": "cage-15-11", "group": "cage", "bound": "lower", "value": { "latex": "620566", "decimal_approx": 620566, "alt_display": "620,566" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-11-lower-620566.yml" }, { "id": "cage-15-12-lower-1158390", "constant": "cage-15-12", "group": "cage", "bound": "lower", "value": { "latex": "1158390", "decimal_approx": 1158390, "alt_display": "1,158,390" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-12-lower-1158390.yml" }, { "id": "cage-15-13-lower-8687926", "constant": "cage-15-13", "group": "cage", "bound": "lower", "value": { "latex": "8687926", "decimal_approx": 8687926, "alt_display": "8,687,926" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-13-lower-8687926.yml" }, { "id": "cage-15-14-lower-16217462", "constant": "cage-15-14", "group": "cage", "bound": "lower", "value": { "latex": "16217462", "decimal_approx": 16217462, "alt_display": "16,217,462" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-14-lower-16217462.yml" }, { "id": "cage-15-15-lower-121630966", "constant": "cage-15-15", "group": "cage", "bound": "lower", "value": { "latex": "121630966", "decimal_approx": 121630966, "alt_display": "121,630,966" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-15-lower-121630966.yml" }, { "id": "cage-15-16-lower-227044470", "constant": "cage-15-16", "group": "cage", "bound": "lower", "value": { "latex": "227044470", "decimal_approx": 227044470, "alt_display": "227,044,470" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-16-lower-227044470.yml" }, { "id": "cage-15-3-lower-16", "constant": "cage-15-3", "group": "cage", "bound": "lower", "value": { "latex": "16", "decimal_approx": 16, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-3-lower-16.yml" }, { "id": "cage-15-4-lower-30", "constant": "cage-15-4", "group": "cage", "bound": "lower", "value": { "latex": "30", "decimal_approx": 30, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-4-lower-30.yml" }, { "id": "cage-15-5-lower-226", "constant": "cage-15-5", "group": "cage", "bound": "lower", "value": { "latex": "226", "decimal_approx": 226, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "230", "decimal_approx": 230, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-15-5-lower-226.yml" }, { "id": "cage-15-6-lower-422", "constant": "cage-15-6", "group": "cage", "bound": "lower", "value": { "latex": "422", "decimal_approx": 422, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "422", "decimal_approx": 422, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-15-6-lower-422.yml" }, { "id": "cage-15-7-lower-3166", "constant": "cage-15-7", "group": "cage", "bound": "lower", "value": { "latex": "3166", "decimal_approx": 3166, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-7-lower-3166.yml" }, { "id": "cage-15-8-lower-5910", "constant": "cage-15-8", "group": "cage", "bound": "lower", "value": { "latex": "5910", "decimal_approx": 5910, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-8-lower-5910.yml" }, { "id": "cage-15-9-lower-44326", "constant": "cage-15-9", "group": "cage", "bound": "lower", "value": { "latex": "44326", "decimal_approx": 44326, "alt_display": "44,326" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-9-lower-44326.yml" }, { "id": "cage-16-10-lower-108482", "constant": "cage-16-10", "group": "cage", "bound": "lower", "value": { "latex": "108482", "decimal_approx": 108482, "alt_display": "108,482" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-10-lower-108482.yml" }, { "id": "cage-16-11-lower-867857", "constant": "cage-16-11", "group": "cage", "bound": "lower", "value": { "latex": "867857", "decimal_approx": 867857, "alt_display": "867,857" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-11-lower-867857.yml" }, { "id": "cage-16-12-lower-1627232", "constant": "cage-16-12", "group": "cage", "bound": "lower", "value": { "latex": "1627232", "decimal_approx": 1627232, "alt_display": "1,627,232" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-12-lower-1627232.yml" }, { "id": "cage-16-13-lower-13017857", "constant": "cage-16-13", "group": "cage", "bound": "lower", "value": { "latex": "13017857", "decimal_approx": 13017857, "alt_display": "13,017,857" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-13-lower-13017857.yml" }, { "id": "cage-16-14-lower-24408482", "constant": "cage-16-14", "group": "cage", "bound": "lower", "value": { "latex": "24408482", "decimal_approx": 24408482, "alt_display": "24,408,482" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-14-lower-24408482.yml" }, { "id": "cage-16-15-lower-195267857", "constant": "cage-16-15", "group": "cage", "bound": "lower", "value": { "latex": "195267857", "decimal_approx": 195267857, "alt_display": "195,267,857" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-15-lower-195267857.yml" }, { "id": "cage-16-16-lower-366127232", "constant": "cage-16-16", "group": "cage", "bound": "lower", "value": { "latex": "366127232", "decimal_approx": 366127232, "alt_display": "366,127,232" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-16-lower-366127232.yml" }, { "id": "cage-16-3-lower-17", "constant": "cage-16-3", "group": "cage", "bound": "lower", "value": { "latex": "17", "decimal_approx": 17, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-3-lower-17.yml" }, { "id": "cage-16-4-lower-32", "constant": "cage-16-4", "group": "cage", "bound": "lower", "value": { "latex": "32", "decimal_approx": 32, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-4-lower-32.yml" }, { "id": "cage-16-5-lower-257", "constant": "cage-16-5", "group": "cage", "bound": "lower", "value": { "latex": "257", "decimal_approx": 257, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "259", "decimal_approx": 259, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-16-5-lower-257.yml" }, { "id": "cage-16-6-lower-482", "constant": "cage-16-6", "group": "cage", "bound": "lower", "value": { "latex": "482", "decimal_approx": 482, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "482", "decimal_approx": 482, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-16-6-lower-482.yml" }, { "id": "cage-16-7-lower-3857", "constant": "cage-16-7", "group": "cage", "bound": "lower", "value": { "latex": "3857", "decimal_approx": 3857, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-7-lower-3857.yml" }, { "id": "cage-16-8-lower-7232", "constant": "cage-16-8", "group": "cage", "bound": "lower", "value": { "latex": "7232", "decimal_approx": 7232, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-8-lower-7232.yml" }, { "id": "cage-16-9-lower-57857", "constant": "cage-16-9", "group": "cage", "bound": "lower", "value": { "latex": "57857", "decimal_approx": 57857, "alt_display": "57,857" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-9-lower-57857.yml" }, { "id": "cage-17-10-lower-139810", "constant": "cage-17-10", "group": "cage", "bound": "lower", "value": { "latex": "139810", "decimal_approx": 139810, "alt_display": "139,810" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-10-lower-139810.yml" }, { "id": "cage-17-11-lower-1188386", "constant": "cage-17-11", "group": "cage", "bound": "lower", "value": { "latex": "1188386", "decimal_approx": 1188386, "alt_display": "1,188,386" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-11-lower-1188386.yml" }, { "id": "cage-17-12-lower-2236962", "constant": "cage-17-12", "group": "cage", "bound": "lower", "value": { "latex": "2236962", "decimal_approx": 2236962, "alt_display": "2,236,962" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-12-lower-2236962.yml" }, { "id": "cage-17-13-lower-19014178", "constant": "cage-17-13", "group": "cage", "bound": "lower", "value": { "latex": "19014178", "decimal_approx": 19014178, "alt_display": "19,014,178" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-13-lower-19014178.yml" }, { "id": "cage-17-14-lower-35791394", "constant": "cage-17-14", "group": "cage", "bound": "lower", "value": { "latex": "35791394", "decimal_approx": 35791394, "alt_display": "35,791,394" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-14-lower-35791394.yml" }, { "id": "cage-17-15-lower-304226850", "constant": "cage-17-15", "group": "cage", "bound": "lower", "value": { "latex": "304226850", "decimal_approx": 304226850, "alt_display": "304,226,850" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-15-lower-304226850.yml" }, { "id": "cage-17-16-lower-572662306", "constant": "cage-17-16", "group": "cage", "bound": "lower", "value": { "latex": "572662306", "decimal_approx": 572662306, "alt_display": "572,662,306" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-16-lower-572662306.yml" }, { "id": "cage-17-3-lower-18", "constant": "cage-17-3", "group": "cage", "bound": "lower", "value": { "latex": "18", "decimal_approx": 18, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-3-lower-18.yml" }, { "id": "cage-17-4-lower-34", "constant": "cage-17-4", "group": "cage", "bound": "lower", "value": { "latex": "34", "decimal_approx": 34, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-4-lower-34.yml" }, { "id": "cage-17-5-lower-290", "constant": "cage-17-5", "group": "cage", "bound": "lower", "value": { "latex": "290", "decimal_approx": 290, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "294", "decimal_approx": 294, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-17-5-lower-290.yml" }, { "id": "cage-17-6-lower-546", "constant": "cage-17-6", "group": "cage", "bound": "lower", "value": { "latex": "546", "decimal_approx": 546, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "546", "decimal_approx": 546, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-17-6-lower-546.yml" }, { "id": "cage-17-7-lower-4642", "constant": "cage-17-7", "group": "cage", "bound": "lower", "value": { "latex": "4642", "decimal_approx": 4642, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-7-lower-4642.yml" }, { "id": "cage-17-8-lower-8738", "constant": "cage-17-8", "group": "cage", "bound": "lower", "value": { "latex": "8738", "decimal_approx": 8738, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-8-lower-8738.yml" }, { "id": "cage-17-9-lower-74274", "constant": "cage-17-9", "group": "cage", "bound": "lower", "value": { "latex": "74274", "decimal_approx": 74274, "alt_display": "74,274" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-9-lower-74274.yml" }, { "id": "cage-18-10-lower-177482", "constant": "cage-18-10", "group": "cage", "bound": "lower", "value": { "latex": "177482", "decimal_approx": 177482, "alt_display": "177,482" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-10-lower-177482.yml" }, { "id": "cage-18-11-lower-1597339", "constant": "cage-18-11", "group": "cage", "bound": "lower", "value": { "latex": "1597339", "decimal_approx": 1597339, "alt_display": "1,597,339" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-11-lower-1597339.yml" }, { "id": "cage-18-12-lower-3017196", "constant": "cage-18-12", "group": "cage", "bound": "lower", "value": { "latex": "3017196", "decimal_approx": 3017196, "alt_display": "3,017,196" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-12-lower-3017196.yml" }, { "id": "cage-18-13-lower-27154765", "constant": "cage-18-13", "group": "cage", "bound": "lower", "value": { "latex": "27154765", "decimal_approx": 27154765, "alt_display": "27,154,765" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-13-lower-27154765.yml" }, { "id": "cage-18-14-lower-51292334", "constant": "cage-18-14", "group": "cage", "bound": "lower", "value": { "latex": "51292334", "decimal_approx": 51292334, "alt_display": "51,292,334" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-14-lower-51292334.yml" }, { "id": "cage-18-15-lower-461631007", "constant": "cage-18-15", "group": "cage", "bound": "lower", "value": { "latex": "461631007", "decimal_approx": 461631007, "alt_display": "461,631,007" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-15-lower-461631007.yml" }, { "id": "cage-18-16-lower-871969680", "constant": "cage-18-16", "group": "cage", "bound": "lower", "value": { "latex": "871969680", "decimal_approx": 871969680, "alt_display": "871,969,680" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-16-lower-871969680.yml" }, { "id": "cage-18-3-lower-19", "constant": "cage-18-3", "group": "cage", "bound": "lower", "value": { "latex": "19", "decimal_approx": 19, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-3-lower-19.yml" }, { "id": "cage-18-4-lower-36", "constant": "cage-18-4", "group": "cage", "bound": "lower", "value": { "latex": "36", "decimal_approx": 36, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-4-lower-36.yml" }, { "id": "cage-18-5-lower-325", "constant": "cage-18-5", "group": "cage", "bound": "lower", "value": { "latex": "325", "decimal_approx": 325, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "327", "decimal_approx": 327, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-18-5-lower-325.yml" }, { "id": "cage-18-6-lower-614", "constant": "cage-18-6", "group": "cage", "bound": "lower", "value": { "latex": "614", "decimal_approx": 614, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "614", "decimal_approx": 614, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-18-6-lower-614.yml" }, { "id": "cage-18-7-lower-5527", "constant": "cage-18-7", "group": "cage", "bound": "lower", "value": { "latex": "5527", "decimal_approx": 5527, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-7-lower-5527.yml" }, { "id": "cage-18-8-lower-10440", "constant": "cage-18-8", "group": "cage", "bound": "lower", "value": { "latex": "10440", "decimal_approx": 10440, "alt_display": "10,440" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-8-lower-10440.yml" }, { "id": "cage-18-9-lower-93961", "constant": "cage-18-9", "group": "cage", "bound": "lower", "value": { "latex": "93961", "decimal_approx": 93961, "alt_display": "93,961" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-9-lower-93961.yml" }, { "id": "cage-19-10-lower-222302", "constant": "cage-19-10", "group": "cage", "bound": "lower", "value": { "latex": "222302", "decimal_approx": 222302, "alt_display": "222,302" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-10-lower-222302.yml" }, { "id": "cage-19-11-lower-2111870", "constant": "cage-19-11", "group": "cage", "bound": "lower", "value": { "latex": "2111870", "decimal_approx": 2111870, "alt_display": "2,111,870" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-11-lower-2111870.yml" }, { "id": "cage-19-12-lower-4001438", "constant": "cage-19-12", "group": "cage", "bound": "lower", "value": { "latex": "4001438", "decimal_approx": 4001438, "alt_display": "4,001,438" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-12-lower-4001438.yml" }, { "id": "cage-19-13-lower-38013662", "constant": "cage-19-13", "group": "cage", "bound": "lower", "value": { "latex": "38013662", "decimal_approx": 38013662, "alt_display": "38,013,662" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-13-lower-38013662.yml" }, { "id": "cage-19-14-lower-72025886", "constant": "cage-19-14", "group": "cage", "bound": "lower", "value": { "latex": "72025886", "decimal_approx": 72025886, "alt_display": "72,025,886" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-14-lower-72025886.yml" }, { "id": "cage-19-15-lower-684245918", "constant": "cage-19-15", "group": "cage", "bound": "lower", "value": { "latex": "684245918", "decimal_approx": 684245918, "alt_display": "684,245,918" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-15-lower-684245918.yml" }, { "id": "cage-19-16-lower-1296465950", "constant": "cage-19-16", "group": "cage", "bound": "lower", "value": { "latex": "1296465950", "decimal_approx": 1296465950, "alt_display": "1,296,465,950" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-16-lower-1296465950.yml" }, { "id": "cage-19-3-lower-20", "constant": "cage-19-3", "group": "cage", "bound": "lower", "value": { "latex": "20", "decimal_approx": 20, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-3-lower-20.yml" }, { "id": "cage-19-4-lower-38", "constant": "cage-19-4", "group": "cage", "bound": "lower", "value": { "latex": "38", "decimal_approx": 38, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-4-lower-38.yml" }, { "id": "cage-19-5-lower-362", "constant": "cage-19-5", "group": "cage", "bound": "lower", "value": { "latex": "362", "decimal_approx": 362, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "364", "decimal_approx": 364, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-19-5-lower-362.yml" }, { "id": "cage-19-6-lower-686", "constant": "cage-19-6", "group": "cage", "bound": "lower", "value": { "latex": "686", "decimal_approx": 686, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "686", "decimal_approx": 686, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-19-6-lower-686.yml" }, { "id": "cage-19-7-lower-6518", "constant": "cage-19-7", "group": "cage", "bound": "lower", "value": { "latex": "6518", "decimal_approx": 6518, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-7-lower-6518.yml" }, { "id": "cage-19-8-lower-12350", "constant": "cage-19-8", "group": "cage", "bound": "lower", "value": { "latex": "12350", "decimal_approx": 12350, "alt_display": "12,350" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-8-lower-12350.yml" }, { "id": "cage-19-9-lower-117326", "constant": "cage-19-9", "group": "cage", "bound": "lower", "value": { "latex": "117326", "decimal_approx": 117326, "alt_display": "117,326" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-9-lower-117326.yml" }, { "id": "cage-20-10-lower-275122", "constant": "cage-20-10", "group": "cage", "bound": "lower", "value": { "latex": "275122", "decimal_approx": 275122, "alt_display": "275,122" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-10-lower-275122.yml" }, { "id": "cage-20-11-lower-2751221", "constant": "cage-20-11", "group": "cage", "bound": "lower", "value": { "latex": "2751221", "decimal_approx": 2751221, "alt_display": "2,751,221" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-11-lower-2751221.yml" }, { "id": "cage-20-12-lower-5227320", "constant": "cage-20-12", "group": "cage", "bound": "lower", "value": { "latex": "5227320", "decimal_approx": 5227320, "alt_display": "5,227,320" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-12-lower-5227320.yml" }, { "id": "cage-20-13-lower-52273201", "constant": "cage-20-13", "group": "cage", "bound": "lower", "value": { "latex": "52273201", "decimal_approx": 52273201, "alt_display": "52,273,201" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-13-lower-52273201.yml" }, { "id": "cage-20-14-lower-99319082", "constant": "cage-20-14", "group": "cage", "bound": "lower", "value": { "latex": "99319082", "decimal_approx": 99319082, "alt_display": "99,319,082" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-14-lower-99319082.yml" }, { "id": "cage-20-15-lower-993190821", "constant": "cage-20-15", "group": "cage", "bound": "lower", "value": { "latex": "993190821", "decimal_approx": 993190821, "alt_display": "993,190,821" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-15-lower-993190821.yml" }, { "id": "cage-20-16-lower-1887062560", "constant": "cage-20-16", "group": "cage", "bound": "lower", "value": { "latex": "1887062560", "decimal_approx": 1887062560, "alt_display": "1,887,062,560" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-16-lower-1887062560.yml" }, { "id": "cage-20-3-lower-21", "constant": "cage-20-3", "group": "cage", "bound": "lower", "value": { "latex": "21", "decimal_approx": 21, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-3-lower-21.yml" }, { "id": "cage-20-4-lower-40", "constant": "cage-20-4", "group": "cage", "bound": "lower", "value": { "latex": "40", "decimal_approx": 40, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-4-lower-40.yml" }, { "id": "cage-20-5-lower-401", "constant": "cage-20-5", "group": "cage", "bound": "lower", "value": { "latex": "401", "decimal_approx": 401, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "403", "decimal_approx": 403, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-20-5-lower-401.yml" }, { "id": "cage-20-6-lower-762", "constant": "cage-20-6", "group": "cage", "bound": "lower", "value": { "latex": "762", "decimal_approx": 762, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "762", "decimal_approx": 762, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-20-6-lower-762.yml" }, { "id": "cage-20-7-lower-7621", "constant": "cage-20-7", "group": "cage", "bound": "lower", "value": { "latex": "7621", "decimal_approx": 7621, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-7-lower-7621.yml" }, { "id": "cage-20-8-lower-14480", "constant": "cage-20-8", "group": "cage", "bound": "lower", "value": { "latex": "14480", "decimal_approx": 14480, "alt_display": "14,480" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-8-lower-14480.yml" }, { "id": "cage-20-9-lower-144801", "constant": "cage-20-9", "group": "cage", "bound": "lower", "value": { "latex": "144801", "decimal_approx": 144801, "alt_display": "144,801" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-9-lower-144801.yml" }, { "id": "cage-3-10-lower-62", "constant": "cage-3-10", "group": "cage", "bound": "lower", "value": { "latex": "62", "decimal_approx": 62, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "70", "decimal_approx": 70, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-3-10-lower-62.yml" }, { "id": "cage-3-11-lower-94", "constant": "cage-3-11", "group": "cage", "bound": "lower", "value": { "latex": "94", "decimal_approx": 94, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "112", "decimal_approx": 112, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-3-11-lower-94.yml" }, { "id": "cage-3-12-lower-126", "constant": "cage-3-12", "group": "cage", "bound": "lower", "value": { "latex": "126", "decimal_approx": 126, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "126", "decimal_approx": 126, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-12-lower-126.yml" }, { "id": "cage-3-13-lower-190", "constant": "cage-3-13", "group": "cage", "bound": "lower", "value": { "latex": "190", "decimal_approx": 190, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "202", "decimal_approx": 202, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-3-13-lower-190.yml" }, { "id": "cage-3-14-lower-254", "constant": "cage-3-14", "group": "cage", "bound": "lower", "value": { "latex": "254", "decimal_approx": 254, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "258", "decimal_approx": 258, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-3-14-lower-254.yml" }, { "id": "cage-3-15-lower-382", "constant": "cage-3-15", "group": "cage", "bound": "lower", "value": { "latex": "382", "decimal_approx": 382, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "384", "decimal_approx": 384, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-3-15-lower-382.yml" }, { "id": "cage-3-16-lower-510", "constant": "cage-3-16", "group": "cage", "bound": "lower", "value": { "latex": "510", "decimal_approx": 510, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "512", "decimal_approx": 512, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-3-16-lower-510.yml" }, { "id": "cage-3-3-lower-4", "constant": "cage-3-3", "group": "cage", "bound": "lower", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-3-lower-4.yml" }, { "id": "cage-3-4-lower-6", "constant": "cage-3-4", "group": "cage", "bound": "lower", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-4-lower-6.yml" }, { "id": "cage-3-5-lower-10", "constant": "cage-3-5", "group": "cage", "bound": "lower", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-5-lower-10.yml" }, { "id": "cage-3-6-lower-14", "constant": "cage-3-6", "group": "cage", "bound": "lower", "value": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-6-lower-14.yml" }, { "id": "cage-3-7-lower-22", "constant": "cage-3-7", "group": "cage", "bound": "lower", "value": { "latex": "22", "decimal_approx": 22, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "24", "decimal_approx": 24, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-3-7-lower-22.yml" }, { "id": "cage-3-8-lower-30", "constant": "cage-3-8", "group": "cage", "bound": "lower", "value": { "latex": "30", "decimal_approx": 30, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "30", "decimal_approx": 30, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-8-lower-30.yml" }, { "id": "cage-3-9-lower-46", "constant": "cage-3-9", "group": "cage", "bound": "lower", "value": { "latex": "46", "decimal_approx": 46, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "58", "decimal_approx": 58, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-3-9-lower-46.yml" }, { "id": "cage-4-10-lower-242", "constant": "cage-4-10", "group": "cage", "bound": "lower", "value": { "latex": "242", "decimal_approx": 242, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-4-10-lower-242.yml" }, { "id": "cage-4-11-lower-485", "constant": "cage-4-11", "group": "cage", "bound": "lower", "value": { "latex": "485", "decimal_approx": 485, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-4-11-lower-485.yml" }, { "id": "cage-4-12-lower-728", "constant": "cage-4-12", "group": "cage", "bound": "lower", "value": { "latex": "728", "decimal_approx": 728, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "728", "decimal_approx": 728, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-4-12-lower-728.yml" }, { "id": "cage-4-13-lower-1457", "constant": "cage-4-13", "group": "cage", "bound": "lower", "value": { "latex": "1457", "decimal_approx": 1457, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-4-13-lower-1457.yml" }, { "id": "cage-4-14-lower-2186", "constant": "cage-4-14", "group": "cage", "bound": "lower", "value": { "latex": "2186", "decimal_approx": 2186, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-4-14-lower-2186.yml" }, { "id": "cage-4-15-lower-4373", "constant": "cage-4-15", "group": "cage", "bound": "lower", "value": { "latex": "4373", "decimal_approx": 4373, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-4-15-lower-4373.yml" }, { "id": "cage-4-16-lower-6560", "constant": "cage-4-16", "group": "cage", "bound": "lower", "value": { "latex": "6560", "decimal_approx": 6560, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-4-16-lower-6560.yml" }, { "id": "cage-4-3-lower-5", "constant": "cage-4-3", "group": "cage", "bound": "lower", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-4-3-lower-5.yml" }, { "id": "cage-4-4-lower-8", "constant": "cage-4-4", "group": "cage", "bound": "lower", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-4-4-lower-8.yml" }, { "id": "cage-4-5-lower-17", "constant": "cage-4-5", "group": "cage", "bound": "lower", "value": { "latex": "17", "decimal_approx": 17, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "19", "decimal_approx": 19, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-4-5-lower-17.yml" }, { "id": "cage-4-6-lower-26", "constant": "cage-4-6", "group": "cage", "bound": "lower", "value": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-4-6-lower-26.yml" }, { "id": "cage-4-7-lower-53", "constant": "cage-4-7", "group": "cage", "bound": "lower", "value": { "latex": "53", "decimal_approx": 53, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "67", "decimal_approx": 67, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-4-7-lower-53.yml" }, { "id": "cage-4-8-lower-80", "constant": "cage-4-8", "group": "cage", "bound": "lower", "value": { "latex": "80", "decimal_approx": 80, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "80", "decimal_approx": 80, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-4-8-lower-80.yml" }, { "id": "cage-4-9-lower-161", "constant": "cage-4-9", "group": "cage", "bound": "lower", "value": { "latex": "161", "decimal_approx": 161, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-4-9-lower-161.yml" }, { "id": "cage-5-10-lower-682", "constant": "cage-5-10", "group": "cage", "bound": "lower", "value": { "latex": "682", "decimal_approx": 682, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-5-10-lower-682.yml" }, { "id": "cage-5-11-lower-1706", "constant": "cage-5-11", "group": "cage", "bound": "lower", "value": { "latex": "1706", "decimal_approx": 1706, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-5-11-lower-1706.yml" }, { "id": "cage-5-12-lower-2730", "constant": "cage-5-12", "group": "cage", "bound": "lower", "value": { "latex": "2730", "decimal_approx": 2730, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "2730", "decimal_approx": 2730, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-5-12-lower-2730.yml" }, { "id": "cage-5-13-lower-6826", "constant": "cage-5-13", "group": "cage", "bound": "lower", "value": { "latex": "6826", "decimal_approx": 6826, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-5-13-lower-6826.yml" }, { "id": "cage-5-14-lower-10922", "constant": "cage-5-14", "group": "cage", "bound": "lower", "value": { "latex": "10922", "decimal_approx": 10922, "alt_display": "10,922" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-5-14-lower-10922.yml" }, { "id": "cage-5-15-lower-27306", "constant": "cage-5-15", "group": "cage", "bound": "lower", "value": { "latex": "27306", "decimal_approx": 27306, "alt_display": "27,306" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-5-15-lower-27306.yml" }, { "id": "cage-5-16-lower-43690", "constant": "cage-5-16", "group": "cage", "bound": "lower", "value": { "latex": "43690", "decimal_approx": 43690, "alt_display": "43,690" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-5-16-lower-43690.yml" }, { "id": "cage-5-3-lower-6", "constant": "cage-5-3", "group": "cage", "bound": "lower", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-5-3-lower-6.yml" }, { "id": "cage-5-4-lower-10", "constant": "cage-5-4", "group": "cage", "bound": "lower", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-5-4-lower-10.yml" }, { "id": "cage-5-5-lower-26", "constant": "cage-5-5", "group": "cage", "bound": "lower", "value": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "30", "decimal_approx": 30, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-5-5-lower-26.yml" }, { "id": "cage-5-6-lower-42", "constant": "cage-5-6", "group": "cage", "bound": "lower", "value": { "latex": "42", "decimal_approx": 42, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "42", "decimal_approx": 42, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-5-6-lower-42.yml" }, { "id": "cage-5-7-lower-106", "constant": "cage-5-7", "group": "cage", "bound": "lower", "value": { "latex": "106", "decimal_approx": 106, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-5-7-lower-106.yml" }, { "id": "cage-5-8-lower-170", "constant": "cage-5-8", "group": "cage", "bound": "lower", "value": { "latex": "170", "decimal_approx": 170, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "170", "decimal_approx": 170, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-5-8-lower-170.yml" }, { "id": "cage-5-9-lower-426", "constant": "cage-5-9", "group": "cage", "bound": "lower", "value": { "latex": "426", "decimal_approx": 426, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-5-9-lower-426.yml" }, { "id": "cage-6-10-lower-1562", "constant": "cage-6-10", "group": "cage", "bound": "lower", "value": { "latex": "1562", "decimal_approx": 1562, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-6-10-lower-1562.yml" }, { "id": "cage-6-11-lower-4687", "constant": "cage-6-11", "group": "cage", "bound": "lower", "value": { "latex": "4687", "decimal_approx": 4687, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-6-11-lower-4687.yml" }, { "id": "cage-6-12-lower-7812", "constant": "cage-6-12", "group": "cage", "bound": "lower", "value": { "latex": "7812", "decimal_approx": 7812, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "7812", "decimal_approx": 7812, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-6-12-lower-7812.yml" }, { "id": "cage-6-13-lower-23437", "constant": "cage-6-13", "group": "cage", "bound": "lower", "value": { "latex": "23437", "decimal_approx": 23437, "alt_display": "23,437" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-6-13-lower-23437.yml" }, { "id": "cage-6-14-lower-39062", "constant": "cage-6-14", "group": "cage", "bound": "lower", "value": { "latex": "39062", "decimal_approx": 39062, "alt_display": "39,062" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-6-14-lower-39062.yml" }, { "id": "cage-6-15-lower-117187", "constant": "cage-6-15", "group": "cage", "bound": "lower", "value": { "latex": "117187", "decimal_approx": 117187, "alt_display": "117,187" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-6-15-lower-117187.yml" }, { "id": "cage-6-16-lower-195312", "constant": "cage-6-16", "group": "cage", "bound": "lower", "value": { "latex": "195312", "decimal_approx": 195312, "alt_display": "195,312" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-6-16-lower-195312.yml" }, { "id": "cage-6-3-lower-7", "constant": "cage-6-3", "group": "cage", "bound": "lower", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-6-3-lower-7.yml" }, { "id": "cage-6-4-lower-12", "constant": "cage-6-4", "group": "cage", "bound": "lower", "value": { "latex": "12", "decimal_approx": 12, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "12", "decimal_approx": 12, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-6-4-lower-12.yml" }, { "id": "cage-6-5-lower-37", "constant": "cage-6-5", "group": "cage", "bound": "lower", "value": { "latex": "37", "decimal_approx": 37, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "40", "decimal_approx": 40, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-6-5-lower-37.yml" }, { "id": "cage-6-6-lower-62", "constant": "cage-6-6", "group": "cage", "bound": "lower", "value": { "latex": "62", "decimal_approx": 62, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "62", "decimal_approx": 62, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-6-6-lower-62.yml" }, { "id": "cage-6-7-lower-187", "constant": "cage-6-7", "group": "cage", "bound": "lower", "value": { "latex": "187", "decimal_approx": 187, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-6-7-lower-187.yml" }, { "id": "cage-6-8-lower-312", "constant": "cage-6-8", "group": "cage", "bound": "lower", "value": { "latex": "312", "decimal_approx": 312, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "312", "decimal_approx": 312, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-6-8-lower-312.yml" }, { "id": "cage-6-9-lower-937", "constant": "cage-6-9", "group": "cage", "bound": "lower", "value": { "latex": "937", "decimal_approx": 937, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-6-9-lower-937.yml" }, { "id": "cage-7-10-lower-3110", "constant": "cage-7-10", "group": "cage", "bound": "lower", "value": { "latex": "3110", "decimal_approx": 3110, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-7-10-lower-3110.yml" }, { "id": "cage-7-11-lower-10886", "constant": "cage-7-11", "group": "cage", "bound": "lower", "value": { "latex": "10886", "decimal_approx": 10886, "alt_display": "10,886" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-7-11-lower-10886.yml" }, { "id": "cage-7-12-lower-18662", "constant": "cage-7-12", "group": "cage", "bound": "lower", "value": { "latex": "18662", "decimal_approx": 18662, "alt_display": "18,662" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-7-12-lower-18662.yml" }, { "id": "cage-7-13-lower-65318", "constant": "cage-7-13", "group": "cage", "bound": "lower", "value": { "latex": "65318", "decimal_approx": 65318, "alt_display": "65,318" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-7-13-lower-65318.yml" }, { "id": "cage-7-14-lower-111974", "constant": "cage-7-14", "group": "cage", "bound": "lower", "value": { "latex": "111974", "decimal_approx": 111974, "alt_display": "111,974" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-7-14-lower-111974.yml" }, { "id": "cage-7-15-lower-391910", "constant": "cage-7-15", "group": "cage", "bound": "lower", "value": { "latex": "391910", "decimal_approx": 391910, "alt_display": "391,910" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-7-15-lower-391910.yml" }, { "id": "cage-7-16-lower-671846", "constant": "cage-7-16", "group": "cage", "bound": "lower", "value": { "latex": "671846", "decimal_approx": 671846, "alt_display": "671,846" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-7-16-lower-671846.yml" }, { "id": "cage-7-3-lower-8", "constant": "cage-7-3", "group": "cage", "bound": "lower", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-7-3-lower-8.yml" }, { "id": "cage-7-4-lower-14", "constant": "cage-7-4", "group": "cage", "bound": "lower", "value": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-7-4-lower-14.yml" }, { "id": "cage-7-5-lower-50", "constant": "cage-7-5", "group": "cage", "bound": "lower", "value": { "latex": "50", "decimal_approx": 50, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "50", "decimal_approx": 50, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-7-5-lower-50.yml" }, { "id": "cage-7-6-lower-86", "constant": "cage-7-6", "group": "cage", "bound": "lower", "value": { "latex": "86", "decimal_approx": 86, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "90", "decimal_approx": 90, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-7-6-lower-86.yml" }, { "id": "cage-7-7-lower-302", "constant": "cage-7-7", "group": "cage", "bound": "lower", "value": { "latex": "302", "decimal_approx": 302, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-7-7-lower-302.yml" }, { "id": "cage-7-8-lower-518", "constant": "cage-7-8", "group": "cage", "bound": "lower", "value": { "latex": "518", "decimal_approx": 518, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-7-8-lower-518.yml" }, { "id": "cage-7-9-lower-1814", "constant": "cage-7-9", "group": "cage", "bound": "lower", "value": { "latex": "1814", "decimal_approx": 1814, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-7-9-lower-1814.yml" }, { "id": "cage-8-10-lower-5602", "constant": "cage-8-10", "group": "cage", "bound": "lower", "value": { "latex": "5602", "decimal_approx": 5602, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-10-lower-5602.yml" }, { "id": "cage-8-11-lower-22409", "constant": "cage-8-11", "group": "cage", "bound": "lower", "value": { "latex": "22409", "decimal_approx": 22409, "alt_display": "22,409" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-11-lower-22409.yml" }, { "id": "cage-8-12-lower-39216", "constant": "cage-8-12", "group": "cage", "bound": "lower", "value": { "latex": "39216", "decimal_approx": 39216, "alt_display": "39,216" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-12-lower-39216.yml" }, { "id": "cage-8-13-lower-156865", "constant": "cage-8-13", "group": "cage", "bound": "lower", "value": { "latex": "156865", "decimal_approx": 156865, "alt_display": "156,865" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-13-lower-156865.yml" }, { "id": "cage-8-14-lower-274514", "constant": "cage-8-14", "group": "cage", "bound": "lower", "value": { "latex": "274514", "decimal_approx": 274514, "alt_display": "274,514" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-14-lower-274514.yml" }, { "id": "cage-8-15-lower-1098057", "constant": "cage-8-15", "group": "cage", "bound": "lower", "value": { "latex": "1098057", "decimal_approx": 1098057, "alt_display": "1,098,057" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-15-lower-1098057.yml" }, { "id": "cage-8-16-lower-1921600", "constant": "cage-8-16", "group": "cage", "bound": "lower", "value": { "latex": "1921600", "decimal_approx": 1921600, "alt_display": "1,921,600" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-16-lower-1921600.yml" }, { "id": "cage-8-3-lower-9", "constant": "cage-8-3", "group": "cage", "bound": "lower", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-3-lower-9.yml" }, { "id": "cage-8-4-lower-16", "constant": "cage-8-4", "group": "cage", "bound": "lower", "value": { "latex": "16", "decimal_approx": 16, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-4-lower-16.yml" }, { "id": "cage-8-5-lower-65", "constant": "cage-8-5", "group": "cage", "bound": "lower", "value": { "latex": "65", "decimal_approx": 65, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "67", "decimal_approx": 67, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-8-5-lower-65.yml" }, { "id": "cage-8-6-lower-114", "constant": "cage-8-6", "group": "cage", "bound": "lower", "value": { "latex": "114", "decimal_approx": 114, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "114", "decimal_approx": 114, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-8-6-lower-114.yml" }, { "id": "cage-8-7-lower-457", "constant": "cage-8-7", "group": "cage", "bound": "lower", "value": { "latex": "457", "decimal_approx": 457, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-7-lower-457.yml" }, { "id": "cage-8-8-lower-800", "constant": "cage-8-8", "group": "cage", "bound": "lower", "value": { "latex": "800", "decimal_approx": 800, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-8-lower-800.yml" }, { "id": "cage-8-9-lower-3201", "constant": "cage-8-9", "group": "cage", "bound": "lower", "value": { "latex": "3201", "decimal_approx": 3201, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-9-lower-3201.yml" }, { "id": "cage-9-10-lower-9362", "constant": "cage-9-10", "group": "cage", "bound": "lower", "value": { "latex": "9362", "decimal_approx": 9362, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-10-lower-9362.yml" }, { "id": "cage-9-11-lower-42130", "constant": "cage-9-11", "group": "cage", "bound": "lower", "value": { "latex": "42130", "decimal_approx": 42130, "alt_display": "42,130" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-11-lower-42130.yml" }, { "id": "cage-9-12-lower-74898", "constant": "cage-9-12", "group": "cage", "bound": "lower", "value": { "latex": "74898", "decimal_approx": 74898, "alt_display": "74,898" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-12-lower-74898.yml" }, { "id": "cage-9-13-lower-337042", "constant": "cage-9-13", "group": "cage", "bound": "lower", "value": { "latex": "337042", "decimal_approx": 337042, "alt_display": "337,042" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-13-lower-337042.yml" }, { "id": "cage-9-14-lower-599186", "constant": "cage-9-14", "group": "cage", "bound": "lower", "value": { "latex": "599186", "decimal_approx": 599186, "alt_display": "599,186" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-14-lower-599186.yml" }, { "id": "cage-9-15-lower-2696338", "constant": "cage-9-15", "group": "cage", "bound": "lower", "value": { "latex": "2696338", "decimal_approx": 2696338, "alt_display": "2,696,338" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-15-lower-2696338.yml" }, { "id": "cage-9-16-lower-4793490", "constant": "cage-9-16", "group": "cage", "bound": "lower", "value": { "latex": "4793490", "decimal_approx": 4793490, "alt_display": "4,793,490" }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-16-lower-4793490.yml" }, { "id": "cage-9-3-lower-10", "constant": "cage-9-3", "group": "cage", "bound": "lower", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-3-lower-10.yml" }, { "id": "cage-9-4-lower-18", "constant": "cage-9-4", "group": "cage", "bound": "lower", "value": { "latex": "18", "decimal_approx": 18, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-4-lower-18.yml" }, { "id": "cage-9-5-lower-82", "constant": "cage-9-5", "group": "cage", "bound": "lower", "value": { "latex": "82", "decimal_approx": 82, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "86", "decimal_approx": 86, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/cage/cage-9-5-lower-82.yml" }, { "id": "cage-9-6-lower-146", "constant": "cage-9-6", "group": "cage", "bound": "lower", "value": { "latex": "146", "decimal_approx": 146, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": { "latex": "146", "decimal_approx": 146, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-9-6-lower-146.yml" }, { "id": "cage-9-7-lower-658", "constant": "cage-9-7", "group": "cage", "bound": "lower", "value": { "latex": "658", "decimal_approx": 658, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-7-lower-658.yml" }, { "id": "cage-9-8-lower-1170", "constant": "cage-9-8", "group": "cage", "bound": "lower", "value": { "latex": "1170", "decimal_approx": 1170, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-8-lower-1170.yml" }, { "id": "cage-9-9-lower-5266", "constant": "cage-9-9", "group": "cage", "bound": "lower", "value": { "latex": "5266", "decimal_approx": 5266, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-29", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-9-lower-5266.yml" }, { "id": "cage-10-3-upper-11", "constant": "cage-10-3", "group": "cage", "bound": "upper", "value": { "latex": "11", "decimal_approx": 11, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-3-upper-11.yml" }, { "id": "cage-10-4-upper-20", "constant": "cage-10-4", "group": "cage", "bound": "upper", "value": { "latex": "20", "decimal_approx": 20, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-10-4-upper-20.yml" }, { "id": "cage-10-6-upper-182", "constant": "cage-10-6", "group": "cage", "bound": "upper", "value": { "latex": "182", "decimal_approx": 182, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "182", "decimal_approx": 182, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-10-6-upper-182.yml" }, { "id": "cage-11-3-upper-12", "constant": "cage-11-3", "group": "cage", "bound": "upper", "value": { "latex": "12", "decimal_approx": 12, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-3-upper-12.yml" }, { "id": "cage-11-4-upper-22", "constant": "cage-11-4", "group": "cage", "bound": "upper", "value": { "latex": "22", "decimal_approx": 22, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-11-4-upper-22.yml" }, { "id": "cage-12-3-upper-13", "constant": "cage-12-3", "group": "cage", "bound": "upper", "value": { "latex": "13", "decimal_approx": 13, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-3-upper-13.yml" }, { "id": "cage-12-4-upper-24", "constant": "cage-12-4", "group": "cage", "bound": "upper", "value": { "latex": "24", "decimal_approx": 24, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-12-4-upper-24.yml" }, { "id": "cage-12-6-upper-266", "constant": "cage-12-6", "group": "cage", "bound": "upper", "value": { "latex": "266", "decimal_approx": 266, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "266", "decimal_approx": 266, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-12-6-upper-266.yml" }, { "id": "cage-13-3-upper-14", "constant": "cage-13-3", "group": "cage", "bound": "upper", "value": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-3-upper-14.yml" }, { "id": "cage-13-4-upper-26", "constant": "cage-13-4", "group": "cage", "bound": "upper", "value": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-13-4-upper-26.yml" }, { "id": "cage-14-3-upper-15", "constant": "cage-14-3", "group": "cage", "bound": "upper", "value": { "latex": "15", "decimal_approx": 15, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-3-upper-15.yml" }, { "id": "cage-14-4-upper-28", "constant": "cage-14-4", "group": "cage", "bound": "upper", "value": { "latex": "28", "decimal_approx": 28, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-14-4-upper-28.yml" }, { "id": "cage-14-6-upper-366", "constant": "cage-14-6", "group": "cage", "bound": "upper", "value": { "latex": "366", "decimal_approx": 366, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "366", "decimal_approx": 366, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-14-6-upper-366.yml" }, { "id": "cage-15-3-upper-16", "constant": "cage-15-3", "group": "cage", "bound": "upper", "value": { "latex": "16", "decimal_approx": 16, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-3-upper-16.yml" }, { "id": "cage-15-4-upper-30", "constant": "cage-15-4", "group": "cage", "bound": "upper", "value": { "latex": "30", "decimal_approx": 30, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-15-4-upper-30.yml" }, { "id": "cage-16-3-upper-17", "constant": "cage-16-3", "group": "cage", "bound": "upper", "value": { "latex": "17", "decimal_approx": 17, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-3-upper-17.yml" }, { "id": "cage-16-4-upper-32", "constant": "cage-16-4", "group": "cage", "bound": "upper", "value": { "latex": "32", "decimal_approx": 32, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-16-4-upper-32.yml" }, { "id": "cage-17-3-upper-18", "constant": "cage-17-3", "group": "cage", "bound": "upper", "value": { "latex": "18", "decimal_approx": 18, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-3-upper-18.yml" }, { "id": "cage-17-4-upper-34", "constant": "cage-17-4", "group": "cage", "bound": "upper", "value": { "latex": "34", "decimal_approx": 34, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-17-4-upper-34.yml" }, { "id": "cage-17-6-upper-546", "constant": "cage-17-6", "group": "cage", "bound": "upper", "value": { "latex": "546", "decimal_approx": 546, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "546", "decimal_approx": 546, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-17-6-upper-546.yml" }, { "id": "cage-18-3-upper-19", "constant": "cage-18-3", "group": "cage", "bound": "upper", "value": { "latex": "19", "decimal_approx": 19, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-3-upper-19.yml" }, { "id": "cage-18-4-upper-36", "constant": "cage-18-4", "group": "cage", "bound": "upper", "value": { "latex": "36", "decimal_approx": 36, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-18-4-upper-36.yml" }, { "id": "cage-18-6-upper-614", "constant": "cage-18-6", "group": "cage", "bound": "upper", "value": { "latex": "614", "decimal_approx": 614, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "614", "decimal_approx": 614, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-18-6-upper-614.yml" }, { "id": "cage-19-3-upper-20", "constant": "cage-19-3", "group": "cage", "bound": "upper", "value": { "latex": "20", "decimal_approx": 20, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-3-upper-20.yml" }, { "id": "cage-19-4-upper-38", "constant": "cage-19-4", "group": "cage", "bound": "upper", "value": { "latex": "38", "decimal_approx": 38, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-19-4-upper-38.yml" }, { "id": "cage-20-3-upper-21", "constant": "cage-20-3", "group": "cage", "bound": "upper", "value": { "latex": "21", "decimal_approx": 21, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-3-upper-21.yml" }, { "id": "cage-20-4-upper-40", "constant": "cage-20-4", "group": "cage", "bound": "upper", "value": { "latex": "40", "decimal_approx": 40, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-20-4-upper-40.yml" }, { "id": "cage-20-6-upper-762", "constant": "cage-20-6", "group": "cage", "bound": "upper", "value": { "latex": "762", "decimal_approx": 762, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "762", "decimal_approx": 762, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-20-6-upper-762.yml" }, { "id": "cage-3-3-upper-4", "constant": "cage-3-3", "group": "cage", "bound": "upper", "value": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "4", "decimal_approx": 4, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-3-upper-4.yml" }, { "id": "cage-3-4-upper-6", "constant": "cage-3-4", "group": "cage", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-4-upper-6.yml" }, { "id": "cage-3-5-upper-10", "constant": "cage-3-5", "group": "cage", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-5-upper-10.yml" }, { "id": "cage-3-6-upper-14", "constant": "cage-3-6", "group": "cage", "bound": "upper", "value": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-6-upper-14.yml" }, { "id": "cage-3-7-upper-24", "constant": "cage-3-7", "group": "cage", "bound": "upper", "value": { "latex": "24", "decimal_approx": 24, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "24", "decimal_approx": 24, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-7-upper-24.yml" }, { "id": "cage-3-8-upper-30", "constant": "cage-3-8", "group": "cage", "bound": "upper", "value": { "latex": "30", "decimal_approx": 30, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "30", "decimal_approx": 30, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-3-8-upper-30.yml" }, { "id": "cage-4-3-upper-5", "constant": "cage-4-3", "group": "cage", "bound": "upper", "value": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "5", "decimal_approx": 5, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-4-3-upper-5.yml" }, { "id": "cage-4-4-upper-8", "constant": "cage-4-4", "group": "cage", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-4-4-upper-8.yml" }, { "id": "cage-4-6-upper-26", "constant": "cage-4-6", "group": "cage", "bound": "upper", "value": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "26", "decimal_approx": 26, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-4-6-upper-26.yml" }, { "id": "cage-4-8-upper-80", "constant": "cage-4-8", "group": "cage", "bound": "upper", "value": { "latex": "80", "decimal_approx": 80, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "80", "decimal_approx": 80, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-4-8-upper-80.yml" }, { "id": "cage-5-3-upper-6", "constant": "cage-5-3", "group": "cage", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-5-3-upper-6.yml" }, { "id": "cage-5-4-upper-10", "constant": "cage-5-4", "group": "cage", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-5-4-upper-10.yml" }, { "id": "cage-5-6-upper-42", "constant": "cage-5-6", "group": "cage", "bound": "upper", "value": { "latex": "42", "decimal_approx": 42, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "42", "decimal_approx": 42, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-5-6-upper-42.yml" }, { "id": "cage-5-8-upper-170", "constant": "cage-5-8", "group": "cage", "bound": "upper", "value": { "latex": "170", "decimal_approx": 170, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "170", "decimal_approx": 170, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-5-8-upper-170.yml" }, { "id": "cage-6-3-upper-7", "constant": "cage-6-3", "group": "cage", "bound": "upper", "value": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "7", "decimal_approx": 7, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-6-3-upper-7.yml" }, { "id": "cage-6-4-upper-12", "constant": "cage-6-4", "group": "cage", "bound": "upper", "value": { "latex": "12", "decimal_approx": 12, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "12", "decimal_approx": 12, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-6-4-upper-12.yml" }, { "id": "cage-6-6-upper-62", "constant": "cage-6-6", "group": "cage", "bound": "upper", "value": { "latex": "62", "decimal_approx": 62, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "62", "decimal_approx": 62, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-6-6-upper-62.yml" }, { "id": "cage-6-8-upper-312", "constant": "cage-6-8", "group": "cage", "bound": "upper", "value": { "latex": "312", "decimal_approx": 312, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "312", "decimal_approx": 312, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-6-8-upper-312.yml" }, { "id": "cage-7-3-upper-8", "constant": "cage-7-3", "group": "cage", "bound": "upper", "value": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "8", "decimal_approx": 8, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-7-3-upper-8.yml" }, { "id": "cage-7-4-upper-14", "constant": "cage-7-4", "group": "cage", "bound": "upper", "value": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-7-4-upper-14.yml" }, { "id": "cage-7-5-upper-50", "constant": "cage-7-5", "group": "cage", "bound": "upper", "value": { "latex": "50", "decimal_approx": 50, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "50", "decimal_approx": 50, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-7-5-upper-50.yml" }, { "id": "cage-8-3-upper-9", "constant": "cage-8-3", "group": "cage", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-3-upper-9.yml" }, { "id": "cage-8-4-upper-16", "constant": "cage-8-4", "group": "cage", "bound": "upper", "value": { "latex": "16", "decimal_approx": 16, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-8-4-upper-16.yml" }, { "id": "cage-8-6-upper-114", "constant": "cage-8-6", "group": "cage", "bound": "upper", "value": { "latex": "114", "decimal_approx": 114, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "114", "decimal_approx": 114, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-8-6-upper-114.yml" }, { "id": "cage-8-8-upper-800", "constant": "cage-8-8", "group": "cage", "bound": "upper", "value": { "latex": "800", "decimal_approx": 800, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "800", "decimal_approx": 800, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-8-8-upper-800.yml" }, { "id": "cage-9-3-upper-10", "constant": "cage-9-3", "group": "cage", "bound": "upper", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-3-upper-10.yml" }, { "id": "cage-9-4-upper-18", "constant": "cage-9-4", "group": "cage", "bound": "upper", "value": { "latex": "18", "decimal_approx": 18, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": null, "comparison": "new", "source": null, "path": "certificates/cage/cage-9-4-upper-18.yml" }, { "id": "cage-9-6-upper-146", "constant": "cage-9-6", "group": "cage", "bound": "upper", "value": { "latex": "146", "decimal_approx": 146, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "146", "decimal_approx": 146, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/cage/cage-9-6-upper-146.yml" }, { "id": "degree-diameter-10-2-lower-91", "constant": "degree-diameter-10-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "91", "decimal_approx": 91, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "91", "decimal_approx": 91, "alt_display": null }, "comparison": "equal", "source": "brown-1966", "path": "certificates/degree-diameter/degree-diameter-10-2-lower-91.yml" }, { "id": "degree-diameter-12-2-lower-133", "constant": "degree-diameter-12-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "133", "decimal_approx": 133, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "133", "decimal_approx": 133, "alt_display": null }, "comparison": "equal", "source": "brown-1966", "path": "certificates/degree-diameter/degree-diameter-12-2-lower-133.yml" }, { "id": "degree-diameter-14-2-lower-183", "constant": "degree-diameter-14-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "183", "decimal_approx": 183, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "183", "decimal_approx": 183, "alt_display": null }, "comparison": "equal", "source": "brown-1966", "path": "certificates/degree-diameter/degree-diameter-14-2-lower-183.yml" }, { "id": "degree-diameter-18-2-lower-307", "constant": "degree-diameter-18-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "307", "decimal_approx": 307, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "307", "decimal_approx": 307, "alt_display": null }, "comparison": "equal", "source": "brown-1966", "path": "certificates/degree-diameter/degree-diameter-18-2-lower-307.yml" }, { "id": "degree-diameter-20-2-lower-381", "constant": "degree-diameter-20-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "381", "decimal_approx": 381, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "381", "decimal_approx": 381, "alt_display": null }, "comparison": "equal", "source": "brown-1966", "path": "certificates/degree-diameter/degree-diameter-20-2-lower-381.yml" }, { "id": "degree-diameter-3-2-lower-10", "constant": "degree-diameter-3-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "10", "decimal_approx": 10, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/degree-diameter/degree-diameter-3-2-lower-10.yml" }, { "id": "degree-diameter-7-2-lower-50", "constant": "degree-diameter-7-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "50", "decimal_approx": 50, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "50", "decimal_approx": 50, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/degree-diameter/degree-diameter-7-2-lower-50.yml" }, { "id": "degree-diameter-8-2-lower-57", "constant": "degree-diameter-8-2", "group": "degree-diameter", "bound": "lower", "value": { "latex": "57", "decimal_approx": 57, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "57", "decimal_approx": 57, "alt_display": null }, "comparison": "equal", "source": "brown-1966", "path": "certificates/degree-diameter/degree-diameter-8-2-lower-57.yml" }, { "id": "minimal-superpermutation-1-upper-1", "constant": "minimal-superpermutation-1", "group": "minimal-superpermutation", "bound": "upper", "value": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "1", "decimal_approx": 1, "alt_display": null }, "comparison": "equal", "source": "egan-superpermutations", "path": "certificates/minimal-superpermutation/minimal-superpermutation-1-upper-1.yml" }, { "id": "minimal-superpermutation-2-upper-3", "constant": "minimal-superpermutation-2", "group": "minimal-superpermutation", "bound": "upper", "value": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "3", "decimal_approx": 3, "alt_display": null }, "comparison": "equal", "source": "egan-superpermutations", "path": "certificates/minimal-superpermutation/minimal-superpermutation-2-upper-3.yml" }, { "id": "minimal-superpermutation-3-upper-9", "constant": "minimal-superpermutation-3", "group": "minimal-superpermutation", "bound": "upper", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": "egan-superpermutations", "path": "certificates/minimal-superpermutation/minimal-superpermutation-3-upper-9.yml" }, { "id": "minimal-superpermutation-4-upper-33", "constant": "minimal-superpermutation-4", "group": "minimal-superpermutation", "bound": "upper", "value": { "latex": "33", "decimal_approx": 33, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "33", "decimal_approx": 33, "alt_display": null }, "comparison": "equal", "source": "egan-superpermutations", "path": "certificates/minimal-superpermutation/minimal-superpermutation-4-upper-33.yml" }, { "id": "minimal-superpermutation-5-upper-153", "constant": "minimal-superpermutation-5", "group": "minimal-superpermutation", "bound": "upper", "value": { "latex": "153", "decimal_approx": 153, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "153", "decimal_approx": 153, "alt_display": null }, "comparison": "equal", "source": "egan-superpermutations", "path": "certificates/minimal-superpermutation/minimal-superpermutation-5-upper-153.yml" }, { "id": "minimal-superpermutation-6-upper-873", "constant": "minimal-superpermutation-6", "group": "minimal-superpermutation", "bound": "upper", "value": { "latex": "873", "decimal_approx": 873, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "872", "decimal_approx": 872, "alt_display": null }, "comparison": "weaker", "source": "egan-superpermutations", "path": "certificates/minimal-superpermutation/minimal-superpermutation-6-upper-873.yml" }, { "id": "minimal-superpermutation-7-upper-5913", "constant": "minimal-superpermutation-7", "group": "minimal-superpermutation", "bound": "upper", "value": { "latex": "5913", "decimal_approx": 5913, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "5905", "decimal_approx": 5905, "alt_display": null }, "comparison": "weaker", "source": "egan-superpermutations", "path": "certificates/minimal-superpermutation/minimal-superpermutation-7-upper-5913.yml" }, { "id": "van-der-waerden-2-3-lower-9", "constant": "van-der-waerden-2-3", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/van-der-waerden/van-der-waerden-2-3-lower-9.yml" }, { "id": "van-der-waerden-2-4-lower-35", "constant": "van-der-waerden-2-4", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "35", "decimal_approx": 35, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "35", "decimal_approx": 35, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/van-der-waerden/van-der-waerden-2-4-lower-35.yml" }, { "id": "van-der-waerden-3-3-lower-27", "constant": "van-der-waerden-3-3", "group": "van-der-waerden", "bound": "lower", "value": { "latex": "27", "decimal_approx": 27, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-28", "current": true, "literature": { "latex": "27", "decimal_approx": 27, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/van-der-waerden/van-der-waerden-3-3-lower-27.yml" }, { "id": "ramsey-3-3-lower-6", "constant": "ramsey-3-3", "group": "ramsey", "bound": "lower", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-22", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/ramsey/ramsey-3-3-lower-6.yml" }, { "id": "ramsey-3-3-upper-6", "constant": "ramsey-3-3", "group": "ramsey", "bound": "upper", "value": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "kind": "lean", "submitted_by": "daniel-munro", "date": "2026-10-22", "current": true, "literature": { "latex": "6", "decimal_approx": 6, "alt_display": null }, "comparison": "equal", "source": null, "path": "certificates/ramsey/ramsey-3-3-upper-6.yml" }, { "id": "ramsey-3-4-lower-9", "constant": "ramsey-3-4", "group": "ramsey", "bound": "lower", "value": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-22", "current": true, "literature": { "latex": "9", "decimal_approx": 9, "alt_display": null }, "comparison": "equal", "source": "greenwood-gleason-1955", "path": "certificates/ramsey/ramsey-3-4-lower-9.yml" }, { "id": "ramsey-3-5-lower-14", "constant": "ramsey-3-5", "group": "ramsey", "bound": "lower", "value": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-22", "current": true, "literature": { "latex": "14", "decimal_approx": 14, "alt_display": null }, "comparison": "equal", "source": "greenwood-gleason-1955", "path": "certificates/ramsey/ramsey-3-5-lower-14.yml" }, { "id": "ramsey-4-4-lower-18", "constant": "ramsey-4-4", "group": "ramsey", "bound": "lower", "value": { "latex": "18", "decimal_approx": 18, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-22", "current": true, "literature": { "latex": "18", "decimal_approx": 18, "alt_display": null }, "comparison": "equal", "source": "greenwood-gleason-1955", "path": "certificates/ramsey/ramsey-4-4-lower-18.yml" }, { "id": "ramsey-5-5-lower-38", "constant": "ramsey-5-5", "group": "ramsey", "bound": "lower", "value": { "latex": "38", "decimal_approx": 38, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-22", "current": false, "literature": { "latex": "43", "decimal_approx": 43, "alt_display": null }, "comparison": "weaker", "source": null, "path": "certificates/ramsey/ramsey-5-5-lower-38.yml" }, { "id": "ramsey-6-6-lower-102", "constant": "ramsey-6-6", "group": "ramsey", "bound": "lower", "value": { "latex": "102", "decimal_approx": 102, "alt_display": null }, "kind": "witness", "submitted_by": "daniel-munro", "date": "2026-10-22", "current": true, "literature": { "latex": "102", "decimal_approx": 102, "alt_display": null }, "comparison": "equal", "source": "kalbfleisch-1966", "path": "certificates/ramsey/ramsey-6-6-lower-102.yml" } ]