id constant group bound kind submitted_by date current comparison source path value_latex value_decimal_approx value_alt_display literature_latex literature_decimal_approx literature_alt_display cap-set-1-lower-2 cap-set-1 cap-set lower witness daniel-munro 2026-11-05 True equal certificates/cap-set/cap-set-1-lower-2.yml 2 2.0 2 2.0 cap-set-2-lower-4 cap-set-2 cap-set lower witness daniel-munro 2026-11-05 True equal certificates/cap-set/cap-set-2-lower-4.yml 4 4.0 4 4.0 cap-set-3-lower-9 cap-set-3 cap-set lower witness daniel-munro 2026-11-05 True equal certificates/cap-set/cap-set-3-lower-9.yml 9 9.0 9 9.0 cap-set-4-lower-20 cap-set-4 cap-set lower witness daniel-munro 2026-11-05 True equal certificates/cap-set/cap-set-4-lower-20.yml 20 20.0 20 20.0 cap-set-5-lower-45 cap-set-5 cap-set lower witness daniel-munro 2026-11-05 True equal certificates/cap-set/cap-set-5-lower-45.yml 45 45.0 45 45.0 cap-set-6-lower-112 cap-set-6 cap-set lower witness daniel-munro 2026-11-05 True equal certificates/cap-set/cap-set-6-lower-112.yml 112 112.0 112 112.0 cap-set-7-lower-236 cap-set-7 cap-set lower witness daniel-munro 2026-11-05 True equal edel-bierbrauer-2001 certificates/cap-set/cap-set-7-lower-236.yml 236 236.0 236 236.0 cap-set-8-lower-512 cap-set-8 cap-set lower witness daniel-munro 2026-11-05 True equal romera-paredes-et-al-2023 certificates/cap-set/cap-set-8-lower-512.yml 512 512.0 512 512.0 isosceles-set-1-lower-3 isosceles-set-1 isosceles-set lower witness daniel-munro 2026-11-05 True equal certificates/isosceles-set/isosceles-set-1-lower-3.yml 3 3.0 3 3.0 isosceles-set-10-lower-56 isosceles-set-10 isosceles-set lower witness daniel-munro 2026-11-05 True new certificates/isosceles-set/isosceles-set-10-lower-56.yml 56 56.0 isosceles-set-11-lower-67 isosceles-set-11 isosceles-set lower witness daniel-munro 2026-11-05 True new certificates/isosceles-set/isosceles-set-11-lower-67.yml 67 67.0 isosceles-set-12-lower-79 isosceles-set-12 isosceles-set lower witness daniel-munro 2026-11-05 True new certificates/isosceles-set/isosceles-set-12-lower-79.yml 79 79.0 isosceles-set-2-lower-6 isosceles-set-2 isosceles-set lower witness daniel-munro 2026-11-05 True equal erdos-1946 certificates/isosceles-set/isosceles-set-2-lower-6.yml 6 6.0 6 6.0 isosceles-set-3-lower-8 isosceles-set-3 isosceles-set lower witness daniel-munro 2026-11-05 True equal kelly-1947 certificates/isosceles-set/isosceles-set-3-lower-8.yml 8 8.0 8 8.0 isosceles-set-4-lower-11 isosceles-set-4 isosceles-set lower witness daniel-munro 2026-11-05 True equal certificates/isosceles-set/isosceles-set-4-lower-11.yml 11 11.0 11 11.0 isosceles-set-5-lower-17 isosceles-set-5 isosceles-set lower witness daniel-munro 2026-11-05 True equal certificates/isosceles-set/isosceles-set-5-lower-17.yml 17 17.0 17 17.0 isosceles-set-6-lower-28 isosceles-set-6 isosceles-set lower witness daniel-munro 2026-11-05 True equal ionin-2009 certificates/isosceles-set/isosceles-set-6-lower-28.yml 28 28.0 28 28.0 isosceles-set-7-lower-30 isosceles-set-7 isosceles-set lower witness daniel-munro 2026-11-05 True equal ionin-2009 certificates/isosceles-set/isosceles-set-7-lower-30.yml 30 30.0 30 30.0 isosceles-set-8-lower-45 isosceles-set-8 isosceles-set lower witness daniel-munro 2026-11-05 True equal lisonek-1997 certificates/isosceles-set/isosceles-set-8-lower-45.yml 45 45.0 45 45.0 isosceles-set-9-lower-46 isosceles-set-9 isosceles-set lower witness daniel-munro 2026-11-05 True new certificates/isosceles-set/isosceles-set-9-lower-46.yml 46 46.0 no-three-in-line-1-lower-1 no-three-in-line-1 no-three-in-line lower witness daniel-munro 2026-11-05 True equal certificates/no-three-in-line/no-three-in-line-1-lower-1.yml 1 1.0 1 1.0 no-three-in-line-10-lower-20 no-three-in-line-10 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-10-lower-20.yml 20 20.0 20 20.0 no-three-in-line-11-lower-22 no-three-in-line-11 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-11-lower-22.yml 22 22.0 22 22.0 no-three-in-line-12-lower-24 no-three-in-line-12 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-12-lower-24.yml 24 24.0 24 24.0 no-three-in-line-13-lower-26 no-three-in-line-13 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-13-lower-26.yml 26 26.0 26 26.0 no-three-in-line-14-lower-28 no-three-in-line-14 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-14-lower-28.yml 28 28.0 28 28.0 no-three-in-line-15-lower-30 no-three-in-line-15 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-15-lower-30.yml 30 30.0 30 30.0 no-three-in-line-16-lower-32 no-three-in-line-16 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-16-lower-32.yml 32 32.0 32 32.0 no-three-in-line-17-lower-34 no-three-in-line-17 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-17-lower-34.yml 34 34.0 34 34.0 no-three-in-line-18-lower-36 no-three-in-line-18 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-18-lower-36.yml 36 36.0 36 36.0 no-three-in-line-19-lower-38 no-three-in-line-19 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-19-lower-38.yml 38 38.0 38 38.0 no-three-in-line-2-lower-4 no-three-in-line-2 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-2-lower-4.yml 4 4.0 4 4.0 no-three-in-line-20-lower-40 no-three-in-line-20 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-20-lower-40.yml 40 40.0 40 40.0 no-three-in-line-21-lower-42 no-three-in-line-21 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-21-lower-42.yml 42 42.0 42 42.0 no-three-in-line-22-lower-44 no-three-in-line-22 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-22-lower-44.yml 44 44.0 44 44.0 no-three-in-line-23-lower-46 no-three-in-line-23 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-23-lower-46.yml 46 46.0 46 46.0 no-three-in-line-24-lower-48 no-three-in-line-24 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-24-lower-48.yml 48 48.0 48 48.0 no-three-in-line-25-lower-50 no-three-in-line-25 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-25-lower-50.yml 50 50.0 50 50.0 no-three-in-line-26-lower-52 no-three-in-line-26 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-26-lower-52.yml 52 52.0 52 52.0 no-three-in-line-27-lower-54 no-three-in-line-27 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-27-lower-54.yml 54 54.0 54 54.0 no-three-in-line-28-lower-56 no-three-in-line-28 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-28-lower-56.yml 56 56.0 56 56.0 no-three-in-line-29-lower-58 no-three-in-line-29 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-29-lower-58.yml 58 58.0 58 58.0 no-three-in-line-3-lower-6 no-three-in-line-3 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-3-lower-6.yml 6 6.0 6 6.0 no-three-in-line-30-lower-60 no-three-in-line-30 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-30-lower-60.yml 60 60.0 60 60.0 no-three-in-line-31-lower-62 no-three-in-line-31 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-31-lower-62.yml 62 62.0 62 62.0 no-three-in-line-32-lower-64 no-three-in-line-32 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-32-lower-64.yml 64 64.0 64 64.0 no-three-in-line-33-lower-66 no-three-in-line-33 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-33-lower-66.yml 66 66.0 66 66.0 no-three-in-line-34-lower-68 no-three-in-line-34 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-34-lower-68.yml 68 68.0 68 68.0 no-three-in-line-35-lower-70 no-three-in-line-35 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-35-lower-70.yml 70 70.0 70 70.0 no-three-in-line-36-lower-72 no-three-in-line-36 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-36-lower-72.yml 72 72.0 72 72.0 no-three-in-line-37-lower-74 no-three-in-line-37 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-37-lower-74.yml 74 74.0 74 74.0 no-three-in-line-38-lower-76 no-three-in-line-38 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-38-lower-76.yml 76 76.0 76 76.0 no-three-in-line-39-lower-78 no-three-in-line-39 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-39-lower-78.yml 78 78.0 78 78.0 no-three-in-line-4-lower-8 no-three-in-line-4 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-4-lower-8.yml 8 8.0 8 8.0 no-three-in-line-40-lower-80 no-three-in-line-40 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-40-lower-80.yml 80 80.0 80 80.0 no-three-in-line-41-lower-82 no-three-in-line-41 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-41-lower-82.yml 82 82.0 82 82.0 no-three-in-line-42-lower-84 no-three-in-line-42 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-42-lower-84.yml 84 84.0 84 84.0 no-three-in-line-43-lower-86 no-three-in-line-43 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-43-lower-86.yml 86 86.0 86 86.0 no-three-in-line-44-lower-88 no-three-in-line-44 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-44-lower-88.yml 88 88.0 88 88.0 no-three-in-line-45-lower-90 no-three-in-line-45 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-45-lower-90.yml 90 90.0 90 90.0 no-three-in-line-46-lower-92 no-three-in-line-46 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-46-lower-92.yml 92 92.0 92 92.0 no-three-in-line-47-lower-94 no-three-in-line-47 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-47-lower-94.yml 94 94.0 94 94.0 no-three-in-line-48-lower-96 no-three-in-line-48 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-48-lower-96.yml 96 96.0 96 96.0 no-three-in-line-49-lower-98 no-three-in-line-49 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-49-lower-98.yml 98 98.0 98 98.0 no-three-in-line-5-lower-10 no-three-in-line-5 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-5-lower-10.yml 10 10.0 10 10.0 no-three-in-line-50-lower-100 no-three-in-line-50 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-50-lower-100.yml 100 100.0 100 100.0 no-three-in-line-51-lower-102 no-three-in-line-51 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-51-lower-102.yml 102 102.0 102 102.0 no-three-in-line-52-lower-104 no-three-in-line-52 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-52-lower-104.yml 104 104.0 104 104.0 no-three-in-line-53-lower-106 no-three-in-line-53 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-53-lower-106.yml 106 106.0 106 106.0 no-three-in-line-54-lower-108 no-three-in-line-54 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-54-lower-108.yml 108 108.0 108 108.0 no-three-in-line-55-lower-110 no-three-in-line-55 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-55-lower-110.yml 110 110.0 110 110.0 no-three-in-line-56-lower-112 no-three-in-line-56 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-56-lower-112.yml 112 112.0 112 112.0 no-three-in-line-57-lower-114 no-three-in-line-57 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-57-lower-114.yml 114 114.0 114 114.0 no-three-in-line-58-lower-116 no-three-in-line-58 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-58-lower-116.yml 116 116.0 116 116.0 no-three-in-line-59-lower-118 no-three-in-line-59 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-59-lower-118.yml 118 118.0 118 118.0 no-three-in-line-6-lower-12 no-three-in-line-6 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-6-lower-12.yml 12 12.0 12 12.0 no-three-in-line-60-lower-120 no-three-in-line-60 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-60-lower-120.yml 120 120.0 120 120.0 no-three-in-line-61-lower-122 no-three-in-line-61 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-61-lower-122.yml 122 122.0 122 122.0 no-three-in-line-62-lower-124 no-three-in-line-62 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-62-lower-124.yml 124 124.0 124 124.0 no-three-in-line-63-lower-126 no-three-in-line-63 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-63-lower-126.yml 126 126.0 126 126.0 no-three-in-line-64-lower-128 no-three-in-line-64 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026 certificates/no-three-in-line/no-three-in-line-64-lower-128.yml 128 128.0 128 128.0 no-three-in-line-65-lower-130 no-three-in-line-65 no-three-in-line lower witness daniel-munro 2026-11-05 True equal heule-2026-06-18 certificates/no-three-in-line/no-three-in-line-65-lower-130.yml 130 130.0 130 130.0 no-three-in-line-66-lower-132 no-three-in-line-66 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026-03-09 certificates/no-three-in-line/no-three-in-line-66-lower-132.yml 132 132.0 132 132.0 no-three-in-line-67-lower-134 no-three-in-line-67 no-three-in-line lower witness daniel-munro 2026-11-05 True equal heule-2026-06-21 certificates/no-three-in-line/no-three-in-line-67-lower-134.yml 134 134.0 134 134.0 no-three-in-line-68-lower-136 no-three-in-line-68 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026-03-23 certificates/no-three-in-line/no-three-in-line-68-lower-136.yml 136 136.0 136 136.0 no-three-in-line-69-lower-138 no-three-in-line-69 no-three-in-line lower witness daniel-munro 2026-11-05 True equal heule-2026-06-21 certificates/no-three-in-line/no-three-in-line-69-lower-138.yml 138 138.0 138 138.0 no-three-in-line-7-lower-14 no-three-in-line-7 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-7-lower-14.yml 14 14.0 14 14.0 no-three-in-line-70-lower-140 no-three-in-line-70 no-three-in-line lower witness daniel-munro 2026-11-05 True equal heule-2026-06-17 certificates/no-three-in-line/no-three-in-line-70-lower-140.yml 140 140.0 140 140.0 no-three-in-line-71-lower-142 no-three-in-line-71 no-three-in-line lower witness daniel-munro 2026-11-05 True equal heule-2026-08-17 certificates/no-three-in-line/no-three-in-line-71-lower-142.yml 142 142.0 142 142.0 no-three-in-line-72-lower-144 no-three-in-line-72 no-three-in-line lower witness daniel-munro 2026-11-05 True equal heule-2026-06-25 certificates/no-three-in-line/no-three-in-line-72-lower-144.yml 144 144.0 144 144.0 no-three-in-line-73-lower-146 no-three-in-line-73 no-three-in-line lower witness daniel-munro 2026-11-05 True equal heule-2026-08-19 certificates/no-three-in-line/no-three-in-line-73-lower-146.yml 146 146.0 146 146.0 no-three-in-line-74-lower-148 no-three-in-line-74 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026-07-20 certificates/no-three-in-line/no-three-in-line-74-lower-148.yml 148 148.0 148 148.0 no-three-in-line-75-lower-148 no-three-in-line-75 no-three-in-line lower witness daniel-munro 2026-11-05 True new certificates/no-three-in-line/no-three-in-line-75-lower-148.yml 148 148.0 no-three-in-line-76-lower-152 no-three-in-line-76 no-three-in-line lower witness daniel-munro 2026-11-05 True equal heule-2026-08-10 certificates/no-three-in-line/no-three-in-line-76-lower-152.yml 152 152.0 152 152.0 no-three-in-line-77-lower-152 no-three-in-line-77 no-three-in-line lower witness daniel-munro 2026-11-05 True new certificates/no-three-in-line/no-three-in-line-77-lower-152.yml 152 152.0 no-three-in-line-78-lower-156 no-three-in-line-78 no-three-in-line lower witness daniel-munro 2026-11-05 True equal prellberg-2026-10-28 certificates/no-three-in-line/no-three-in-line-78-lower-156.yml 156 156.0 156 156.0 no-three-in-line-8-lower-16 no-three-in-line-8 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-8-lower-16.yml 16 16.0 16 16.0 no-three-in-line-9-lower-18 no-three-in-line-9 no-three-in-line lower witness daniel-munro 2026-11-05 True equal flammenkamp-no3in certificates/no-three-in-line/no-three-in-line-9-lower-18.yml 18 18.0 18 18.0 affine-line-arrangements-1-lower-1 affine-line-arrangements-1 affine-line-arrangements lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements/affine-line-arrangements-1-lower-1.yml 1 1.0 1 1.0 affine-line-arrangements-2-lower-2 affine-line-arrangements-2 affine-line-arrangements lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements/affine-line-arrangements-2-lower-2.yml 2 2.0 2 2.0 affine-line-arrangements-3-lower-4 affine-line-arrangements-3 affine-line-arrangements lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements/affine-line-arrangements-3-lower-4.yml 4 4.0 4 4.0 affine-line-arrangements-4-lower-9 affine-line-arrangements-4 affine-line-arrangements lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements/affine-line-arrangements-4-lower-9.yml 9 9.0 9 9.0 affine-line-arrangements-5-lower-47 affine-line-arrangements-5 affine-line-arrangements lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements/affine-line-arrangements-5-lower-47.yml 47 47.0 47 47.0 affine-line-arrangements-6-lower-791 affine-line-arrangements-6 affine-line-arrangements lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements/affine-line-arrangements-6-lower-791.yml 791 791.0 791 791.0 affine-line-arrangements-general-position-1-lower-1 affine-line-arrangements-general-position-1 affine-line-arrangements-general-position lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-1-lower-1.yml 1 1.0 1 1.0 affine-line-arrangements-general-position-2-lower-1 affine-line-arrangements-general-position-2 affine-line-arrangements-general-position lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-2-lower-1.yml 1 1.0 1 1.0 affine-line-arrangements-general-position-3-lower-1 affine-line-arrangements-general-position-3 affine-line-arrangements-general-position lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-3-lower-1.yml 1 1.0 1 1.0 affine-line-arrangements-general-position-4-lower-1 affine-line-arrangements-general-position-4 affine-line-arrangements-general-position lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-4-lower-1.yml 1 1.0 1 1.0 affine-line-arrangements-general-position-5-lower-6 affine-line-arrangements-general-position-5 affine-line-arrangements-general-position lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-5-lower-6.yml 6 6.0 6 6.0 affine-line-arrangements-general-position-6-lower-43 affine-line-arrangements-general-position-6 affine-line-arrangements-general-position lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-6-lower-43.yml 43 43.0 43 43.0 affine-line-arrangements-general-position-7-lower-922 affine-line-arrangements-general-position-7 affine-line-arrangements-general-position lower witness daniel-munro 2026-11-04 True equal certificates/affine-line-arrangements-general-position/affine-line-arrangements-general-position-7-lower-922.yml 922 922.0 922 922.0 coil-in-the-box-10-lower-374 coil-in-the-box-10 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal orland-et-al-2026 certificates/coil-in-the-box/coil-in-the-box-10-lower-374.yml 374 374.0 374 374.0 coil-in-the-box-11-lower-740 coil-in-the-box-11 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal echols-2026-07-23 certificates/coil-in-the-box/coil-in-the-box-11-lower-740.yml 740 740.0 740 740.0 coil-in-the-box-12-lower-1468 coil-in-the-box-12 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal echols-2026-07-22 certificates/coil-in-the-box/coil-in-the-box-12-lower-1468.yml 1468 1468.0 1468 1468.0 coil-in-the-box-13-lower-2930 coil-in-the-box-13 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal echols-2026-08-29 certificates/coil-in-the-box/coil-in-the-box-13-lower-2930.yml 2930 2930.0 2930 2930.0 coil-in-the-box-2-lower-4 coil-in-the-box-2 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal certificates/coil-in-the-box/coil-in-the-box-2-lower-4.yml 4 4.0 4 4.0 coil-in-the-box-3-lower-6 coil-in-the-box-3 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal certificates/coil-in-the-box/coil-in-the-box-3-lower-6.yml 6 6.0 6 6.0 coil-in-the-box-4-lower-8 coil-in-the-box-4 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal certificates/coil-in-the-box/coil-in-the-box-4-lower-8.yml 8 8.0 8 8.0 coil-in-the-box-5-lower-14 coil-in-the-box-5 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal certificates/coil-in-the-box/coil-in-the-box-5-lower-14.yml 14 14.0 14 14.0 coil-in-the-box-6-lower-26 coil-in-the-box-6 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal certificates/coil-in-the-box/coil-in-the-box-6-lower-26.yml 26 26.0 26 26.0 coil-in-the-box-7-lower-48 coil-in-the-box-7 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal kochut-1996 certificates/coil-in-the-box/coil-in-the-box-7-lower-48.yml 48 48.0 48 48.0 coil-in-the-box-8-lower-96 coil-in-the-box-8 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal ostergard-pettersson-2014-coil certificates/coil-in-the-box/coil-in-the-box-8-lower-96.yml 96 96.0 96 96.0 coil-in-the-box-9-lower-192 coil-in-the-box-9 coil-in-the-box lower witness daniel-munro 2026-11-04 True equal orland-et-al-2026 certificates/coil-in-the-box/coil-in-the-box-9-lower-192.yml 192 192.0 192 192.0 schur-8-lower-5372 schur-8 schur lower lean darkhipo 2026-11-04 True equal chen-zhu-long-2026 certificates/schur/schur-8-lower-5372.yml 5372 5372.0 5372 5372.0 snake-in-the-box-1-lower-1 snake-in-the-box-1 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal certificates/snake-in-the-box/snake-in-the-box-1-lower-1.yml 1 1.0 1 1.0 snake-in-the-box-10-lower-379 snake-in-the-box-10 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal orland-et-al-2026 certificates/snake-in-the-box/snake-in-the-box-10-lower-379.yml 379 379.0 379 379.0 snake-in-the-box-11-lower-750 snake-in-the-box-11 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal echols-2026-08-29 certificates/snake-in-the-box/snake-in-the-box-11-lower-750.yml 750 750.0 750 750.0 snake-in-the-box-12-lower-1480 snake-in-the-box-12 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal itty-2026 certificates/snake-in-the-box/snake-in-the-box-12-lower-1480.yml 1480 1480.0 1480 1480.0 snake-in-the-box-13-lower-2946 snake-in-the-box-13 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal toner-2026 certificates/snake-in-the-box/snake-in-the-box-13-lower-2946.yml 2946 2946.0 2946 2946.0 snake-in-the-box-2-lower-2 snake-in-the-box-2 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal certificates/snake-in-the-box/snake-in-the-box-2-lower-2.yml 2 2.0 2 2.0 snake-in-the-box-3-lower-4 snake-in-the-box-3 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal certificates/snake-in-the-box/snake-in-the-box-3-lower-4.yml 4 4.0 4 4.0 snake-in-the-box-4-lower-7 snake-in-the-box-4 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal certificates/snake-in-the-box/snake-in-the-box-4-lower-7.yml 7 7.0 7 7.0 snake-in-the-box-5-lower-13 snake-in-the-box-5 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal certificates/snake-in-the-box/snake-in-the-box-5-lower-13.yml 13 13.0 13 13.0 snake-in-the-box-6-lower-26 snake-in-the-box-6 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal certificates/snake-in-the-box/snake-in-the-box-6-lower-26.yml 26 26.0 26 26.0 snake-in-the-box-7-lower-50 snake-in-the-box-7 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal potter-et-al-1994 certificates/snake-in-the-box/snake-in-the-box-7-lower-50.yml 50 50.0 50 50.0 snake-in-the-box-8-lower-98 snake-in-the-box-8 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal carlson-hougen-2010 certificates/snake-in-the-box/snake-in-the-box-8-lower-98.yml 98 98.0 98 98.0 snake-in-the-box-9-lower-191 snake-in-the-box-9 snake-in-the-box lower witness daniel-munro 2026-11-04 True equal orland-et-al-2026 certificates/snake-in-the-box/snake-in-the-box-9-lower-191.yml 191 191.0 191 191.0 golomb-ruler-1-upper-0 golomb-ruler-1 golomb-ruler upper witness daniel-munro 2026-11-03 True equal certificates/golomb-ruler/golomb-ruler-1-upper-0.yml 0 0.0 0 0.0 golomb-ruler-10-upper-55 golomb-ruler-10 golomb-ruler upper witness daniel-munro 2026-11-03 True equal robinson-bernstein-1967 certificates/golomb-ruler/golomb-ruler-10-upper-55.yml 55 55.0 55 55.0 golomb-ruler-11-upper-72 golomb-ruler-11 golomb-ruler upper witness daniel-munro 2026-11-03 True equal robinson-bernstein-1967 certificates/golomb-ruler/golomb-ruler-11-upper-72.yml 72 72.0 72 72.0 golomb-ruler-12-upper-85 golomb-ruler-12 golomb-ruler upper witness daniel-munro 2026-11-03 True equal robinson-bernstein-1967 certificates/golomb-ruler/golomb-ruler-12-upper-85.yml 85 85.0 85 85.0 golomb-ruler-13-upper-106 golomb-ruler-13 golomb-ruler upper witness daniel-munro 2026-11-03 True equal robinson-1983 certificates/golomb-ruler/golomb-ruler-13-upper-106.yml 106 106.0 106 106.0 golomb-ruler-14-upper-127 golomb-ruler-14 golomb-ruler upper witness daniel-munro 2026-11-03 True equal robinson-bernstein-1967 certificates/golomb-ruler/golomb-ruler-14-upper-127.yml 127 127.0 127 127.0 golomb-ruler-15-upper-151 golomb-ruler-15 golomb-ruler upper witness daniel-munro 2026-11-03 True equal shearer-1990 certificates/golomb-ruler/golomb-ruler-15-upper-151.yml 151 151.0 151 151.0 golomb-ruler-16-upper-177 golomb-ruler-16 golomb-ruler upper witness daniel-munro 2026-11-03 True equal shearer-1990 certificates/golomb-ruler/golomb-ruler-16-upper-177.yml 177 177.0 177 177.0 golomb-ruler-17-upper-199 golomb-ruler-17 golomb-ruler upper witness daniel-munro 2026-11-03 True equal atkinson-hassenklover-1984 certificates/golomb-ruler/golomb-ruler-17-upper-199.yml 199 199.0 199 199.0 golomb-ruler-18-upper-216 golomb-ruler-18 golomb-ruler upper witness daniel-munro 2026-11-03 True equal robinson-bernstein-1967 certificates/golomb-ruler/golomb-ruler-18-upper-216.yml 216 216.0 216 216.0 golomb-ruler-19-upper-246 golomb-ruler-19 golomb-ruler upper witness daniel-munro 2026-11-03 True equal robinson-bernstein-1967 certificates/golomb-ruler/golomb-ruler-19-upper-246.yml 246 246.0 246 246.0 golomb-ruler-2-upper-1 golomb-ruler-2 golomb-ruler upper witness daniel-munro 2026-11-03 True equal certificates/golomb-ruler/golomb-ruler-2-upper-1.yml 1 1.0 1 1.0 golomb-ruler-20-upper-283 golomb-ruler-20 golomb-ruler upper witness daniel-munro 2026-11-03 True equal robinson-bernstein-1967 certificates/golomb-ruler/golomb-ruler-20-upper-283.yml 283 283.0 283 283.0 golomb-ruler-21-upper-333 golomb-ruler-21 golomb-ruler upper witness daniel-munro 2026-11-03 True equal robinson-bernstein-1967 certificates/golomb-ruler/golomb-ruler-21-upper-333.yml 333 333.0 333 333.0 golomb-ruler-22-upper-356 golomb-ruler-22 golomb-ruler upper witness daniel-munro 2026-11-03 True equal atkinson-hassenklover-1984 certificates/golomb-ruler/golomb-ruler-22-upper-356.yml 356 356.0 356 356.0 golomb-ruler-23-upper-372 golomb-ruler-23 golomb-ruler upper witness daniel-munro 2026-11-03 True equal robinson-bernstein-1967 certificates/golomb-ruler/golomb-ruler-23-upper-372.yml 372 372.0 372 372.0 golomb-ruler-24-upper-425 golomb-ruler-24 golomb-ruler upper witness daniel-munro 2026-11-03 True equal robinson-bernstein-1967 certificates/golomb-ruler/golomb-ruler-24-upper-425.yml 425 425.0 425 425.0 golomb-ruler-25-upper-480 golomb-ruler-25 golomb-ruler upper witness daniel-munro 2026-11-03 True equal atkinson-hassenklover-1984 certificates/golomb-ruler/golomb-ruler-25-upper-480.yml 480 480.0 480 480.0 golomb-ruler-26-upper-492 golomb-ruler-26 golomb-ruler upper witness daniel-munro 2026-11-03 True equal atkinson-hassenklover-1984 certificates/golomb-ruler/golomb-ruler-26-upper-492.yml 492 492.0 492 492.0 golomb-ruler-27-upper-553 golomb-ruler-27 golomb-ruler upper witness daniel-munro 2026-11-03 True equal atkinson-hassenklover-1984 certificates/golomb-ruler/golomb-ruler-27-upper-553.yml 553 553.0 553 553.0 golomb-ruler-28-upper-585 golomb-ruler-28 golomb-ruler upper witness daniel-munro 2026-11-03 True equal atkinson-hassenklover-1984 certificates/golomb-ruler/golomb-ruler-28-upper-585.yml 585 585.0 585 585.0 golomb-ruler-29-upper-623 golomb-ruler-29 golomb-ruler upper witness daniel-munro 2026-11-03 True equal atkinson-hassenklover-1984 certificates/golomb-ruler/golomb-ruler-29-upper-623.yml 623 623.0 623 623.0 golomb-ruler-3-upper-3 golomb-ruler-3 golomb-ruler upper witness daniel-munro 2026-11-03 True equal certificates/golomb-ruler/golomb-ruler-3-upper-3.yml 3 3.0 3 3.0 golomb-ruler-30-upper-680 golomb-ruler-30 golomb-ruler upper witness daniel-munro 2026-11-03 True equal atkinson-hassenklover-1984 certificates/golomb-ruler/golomb-ruler-30-upper-680.yml 680 680.0 680 680.0 golomb-ruler-4-upper-6 golomb-ruler-4 golomb-ruler upper witness daniel-munro 2026-11-03 True equal certificates/golomb-ruler/golomb-ruler-4-upper-6.yml 6 6.0 6 6.0 golomb-ruler-5-upper-11 golomb-ruler-5 golomb-ruler upper witness daniel-munro 2026-11-03 True equal babcock-1953 certificates/golomb-ruler/golomb-ruler-5-upper-11.yml 11 11.0 11 11.0 golomb-ruler-6-upper-17 golomb-ruler-6 golomb-ruler upper witness daniel-munro 2026-11-03 True equal babcock-1953 certificates/golomb-ruler/golomb-ruler-6-upper-17.yml 17 17.0 17 17.0 golomb-ruler-7-upper-25 golomb-ruler-7 golomb-ruler upper witness daniel-munro 2026-11-03 True equal babcock-1953 certificates/golomb-ruler/golomb-ruler-7-upper-25.yml 25 25.0 25 25.0 golomb-ruler-8-upper-34 golomb-ruler-8 golomb-ruler upper witness daniel-munro 2026-11-03 True equal babcock-1953 certificates/golomb-ruler/golomb-ruler-8-upper-34.yml 34 34.0 34 34.0 golomb-ruler-9-upper-44 golomb-ruler-9 golomb-ruler upper witness daniel-munro 2026-11-03 True equal mixon-1972 certificates/golomb-ruler/golomb-ruler-9-upper-44.yml 44 44.0 44 44.0 schur-1-lower-1 schur-1 schur lower witness daniel-munro 2026-11-03 True equal certificates/schur/schur-1-lower-1.yml 1 1.0 1 1.0 schur-2-lower-4 schur-2 schur lower witness daniel-munro 2026-11-03 True equal certificates/schur/schur-2-lower-4.yml 4 4.0 4 4.0 schur-3-lower-13 schur-3 schur lower witness daniel-munro 2026-11-03 True equal certificates/schur/schur-3-lower-13.yml 13 13.0 13 13.0 schur-4-lower-44 schur-4 schur lower witness daniel-munro 2026-11-03 True equal golomb-baumert-1965 certificates/schur/schur-4-lower-44.yml 44 44.0 44 44.0 schur-5-lower-160 schur-5 schur lower witness daniel-munro 2026-11-03 True equal exoo-1994 certificates/schur/schur-5-lower-160.yml 160 160.0 160 160.0 schur-6-lower-537 schur-6 schur lower witness daniel-munro 2026-11-03 True equal chen-zhu-long-2026 certificates/schur/schur-6-lower-537.yml 537 537.0 537 537.0 schur-7-lower-1696 schur-7 schur lower witness daniel-munro 2026-11-03 True equal rowley-2021 certificates/schur/schur-7-lower-1696.yml 1696 1696.0 1696 1696.0 van-der-waerden-2-11-lower-193942 van-der-waerden-2-11 van-der-waerden lower witness daniel-munro 2026-11-03 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-2-11-lower-193942.yml 193942 193942.0 193,942 193942 193942.0 193,942 van-der-waerden-2-5-lower-178 van-der-waerden-2-5 van-der-waerden lower witness daniel-munro 2026-11-03 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-2-5-lower-178.yml 178 178.0 178 178.0 van-der-waerden-2-6-lower-1132 van-der-waerden-2-6 van-der-waerden lower witness daniel-munro 2026-11-03 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-2-6-lower-1132.yml 1132 1132.0 1132 1132.0 van-der-waerden-2-8-lower-11496 van-der-waerden-2-8 van-der-waerden lower witness daniel-munro 2026-11-03 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-2-8-lower-11496.yml 11496 11496.0 11,496 11496 11496.0 11,496 van-der-waerden-2-9-lower-41266 van-der-waerden-2-9 van-der-waerden lower witness daniel-munro 2026-11-03 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-2-9-lower-41266.yml 41266 41266.0 41,266 41266 41266.0 41,266 van-der-waerden-4-5-lower-17706 van-der-waerden-4-5 van-der-waerden lower witness daniel-munro 2026-11-03 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-4-5-lower-17706.yml 17706 17706.0 17,706 17706 17706.0 17,706 weak-schur-1-lower-2 weak-schur-1 weak-schur lower witness daniel-munro 2026-11-03 True equal certificates/weak-schur/weak-schur-1-lower-2.yml 2 2.0 2 2.0 weak-schur-2-lower-8 weak-schur-2 weak-schur lower witness daniel-munro 2026-11-03 True equal certificates/weak-schur/weak-schur-2-lower-8.yml 8 8.0 8 8.0 weak-schur-3-lower-23 weak-schur-3 weak-schur lower witness daniel-munro 2026-11-03 True equal certificates/weak-schur/weak-schur-3-lower-23.yml 23 23.0 23 23.0 weak-schur-4-lower-66 weak-schur-4 weak-schur lower witness daniel-munro 2026-11-03 True equal certificates/weak-schur/weak-schur-4-lower-66.yml 66 66.0 66 66.0 weak-schur-5-lower-207 weak-schur-5 weak-schur lower witness daniel-munro 2026-11-03 True equal rowley-2025 certificates/weak-schur/weak-schur-5-lower-207.yml 207 207.0 207 207.0 weak-schur-6-lower-650 weak-schur-6 weak-schur lower witness daniel-munro 2026-11-03 True equal rodrigo-2026 certificates/weak-schur/weak-schur-6-lower-650.yml 650 650.0 650 650.0 degree-diameter-10-3-lower-366 degree-diameter-10-3 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-10-3-lower-366.yml 366 366.0 650 650.0 degree-diameter-11-2-lower-98 degree-diameter-11-2 degree-diameter lower witness daniel-munro 2026-11-02 True weaker mmsgraphs certificates/degree-diameter/degree-diameter-11-2-lower-98.yml 98 98.0 106 106.0 degree-diameter-11-3-lower-420 degree-diameter-11-3 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-11-3-lower-420.yml 420 420.0 715 715.0 degree-diameter-12-3-lower-558 degree-diameter-12-3 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-12-3-lower-558.yml 558 558.0 810 810.0 degree-diameter-13-2-lower-162 degree-diameter-13-2 degree-diameter lower witness daniel-munro 2026-11-02 True equal mmsgraphs certificates/degree-diameter/degree-diameter-13-2-lower-162.yml 162 162.0 162 162.0 degree-diameter-13-3-lower-630 degree-diameter-13-3 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-13-3-lower-630.yml 630 630.0 972 972.0 degree-diameter-14-3-lower-791 degree-diameter-14-3 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-14-3-lower-791.yml 791 791.0 1201 1201.0 degree-diameter-15-2-lower-183 degree-diameter-15-2 degree-diameter lower witness daniel-munro 2026-11-02 True weaker brown-1966 certificates/degree-diameter/degree-diameter-15-2-lower-183.yml 183 183.0 190 190.0 degree-diameter-15-3-lower-812 degree-diameter-15-3 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-15-3-lower-812.yml 812 812.0 1620 1620.0 degree-diameter-16-2-lower-183 degree-diameter-16-2 degree-diameter lower witness daniel-munro 2026-11-02 True weaker brown-1966 certificates/degree-diameter/degree-diameter-16-2-lower-183.yml 183 183.0 216 216.0 degree-diameter-16-3-lower-1055 degree-diameter-16-3 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-16-3-lower-1055.yml 1055 1055.0 1920 1920.0 degree-diameter-17-2-lower-274 degree-diameter-17-2 degree-diameter lower witness daniel-munro 2026-11-02 True equal brown-1966 certificates/degree-diameter/degree-diameter-17-2-lower-274.yml 274 274.0 274 274.0 degree-diameter-19-2-lower-338 degree-diameter-19-2 degree-diameter lower witness daniel-munro 2026-11-02 True equal mmsgraphs certificates/degree-diameter/degree-diameter-19-2-lower-338.yml 338 338.0 338 338.0 degree-diameter-3-10-lower-820 degree-diameter-3-10 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-3-10-lower-820.yml 820 820.0 1250 1250.0 degree-diameter-3-3-lower-20 degree-diameter-3-3 degree-diameter lower witness daniel-munro 2026-11-02 True equal certificates/degree-diameter/degree-diameter-3-3-lower-20.yml 20 20.0 20 20.0 degree-diameter-3-4-lower-38 degree-diameter-3-4 degree-diameter lower witness daniel-munro 2026-11-02 True equal certificates/degree-diameter/degree-diameter-3-4-lower-38.yml 38 38.0 38 38.0 degree-diameter-3-5-lower-64 degree-diameter-3-5 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-3-5-lower-64.yml 64 64.0 70 70.0 degree-diameter-3-6-lower-64 degree-diameter-3-6 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-3-6-lower-64.yml 64 64.0 132 132.0 degree-diameter-3-7-lower-162 degree-diameter-3-7 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-3-7-lower-162.yml 162 162.0 200 200.0 degree-diameter-3-8-lower-272 degree-diameter-3-8 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-3-8-lower-272.yml 272 272.0 360 360.0 degree-diameter-3-9-lower-506 degree-diameter-3-9 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-3-9-lower-506.yml 506 506.0 600 600.0 degree-diameter-4-2-lower-15 degree-diameter-4-2 degree-diameter lower witness daniel-munro 2026-11-02 True equal certificates/degree-diameter/degree-diameter-4-2-lower-15.yml 15 15.0 15 15.0 degree-diameter-4-3-lower-41 degree-diameter-4-3 degree-diameter lower witness daniel-munro 2026-11-02 True equal certificates/degree-diameter/degree-diameter-4-3-lower-41.yml 41 41.0 41 41.0 degree-diameter-4-4-lower-84 degree-diameter-4-4 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-4-4-lower-84.yml 84 84.0 104 104.0 degree-diameter-4-5-lower-205 degree-diameter-4-5 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-4-5-lower-205.yml 205 205.0 364 364.0 degree-diameter-4-6-lower-513 degree-diameter-4-6 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-4-6-lower-513.yml 513 513.0 760 760.0 degree-diameter-4-7-lower-1155 degree-diameter-4-7 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-4-7-lower-1155.yml 1155 1155.0 1344 1344.0 degree-diameter-5-2-lower-24 degree-diameter-5-2 degree-diameter lower witness daniel-munro 2026-11-02 True equal certificates/degree-diameter/degree-diameter-5-2-lower-24.yml 24 24.0 24 24.0 degree-diameter-5-3-lower-54 degree-diameter-5-3 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-5-3-lower-54.yml 54 54.0 72 72.0 degree-diameter-5-4-lower-210 degree-diameter-5-4 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-5-4-lower-210.yml 210 210.0 252 252.0 degree-diameter-5-5-lower-506 degree-diameter-5-5 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-5-5-lower-506.yml 506 506.0 650 650.0 degree-diameter-6-2-lower-32 degree-diameter-6-2 degree-diameter lower witness daniel-munro 2026-11-02 True equal mmsgraphs certificates/degree-diameter/degree-diameter-6-2-lower-32.yml 32 32.0 32 32.0 degree-diameter-6-3-lower-90 degree-diameter-6-3 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-6-3-lower-90.yml 90 90.0 120 120.0 degree-diameter-6-4-lower-355 degree-diameter-6-4 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-6-4-lower-355.yml 355 355.0 441 441.0 degree-diameter-6-5-lower-1395 degree-diameter-6-5 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-6-5-lower-1395.yml 1395 1395.0 1518 1518.0 degree-diameter-7-3-lower-140 degree-diameter-7-3 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-7-3-lower-140.yml 140 140.0 170 170.0 degree-diameter-7-4-lower-602 degree-diameter-7-4 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-7-4-lower-602.yml 602 602.0 684 684.0 degree-diameter-8-3-lower-253 degree-diameter-8-3 degree-diameter lower witness daniel-munro 2026-11-02 True equal certificates/degree-diameter/degree-diameter-8-3-lower-253.yml 253 253.0 253 253.0 degree-diameter-8-4-lower-1029 degree-diameter-8-4 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-8-4-lower-1029.yml 1029 1029.0 1100 1100.0 degree-diameter-9-2-lower-74 degree-diameter-9-2 degree-diameter lower witness daniel-munro 2026-11-02 True equal brown-1966 certificates/degree-diameter/degree-diameter-9-2-lower-74.yml 74 74.0 74 74.0 degree-diameter-9-3-lower-256 degree-diameter-9-3 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-9-3-lower-256.yml 256 256.0 585 585.0 degree-diameter-9-4-lower-1254 degree-diameter-9-4 degree-diameter lower witness daniel-munro 2026-11-02 True weaker certificates/degree-diameter/degree-diameter-9-4-lower-1254.yml 1254 1254.0 1768 1768.0 ramsey-3-10-lower-39 ramsey-3-10 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-3-10-lower-39.yml 39 39.0 40 40.0 ramsey-3-11-lower-46 ramsey-3-11 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-3-11-lower-46.yml 46 46.0 47 47.0 ramsey-3-12-lower-49 ramsey-3-12 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-3-12-lower-49.yml 49 49.0 53 53.0 ramsey-3-13-lower-58 ramsey-3-13 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-3-13-lower-58.yml 58 58.0 61 61.0 ramsey-3-14-lower-64 ramsey-3-14 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-3-14-lower-64.yml 64 64.0 67 67.0 ramsey-3-15-lower-72 ramsey-3-15 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-3-15-lower-72.yml 72 72.0 74 74.0 ramsey-3-6-lower-18 ramsey-3-6 ramsey lower witness daniel-munro 2026-11-02 True equal certificates/ramsey/ramsey-3-6-lower-18.yml 18 18.0 18 18.0 ramsey-3-7-lower-23 ramsey-3-7 ramsey lower witness daniel-munro 2026-11-02 True equal certificates/ramsey/ramsey-3-7-lower-23.yml 23 23.0 23 23.0 ramsey-3-8-lower-28 ramsey-3-8 ramsey lower witness daniel-munro 2026-11-02 True equal certificates/ramsey/ramsey-3-8-lower-28.yml 28 28.0 28 28.0 ramsey-3-9-lower-36 ramsey-3-9 ramsey lower witness daniel-munro 2026-11-02 True equal certificates/ramsey/ramsey-3-9-lower-36.yml 36 36.0 36 36.0 ramsey-4-5-lower-25 ramsey-4-5 ramsey lower witness daniel-munro 2026-11-02 True equal certificates/ramsey/ramsey-4-5-lower-25.yml 25 25.0 25 25.0 ramsey-4-6-lower-34 ramsey-4-6 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-4-6-lower-34.yml 34 34.0 36 36.0 ramsey-4-7-lower-47 ramsey-4-7 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-4-7-lower-47.yml 47 47.0 49 49.0 ramsey-4-8-lower-52 ramsey-4-8 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-4-8-lower-52.yml 52 52.0 59 59.0 ramsey-4-9-lower-69 ramsey-4-9 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-4-9-lower-69.yml 69 69.0 73 73.0 ramsey-5-5-lower-42 ramsey-5-5 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-5-5-lower-42.yml 42 42.0 43 43.0 ramsey-5-6-lower-54 ramsey-5-6 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-5-6-lower-54.yml 54 54.0 59 59.0 ramsey-5-7-lower-71 ramsey-5-7 ramsey lower witness daniel-munro 2026-11-02 True weaker certificates/ramsey/ramsey-5-7-lower-71.yml 71 71.0 80 80.0 ramsey-7-7-lower-205 ramsey-7-7 ramsey lower witness daniel-munro 2026-11-02 True equal mathon-1987 certificates/ramsey/ramsey-7-7-lower-205.yml 205 205.0 205 205.0 ramsey-8-8-lower-282 ramsey-8-8 ramsey lower witness daniel-munro 2026-11-02 True equal burling-reyner-1972 certificates/ramsey/ramsey-8-8-lower-282.yml 282 282.0 282 282.0 circle-in-equilateral-1-lower-2sqrt3 circle-in-equilateral-1 circle-in-equilateral lower lean daniel-munro 2026-11-01 True equal certificates/circle-in-equilateral/circle-in-equilateral-1-lower-2sqrt3.yml 2\sqrt{3} 3.464102 ≈3.464102 2\sqrt{3} 3.464102 ≈3.464102 circle-in-equilateral-1-upper-2sqrt3 circle-in-equilateral-1 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal certificates/circle-in-equilateral/circle-in-equilateral-1-upper-2sqrt3.yml 2\sqrt{3} 3.464102 ≈3.464102 2\sqrt{3} 3.464102 ≈3.464102 circle-in-equilateral-10-lower-6-2sqrt3 circle-in-equilateral-10 circle-in-equilateral lower lean daniel-munro 2026-11-01 True equal certificates/circle-in-equilateral/circle-in-equilateral-10-lower-6-2sqrt3.yml 6+2\sqrt{3} 9.464102 ≈9.464102 6+2\sqrt{3} 9.464102 ≈9.464102 circle-in-equilateral-10-upper-6-2sqrt3 circle-in-equilateral-10 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal oler-groemer-1961 certificates/circle-in-equilateral/circle-in-equilateral-10-upper-6-2sqrt3.yml 6+2\sqrt{3} 9.464102 ≈9.464102 6+2\sqrt{3} 9.464102 ≈9.464102 circle-in-equilateral-11-upper-4-2sqrt3-4sqrt6over3 circle-in-equilateral-11 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal melissen-1994a certificates/circle-in-equilateral/circle-in-equilateral-11-upper-4-2sqrt3-4sqrt6over3.yml 4+2\sqrt{3}+\frac{4\sqrt{6}}{3} 10.73009 ≈10.73009 4+2\sqrt{3}+\frac{4\sqrt{6}}{3} 10.73009 ≈10.73009 circle-in-equilateral-12-upper-4-4sqrt3 circle-in-equilateral-12 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal melissen-1994b certificates/circle-in-equilateral/circle-in-equilateral-12-upper-4-4sqrt3.yml 4+4\sqrt{3} 10.9282 ≈10.9282 4+4\sqrt{3} 10.9282 ≈10.9282 circle-in-equilateral-13-upper-4-10sqrt3over3-2sqrt6over3 circle-in-equilateral-13 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal melissen-1993 certificates/circle-in-equilateral/circle-in-equilateral-13-upper-4-10sqrt3over3-2sqrt6over3.yml 4+\frac{10\sqrt{3}}{3}+\frac{2\sqrt{6}}{3} 11.4065 ≈11.4065 4+\frac{2\sqrt{6}}{3} + \frac{10\sqrt{3}}{3} 11.4065 ≈11.4065 circle-in-equilateral-14-upper-8-2sqrt3 circle-in-equilateral-14 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal oler-groemer-1961 certificates/circle-in-equilateral/circle-in-equilateral-14-upper-8-2sqrt3.yml 8+2\sqrt{3} 11.4641 ≈11.4641 8+2\sqrt{3} 11.4641 ≈11.4641 circle-in-equilateral-15-upper-8-2sqrt3 circle-in-equilateral-15 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal oler-groemer-1961 certificates/circle-in-equilateral/circle-in-equilateral-15-upper-8-2sqrt3.yml 8+2\sqrt{3} 11.4641 ≈11.4641 8+2\sqrt{3} 11.4641 ≈11.4641 circle-in-equilateral-2-lower-2-2sqrt3 circle-in-equilateral-2 circle-in-equilateral lower lean daniel-munro 2026-11-01 True equal certificates/circle-in-equilateral/circle-in-equilateral-2-lower-2-2sqrt3.yml 2+2\sqrt{3} 5.464102 ≈5.464102 2+2\sqrt{3} 5.464102 ≈5.464102 circle-in-equilateral-2-upper-2-2sqrt3 circle-in-equilateral-2 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal certificates/circle-in-equilateral/circle-in-equilateral-2-upper-2-2sqrt3.yml 2+2\sqrt{3} 5.464102 ≈5.464102 2+2\sqrt{3} 5.464102 ≈5.464102 circle-in-equilateral-3-lower-2-2sqrt3 circle-in-equilateral-3 circle-in-equilateral lower lean daniel-munro 2026-11-01 True equal certificates/circle-in-equilateral/circle-in-equilateral-3-lower-2-2sqrt3.yml 2+2\sqrt{3} 5.464102 ≈5.464102 2+2\sqrt{3} 5.464102 ≈5.464102 circle-in-equilateral-3-upper-2-2sqrt3 circle-in-equilateral-3 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal certificates/circle-in-equilateral/circle-in-equilateral-3-upper-2-2sqrt3.yml 2+2\sqrt{3} 5.464102 ≈5.464102 2+2\sqrt{3} 5.464102 ≈5.464102 circle-in-equilateral-4-lower-4sqrt3 circle-in-equilateral-4 circle-in-equilateral lower lean daniel-munro 2026-11-01 True equal certificates/circle-in-equilateral/circle-in-equilateral-4-lower-4sqrt3.yml 4\sqrt{3} 6.928203 ≈6.928203 4\sqrt{3} 6.928203 ≈6.928203 circle-in-equilateral-4-upper-4sqrt3 circle-in-equilateral-4 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal milano-1987 certificates/circle-in-equilateral/circle-in-equilateral-4-upper-4sqrt3.yml 4\sqrt{3} 6.928203 ≈6.928203 4\sqrt{3} 6.928203 ≈6.928203 circle-in-equilateral-5-lower-4-2sqrt3 circle-in-equilateral-5 circle-in-equilateral lower lean daniel-munro 2026-11-01 True equal certificates/circle-in-equilateral/circle-in-equilateral-5-lower-4-2sqrt3.yml 4+2\sqrt{3} 7.464102 ≈7.464102 4+2\sqrt{3} 7.464102 ≈7.464102 circle-in-equilateral-5-upper-4-2sqrt3 circle-in-equilateral-5 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal oler-groemer-1961 certificates/circle-in-equilateral/circle-in-equilateral-5-upper-4-2sqrt3.yml 4+2\sqrt{3} 7.464102 ≈7.464102 4+2\sqrt{3} 7.464102 ≈7.464102 circle-in-equilateral-6-lower-4-2sqrt3 circle-in-equilateral-6 circle-in-equilateral lower lean daniel-munro 2026-11-01 True equal certificates/circle-in-equilateral/circle-in-equilateral-6-lower-4-2sqrt3.yml 4+2\sqrt{3} 7.464102 ≈7.464102 4+2\sqrt{3} 7.464102 ≈7.464102 circle-in-equilateral-6-upper-4-2sqrt3 circle-in-equilateral-6 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal oler-groemer-1961 certificates/circle-in-equilateral/circle-in-equilateral-6-upper-4-2sqrt3.yml 4+2\sqrt{3} 7.464102 ≈7.464102 4+2\sqrt{3} 7.464102 ≈7.464102 circle-in-equilateral-7-upper-2-4sqrt3 circle-in-equilateral-7 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal melissen-1993 certificates/circle-in-equilateral/circle-in-equilateral-7-upper-2-4sqrt3.yml 2+4\sqrt{3} 8.928203 ≈8.928203 2+4\sqrt{3} 8.928203 ≈8.928203 circle-in-equilateral-8-upper-2-2sqrt3-2sqrt33over3 circle-in-equilateral-8 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal melissen-1993 certificates/circle-in-equilateral/circle-in-equilateral-8-upper-2-2sqrt3-2sqrt33over3.yml 2+2\sqrt{3}+\frac{2\sqrt{33}}{3} 9.29381 ≈9.29381 2+2\sqrt{3}+\frac{2\sqrt{33}}{3} 9.29381 ≈9.29381 circle-in-equilateral-9-upper-6-2sqrt3 circle-in-equilateral-9 circle-in-equilateral upper witness daniel-munro 2026-11-01 True equal melissen-1993 certificates/circle-in-equilateral/circle-in-equilateral-9-upper-6-2sqrt3.yml 6+2\sqrt{3} 9.464102 ≈9.464102 6+2\sqrt{3} 9.464102 ≈9.464102 van-der-waerden-2-10-lower-103475 van-der-waerden-2-10 van-der-waerden lower witness daniel-munro 2026-10-31 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-2-10-lower-103475.yml 103475 103475.0 103,475 103475 103475.0 103,475 van-der-waerden-2-7-lower-3704 van-der-waerden-2-7 van-der-waerden lower witness daniel-munro 2026-10-31 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-2-7-lower-3704.yml 3704 3704.0 3704 3704.0 van-der-waerden-3-4-lower-293 van-der-waerden-3-4 van-der-waerden lower witness daniel-munro 2026-10-31 True equal rabung-1979 certificates/van-der-waerden/van-der-waerden-3-4-lower-293.yml 293 293.0 293 293.0 van-der-waerden-3-8-lower-238401 van-der-waerden-3-8 van-der-waerden lower witness daniel-munro 2026-10-31 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-3-8-lower-238401.yml 238401 238401.0 238,401 238401 238401.0 238,401 van-der-waerden-4-3-lower-76 van-der-waerden-4-3 van-der-waerden lower witness daniel-munro 2026-10-31 True equal rabung-1979 certificates/van-der-waerden/van-der-waerden-4-3-lower-76.yml 76 76.0 76 76.0 van-der-waerden-4-4-lower-1049 van-der-waerden-4-4 van-der-waerden lower witness daniel-munro 2026-10-31 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-4-4-lower-1049.yml 1049 1049.0 1049 1049.0 van-der-waerden-5-4-lower-2255 van-der-waerden-5-4 van-der-waerden lower witness daniel-munro 2026-10-31 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-5-4-lower-2255.yml 2255 2255.0 2255 2255.0 van-der-waerden-6-4-lower-9779 van-der-waerden-6-4 van-der-waerden lower witness daniel-munro 2026-10-31 True equal rabung-lotts-2012 certificates/van-der-waerden/van-der-waerden-6-4-lower-9779.yml 9779 9779.0 9779 9779.0 kissing-number-1-lower-2 kissing-number-1 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-1-lower-2.yml 2 2.0 2 2.0 kissing-number-10-lower-336 kissing-number-10 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-10-lower-336.yml 336 336.0 510 510.0 kissing-number-11-lower-438 kissing-number-11 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-11-lower-438.yml 438 438.0 604 604.0 kissing-number-12-lower-756 kissing-number-12 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-12-lower-756.yml 756 756.0 841 841.0 kissing-number-13-lower-906 kissing-number-13 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-13-lower-906.yml 906 906.0 1154 1154.0 kissing-number-14-lower-1422 kissing-number-14 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-14-lower-1422.yml 1422 1422.0 1932 1932.0 kissing-number-15-lower-2340 kissing-number-15 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-15-lower-2340.yml 2340 2340.0 2564 2564.0 kissing-number-16-lower-4320 kissing-number-16 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-16-lower-4320.yml 4320 4320.0 4320 4320.0 kissing-number-17-lower-5346 kissing-number-17 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-17-lower-5346.yml 5346 5346.0 5730 5730.0 kissing-number-18-lower-7398 kissing-number-18 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-18-lower-7398.yml 7398 7398.0 8358 8358.0 kissing-number-19-lower-10668 kissing-number-19 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-19-lower-10668.yml 10668 10668.0 10,668 12460 12460.0 12,460 kissing-number-2-lower-6 kissing-number-2 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-2-lower-6.yml 6 6.0 6 6.0 kissing-number-20-lower-17400 kissing-number-20 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-20-lower-17400.yml 17400 17400.0 17,400 19448 19448.0 19,448 kissing-number-21-lower-27720 kissing-number-21 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-21-lower-27720.yml 27720 27720.0 27,720 31560 31560.0 31,560 kissing-number-22-lower-49896 kissing-number-22 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-22-lower-49896.yml 49896 49896.0 49,896 49896 49896.0 49,896 kissing-number-23-lower-93150 kissing-number-23 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-23-lower-93150.yml 93150 93150.0 93,150 93150 93150.0 93,150 kissing-number-24-lower-196560 kissing-number-24 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-24-lower-196560.yml 196560 196560.0 196,560 196560 196560.0 196,560 kissing-number-3-lower-12 kissing-number-3 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-3-lower-12.yml 12 12.0 12 12.0 kissing-number-4-lower-24 kissing-number-4 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-4-lower-24.yml 24 24.0 24 24.0 kissing-number-5-lower-40 kissing-number-5 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-5-lower-40.yml 40 40.0 40 40.0 kissing-number-6-lower-72 kissing-number-6 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-6-lower-72.yml 72 72.0 72 72.0 kissing-number-7-lower-126 kissing-number-7 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-7-lower-126.yml 126 126.0 126 126.0 kissing-number-8-lower-240 kissing-number-8 kissing-number lower witness daniel-munro 2026-10-30 True equal certificates/kissing-number/kissing-number-8-lower-240.yml 240 240.0 240 240.0 kissing-number-9-lower-272 kissing-number-9 kissing-number lower witness daniel-munro 2026-10-30 True weaker certificates/kissing-number/kissing-number-9-lower-272.yml 272 272.0 306 306.0 square-packing-in-square-1-lower-1 square-packing-in-square-1 square-packing lower lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-1-lower-1.yml 1 1.0 1 1.0 square-packing-in-square-1-upper-1 square-packing-in-square-1 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-1-upper-1.yml 1 1.0 1 1.0 square-packing-in-square-10-lower-sqrt10 square-packing-in-square-10 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-10-lower-sqrt10.yml \sqrt{10} 3.162278 ≈3.162278 3 + \frac{1}{\sqrt{2}} 3.707107 ≈3.707107 square-packing-in-square-10-upper-4 square-packing-in-square-10 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-10-upper-4.yml 4 4.0 3 + \frac{1}{\sqrt{2}} 3.707107 ≈3.707107 square-packing-in-square-100-lower-10 square-packing-in-square-100 square-packing lower lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-100-lower-10.yml 10 10.0 10 10.0 square-packing-in-square-100-upper-10 square-packing-in-square-100 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-100-upper-10.yml 10 10.0 10 10.0 square-packing-in-square-11-lower-sqrt11 square-packing-in-square-11 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-11-lower-sqrt11.yml \sqrt{11} 3.316625 ≈3.316625 2 + \frac{4}{\sqrt{5}} 3.788854 ≈3.788854 square-packing-in-square-11-upper-4 square-packing-in-square-11 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-11-upper-4.yml 4 4.0 {\approx}3.8771 3.8771 square-packing-in-square-12-lower-sqrt12 square-packing-in-square-12 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-12-lower-sqrt12.yml \sqrt{12} 3.464102 ≈3.464102 2 + \frac{4}{\sqrt{5}} 3.788854 ≈3.788854 square-packing-in-square-12-upper-4 square-packing-in-square-12 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-12-upper-4.yml 4 4.0 4 4.0 square-packing-in-square-13-lower-sqrt13 square-packing-in-square-13 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-13-lower-sqrt13.yml \sqrt{13} 3.605551 ≈3.605551 4 4.0 square-packing-in-square-13-upper-4 square-packing-in-square-13 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-13-upper-4.yml 4 4.0 4 4.0 square-packing-in-square-14-lower-sqrt14 square-packing-in-square-14 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-14-lower-sqrt14.yml \sqrt{14} 3.741657 ≈3.741657 4 4.0 square-packing-in-square-14-upper-4 square-packing-in-square-14 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-14-upper-4.yml 4 4.0 4 4.0 square-packing-in-square-15-lower-sqrt15 square-packing-in-square-15 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-15-lower-sqrt15.yml \sqrt{15} 3.872983 ≈3.872983 4 4.0 square-packing-in-square-15-upper-4 square-packing-in-square-15 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-15-upper-4.yml 4 4.0 4 4.0 square-packing-in-square-16-lower-4 square-packing-in-square-16 square-packing lower lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-16-lower-4.yml 4 4.0 4 4.0 square-packing-in-square-16-upper-4 square-packing-in-square-16 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-16-upper-4.yml 4 4.0 4 4.0 square-packing-in-square-17-lower-sqrt17 square-packing-in-square-17 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-17-lower-sqrt17.yml \sqrt{17} 4.123106 ≈4.123106 \frac{40\sqrt{2}+19}{17} 4.445208 ≈4.445208 square-packing-in-square-17-upper-5 square-packing-in-square-17 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-17-upper-5.yml 5 5.0 {\approx}4.6755 4.6755 square-packing-in-square-18-lower-sqrt18 square-packing-in-square-18 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-18-lower-sqrt18.yml \sqrt{18} 4.242641 ≈4.242641 \frac{40\sqrt{2}+19}{17} 4.445208 ≈4.445208 square-packing-in-square-18-upper-5 square-packing-in-square-18 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-18-upper-5.yml 5 5.0 \frac{7+\sqrt{7}}{2} 4.822876 ≈4.822876 square-packing-in-square-19-lower-sqrt19 square-packing-in-square-19 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-19-lower-sqrt19.yml \sqrt{19} 4.358899 ≈4.358899 6\sqrt{2}-4 4.485281 ≈4.485281 square-packing-in-square-19-upper-5 square-packing-in-square-19 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-19-upper-5.yml 5 5.0 3+\frac{4\sqrt{2}}{3} 4.885618 ≈4.885618 square-packing-in-square-2-lower-sqrt2 square-packing-in-square-2 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-2-lower-sqrt2.yml \sqrt{2} 1.414214 ≈1.414214 2 2.0 square-packing-in-square-2-upper-2 square-packing-in-square-2 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-2-upper-2.yml 2 2.0 2 2.0 square-packing-in-square-20-lower-sqrt20 square-packing-in-square-20 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-20-lower-sqrt20.yml \sqrt{20} 4.472136 ≈4.472136 6\sqrt{2}-4 4.485281 ≈4.485281 square-packing-in-square-20-upper-5 square-packing-in-square-20 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-20-upper-5.yml 5 5.0 5 5.0 square-packing-in-square-21-lower-sqrt21 square-packing-in-square-21 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-21-lower-sqrt21.yml \sqrt{21} 4.582576 ≈4.582576 4.7438 4.7438 square-packing-in-square-21-upper-5 square-packing-in-square-21 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-21-upper-5.yml 5 5.0 5 5.0 square-packing-in-square-22-lower-sqrt22 square-packing-in-square-22 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-22-lower-sqrt22.yml \sqrt{22} 4.690416 ≈4.690416 5 5.0 square-packing-in-square-22-upper-5 square-packing-in-square-22 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-22-upper-5.yml 5 5.0 5 5.0 square-packing-in-square-23-lower-sqrt23 square-packing-in-square-23 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-23-lower-sqrt23.yml \sqrt{23} 4.795832 ≈4.795832 5 5.0 square-packing-in-square-23-upper-5 square-packing-in-square-23 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-23-upper-5.yml 5 5.0 5 5.0 square-packing-in-square-24-lower-sqrt24 square-packing-in-square-24 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-24-lower-sqrt24.yml \sqrt{24} 4.898979 ≈4.898979 5 5.0 square-packing-in-square-24-upper-5 square-packing-in-square-24 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-24-upper-5.yml 5 5.0 5 5.0 square-packing-in-square-25-lower-5 square-packing-in-square-25 square-packing lower lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-25-lower-5.yml 5 5.0 5 5.0 square-packing-in-square-25-upper-5 square-packing-in-square-25 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-25-upper-5.yml 5 5.0 5 5.0 square-packing-in-square-26-lower-sqrt26 square-packing-in-square-26 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-26-lower-sqrt26.yml \sqrt{26} 5.09902 ≈5.09902 2\sqrt{2}+\frac{27+2\sqrt{10}}{13} 5.391854 ≈5.391854 square-packing-in-square-26-upper-6 square-packing-in-square-26 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-26-upper-6.yml 6 6.0 \frac{7}{2}+\frac{3\sqrt{2}}{2} 5.62132 ≈5.62132 square-packing-in-square-27-lower-sqrt27 square-packing-in-square-27 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-27-lower-sqrt27.yml \sqrt{27} 5.196152 ≈5.196152 2\sqrt{2}+\frac{27+2\sqrt{10}}{13} 5.391854 ≈5.391854 square-packing-in-square-27-upper-6 square-packing-in-square-27 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-27-upper-6.yml 6 6.0 5+\frac{1}{\sqrt{2}} 5.707107 ≈5.707107 square-packing-in-square-28-lower-sqrt28 square-packing-in-square-28 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-28-lower-sqrt28.yml \sqrt{28} 5.291503 ≈5.291503 2\sqrt{2}+\frac{6}{\sqrt{5}} 5.511709 ≈5.511709 square-packing-in-square-28-upper-6 square-packing-in-square-28 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-28-upper-6.yml 6 6.0 {\approx}5.8244 5.8244 square-packing-in-square-29-lower-sqrt29 square-packing-in-square-29 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-29-lower-sqrt29.yml \sqrt{29} 5.385165 ≈5.385165 2\sqrt{2}+\frac{6}{\sqrt{5}} 5.511709 ≈5.511709 square-packing-in-square-29-upper-6 square-packing-in-square-29 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-29-upper-6.yml 6 6.0 {\approx}5.9338 5.9338 square-packing-in-square-3-lower-sqrt3 square-packing-in-square-3 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-3-lower-sqrt3.yml \sqrt{3} 1.732051 ≈1.732051 2 2.0 square-packing-in-square-3-upper-2 square-packing-in-square-3 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-3-upper-2.yml 2 2.0 2 2.0 square-packing-in-square-30-lower-sqrt30 square-packing-in-square-30 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-30-lower-sqrt30.yml \sqrt{30} 5.477226 ≈5.477226 2\sqrt{2}+\frac{6}{\sqrt{5}} 5.511709 ≈5.511709 square-packing-in-square-30-upper-6 square-packing-in-square-30 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-30-upper-6.yml 6 6.0 6 6.0 square-packing-in-square-31-lower-sqrt31 square-packing-in-square-31 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-31-lower-sqrt31.yml \sqrt{31} 5.567764 ≈5.567764 5.6415 5.6415 square-packing-in-square-31-upper-6 square-packing-in-square-31 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-31-upper-6.yml 6 6.0 6 6.0 square-packing-in-square-32-lower-sqrt32 square-packing-in-square-32 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-32-lower-sqrt32.yml \sqrt{32} 5.656854 ≈5.656854 square-packing-in-square-32-upper-6 square-packing-in-square-32 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-32-upper-6.yml 6 6.0 6 6.0 square-packing-in-square-33-lower-sqrt33 square-packing-in-square-33 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-33-lower-sqrt33.yml \sqrt{33} 5.744563 ≈5.744563 6 6.0 square-packing-in-square-33-upper-6 square-packing-in-square-33 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-33-upper-6.yml 6 6.0 6 6.0 square-packing-in-square-34-lower-sqrt34 square-packing-in-square-34 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-34-lower-sqrt34.yml \sqrt{34} 5.830952 ≈5.830952 6 6.0 square-packing-in-square-34-upper-6 square-packing-in-square-34 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-34-upper-6.yml 6 6.0 6 6.0 square-packing-in-square-35-lower-sqrt35 square-packing-in-square-35 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-35-lower-sqrt35.yml \sqrt{35} 5.91608 ≈5.91608 6 6.0 square-packing-in-square-35-upper-6 square-packing-in-square-35 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-35-upper-6.yml 6 6.0 6 6.0 square-packing-in-square-36-lower-6 square-packing-in-square-36 square-packing lower lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-36-lower-6.yml 6 6.0 6 6.0 square-packing-in-square-36-upper-6 square-packing-in-square-36 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-36-upper-6.yml 6 6.0 6 6.0 square-packing-in-square-37-lower-sqrt37 square-packing-in-square-37 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-37-lower-sqrt37.yml \sqrt{37} 6.082763 ≈6.082763 2\sqrt{2}+\frac{113+10\sqrt{3}}{37} 6.350603 ≈6.350603 square-packing-in-square-37-upper-7 square-packing-in-square-37 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-37-upper-7.yml 7 7.0 {\approx}6.5986 6.5986 square-packing-in-square-38-lower-sqrt38 square-packing-in-square-38 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-38-lower-sqrt38.yml \sqrt{38} 6.164414 ≈6.164414 2\sqrt{2}+\frac{113+10\sqrt{3}}{37} 6.350603 ≈6.350603 square-packing-in-square-38-upper-7 square-packing-in-square-38 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-38-upper-7.yml 7 7.0 6+\frac{1}{\sqrt{2}} 6.707107 ≈6.707107 square-packing-in-square-39-lower-sqrt39 square-packing-in-square-39 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-39-lower-sqrt39.yml \sqrt{39} 6.244998 ≈6.244998 2\sqrt{2}+\frac{113+10\sqrt{3}}{37} 6.350603 ≈6.350603 square-packing-in-square-39-upper-7 square-packing-in-square-39 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-39-upper-7.yml 7 7.0 {\approx}6.8107 6.8107 square-packing-in-square-4-lower-2 square-packing-in-square-4 square-packing lower lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-4-lower-2.yml 2 2.0 2 2.0 square-packing-in-square-4-upper-2 square-packing-in-square-4 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-4-upper-2.yml 2 2.0 2 2.0 square-packing-in-square-40-lower-sqrt40 square-packing-in-square-40 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-40-lower-sqrt40.yml \sqrt{40} 6.324555 ≈6.324555 2\sqrt{2}+\frac{8}{\sqrt{5}} 6.406136 ≈6.406136 square-packing-in-square-40-upper-7 square-packing-in-square-40 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-40-upper-7.yml 7 7.0 4+2\sqrt{2} 6.828427 ≈6.828427 square-packing-in-square-41-lower-sqrt41 square-packing-in-square-41 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-41-lower-sqrt41.yml \sqrt{41} 6.403124 ≈6.403124 2\sqrt{2}+\frac{8}{\sqrt{5}} 6.406136 ≈6.406136 square-packing-in-square-41-upper-7 square-packing-in-square-41 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-41-upper-7.yml 7 7.0 {\approx}6.9267 6.9267 square-packing-in-square-42-lower-sqrt42 square-packing-in-square-42 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-42-lower-sqrt42.yml \sqrt{42} 6.480741 ≈6.480741 square-packing-in-square-42-upper-7 square-packing-in-square-42 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-42-upper-7.yml 7 7.0 7 7.0 square-packing-in-square-43-lower-sqrt43 square-packing-in-square-43 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-43-lower-sqrt43.yml \sqrt{43} 6.557439 ≈6.557439 square-packing-in-square-43-upper-7 square-packing-in-square-43 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-43-upper-7.yml 7 7.0 7 7.0 square-packing-in-square-44-lower-sqrt44 square-packing-in-square-44 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-44-lower-sqrt44.yml \sqrt{44} 6.63325 ≈6.63325 square-packing-in-square-44-upper-7 square-packing-in-square-44 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-44-upper-7.yml 7 7.0 7 7.0 square-packing-in-square-45-lower-sqrt45 square-packing-in-square-45 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-45-lower-sqrt45.yml \sqrt{45} 6.708204 ≈6.708204 square-packing-in-square-45-upper-7 square-packing-in-square-45 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-45-upper-7.yml 7 7.0 7 7.0 square-packing-in-square-46-lower-sqrt46 square-packing-in-square-46 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-46-lower-sqrt46.yml \sqrt{46} 6.78233 ≈6.78233 7 7.0 square-packing-in-square-46-upper-7 square-packing-in-square-46 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-46-upper-7.yml 7 7.0 7 7.0 square-packing-in-square-47-lower-sqrt47 square-packing-in-square-47 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-47-lower-sqrt47.yml \sqrt{47} 6.855655 ≈6.855655 7 7.0 square-packing-in-square-47-upper-7 square-packing-in-square-47 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-47-upper-7.yml 7 7.0 7 7.0 square-packing-in-square-48-lower-sqrt48 square-packing-in-square-48 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-48-lower-sqrt48.yml \sqrt{48} 6.928203 ≈6.928203 7 7.0 square-packing-in-square-48-upper-7 square-packing-in-square-48 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-48-upper-7.yml 7 7.0 7 7.0 square-packing-in-square-49-lower-7 square-packing-in-square-49 square-packing lower lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-49-lower-7.yml 7 7.0 7 7.0 square-packing-in-square-49-upper-7 square-packing-in-square-49 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-49-upper-7.yml 7 7.0 7 7.0 square-packing-in-square-5-lower-sqrt5 square-packing-in-square-5 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-5-lower-sqrt5.yml \sqrt{5} 2.236068 ≈2.236068 2 + \frac{1}{\sqrt{2}} 2.707107 ≈2.707107 square-packing-in-square-5-upper-3 square-packing-in-square-5 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-5-upper-3.yml 3 3.0 2 + \frac{1}{\sqrt{2}} 2.707107 ≈2.707107 square-packing-in-square-50-lower-sqrt50 square-packing-in-square-50 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-50-lower-sqrt50.yml \sqrt{50} 7.071068 ≈7.071068 2\sqrt{2}+\frac{101+3\sqrt{14}}{25} 7.317426 ≈7.317426 square-packing-in-square-50-upper-8 square-packing-in-square-50 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-50-upper-8.yml 8 8.0 7+\frac{4}{7} 7.571429 ≈7.571429 square-packing-in-square-51-lower-sqrt51 square-packing-in-square-51 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-51-lower-sqrt51.yml \sqrt{51} 7.141428 ≈7.141428 2\sqrt{2}+\frac{101+3\sqrt{14}}{25} 7.317426 ≈7.317426 square-packing-in-square-51-upper-8 square-packing-in-square-51 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-51-upper-8.yml 8 8.0 {\approx}7.7008 7.7008 square-packing-in-square-52-lower-sqrt52 square-packing-in-square-52 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-52-lower-sqrt52.yml \sqrt{52} 7.211103 ≈7.211103 2\sqrt{2}+\frac{101+3\sqrt{14}}{25} 7.317426 ≈7.317426 square-packing-in-square-52-upper-8 square-packing-in-square-52 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-52-upper-8.yml 8 8.0 7+\frac{1}{\sqrt{2}} 7.707107 ≈7.707107 square-packing-in-square-53-lower-sqrt53 square-packing-in-square-53 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-53-lower-sqrt53.yml \sqrt{53} 7.28011 ≈7.28011 2\sqrt{2}+\frac{101+3\sqrt{14}}{25} 7.317426 ≈7.317426 square-packing-in-square-53-upper-8 square-packing-in-square-53 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-53-upper-8.yml 8 8.0 \frac{13}{2}+\frac{\sqrt{7}}{2} 7.822876 ≈7.822876 square-packing-in-square-54-lower-sqrt54 square-packing-in-square-54 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-54-lower-sqrt54.yml \sqrt{54} 7.348469 ≈7.348469 square-packing-in-square-54-upper-8 square-packing-in-square-54 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-54-upper-8.yml 8 8.0 7-\frac{\sqrt{2}}{2}+\sqrt{1+\sqrt{2}} 7.846667 ≈7.846667 square-packing-in-square-55-lower-sqrt55 square-packing-in-square-55 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-55-lower-sqrt55.yml \sqrt{55} 7.416198 ≈7.416198 square-packing-in-square-55-upper-8 square-packing-in-square-55 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-55-upper-8.yml 8 8.0 {\approx}7.9458 7.9458 square-packing-in-square-56-lower-sqrt56 square-packing-in-square-56 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-56-lower-sqrt56.yml \sqrt{56} 7.483315 ≈7.483315 square-packing-in-square-56-upper-8 square-packing-in-square-56 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-56-upper-8.yml 8 8.0 8 8.0 square-packing-in-square-57-lower-sqrt57 square-packing-in-square-57 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-57-lower-sqrt57.yml \sqrt{57} 7.549834 ≈7.549834 square-packing-in-square-57-upper-8 square-packing-in-square-57 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-57-upper-8.yml 8 8.0 8 8.0 square-packing-in-square-58-lower-sqrt58 square-packing-in-square-58 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-58-lower-sqrt58.yml \sqrt{58} 7.615773 ≈7.615773 square-packing-in-square-58-upper-8 square-packing-in-square-58 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-58-upper-8.yml 8 8.0 8 8.0 square-packing-in-square-59-lower-sqrt59 square-packing-in-square-59 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-59-lower-sqrt59.yml \sqrt{59} 7.681146 ≈7.681146 square-packing-in-square-59-upper-8 square-packing-in-square-59 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-59-upper-8.yml 8 8.0 8 8.0 square-packing-in-square-6-lower-sqrt6 square-packing-in-square-6 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-6-lower-sqrt6.yml \sqrt{6} 2.44949 ≈2.44949 3 3.0 square-packing-in-square-6-upper-3 square-packing-in-square-6 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-6-upper-3.yml 3 3.0 3 3.0 square-packing-in-square-60-lower-sqrt60 square-packing-in-square-60 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-60-lower-sqrt60.yml \sqrt{60} 7.745967 ≈7.745967 square-packing-in-square-60-upper-8 square-packing-in-square-60 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-60-upper-8.yml 8 8.0 8 8.0 square-packing-in-square-61-lower-sqrt61 square-packing-in-square-61 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-61-lower-sqrt61.yml \sqrt{61} 7.81025 ≈7.81025 square-packing-in-square-61-upper-8 square-packing-in-square-61 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-61-upper-8.yml 8 8.0 8 8.0 square-packing-in-square-62-lower-sqrt62 square-packing-in-square-62 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-62-lower-sqrt62.yml \sqrt{62} 7.874008 ≈7.874008 8 8.0 square-packing-in-square-62-upper-8 square-packing-in-square-62 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-62-upper-8.yml 8 8.0 8 8.0 square-packing-in-square-63-lower-sqrt63 square-packing-in-square-63 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-63-lower-sqrt63.yml \sqrt{63} 7.937254 ≈7.937254 8 8.0 square-packing-in-square-63-upper-8 square-packing-in-square-63 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-63-upper-8.yml 8 8.0 8 8.0 square-packing-in-square-64-lower-8 square-packing-in-square-64 square-packing lower lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-64-lower-8.yml 8 8.0 8 8.0 square-packing-in-square-64-upper-8 square-packing-in-square-64 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-64-upper-8.yml 8 8.0 8 8.0 square-packing-in-square-65-lower-sqrt65 square-packing-in-square-65 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-65-lower-sqrt65.yml \sqrt{65} 8.062258 ≈8.062258 2\sqrt{2}+\frac{71}{13} 8.289966 ≈8.289966 square-packing-in-square-65-upper-9 square-packing-in-square-65 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-65-upper-9.yml 9 9.0 5+\frac{5}{\sqrt{2}} 8.535534 ≈8.535534 square-packing-in-square-66-lower-sqrt66 square-packing-in-square-66 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-66-lower-sqrt66.yml \sqrt{66} 8.124038 ≈8.124038 2\sqrt{2}+\frac{71}{13} 8.289966 ≈8.289966 square-packing-in-square-66-upper-9 square-packing-in-square-66 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-66-upper-9.yml 9 9.0 3+4\sqrt{2} 8.656854 ≈8.656854 square-packing-in-square-67-lower-sqrt67 square-packing-in-square-67 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-67-lower-sqrt67.yml \sqrt{67} 8.185353 ≈8.185353 2\sqrt{2}+\frac{71}{13} 8.289966 ≈8.289966 square-packing-in-square-67-upper-9 square-packing-in-square-67 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-67-upper-9.yml 9 9.0 8+\frac{1}{\sqrt{2}} 8.707107 ≈8.707107 square-packing-in-square-68-lower-sqrt68 square-packing-in-square-68 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-68-lower-sqrt68.yml \sqrt{68} 8.246211 ≈8.246211 2\sqrt{2}+\frac{71}{13} 8.289966 ≈8.289966 square-packing-in-square-68-upper-9 square-packing-in-square-68 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-68-upper-9.yml 9 9.0 {\approx}8.7988 8.7988 square-packing-in-square-69-lower-sqrt69 square-packing-in-square-69 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-69-lower-sqrt69.yml \sqrt{69} 8.306624 ≈8.306624 square-packing-in-square-69-upper-9 square-packing-in-square-69 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-69-upper-9.yml 9 9.0 {\approx}8.8272 8.8272 square-packing-in-square-7-lower-sqrt7 square-packing-in-square-7 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-7-lower-sqrt7.yml \sqrt{7} 2.645751 ≈2.645751 3 3.0 square-packing-in-square-7-upper-3 square-packing-in-square-7 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-7-upper-3.yml 3 3.0 3 3.0 square-packing-in-square-70-lower-sqrt70 square-packing-in-square-70 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-70-lower-sqrt70.yml \sqrt{70} 8.3666 ≈8.3666 square-packing-in-square-70-upper-9 square-packing-in-square-70 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-70-upper-9.yml 9 9.0 {\approx}8.8817 8.8817 square-packing-in-square-71-lower-sqrt71 square-packing-in-square-71 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-71-lower-sqrt71.yml \sqrt{71} 8.42615 ≈8.42615 square-packing-in-square-71-upper-9 square-packing-in-square-71 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-71-upper-9.yml 9 9.0 {\approx}8.9441 8.9441 square-packing-in-square-72-lower-sqrt72 square-packing-in-square-72 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-72-lower-sqrt72.yml \sqrt{72} 8.485281 ≈8.485281 square-packing-in-square-72-upper-9 square-packing-in-square-72 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-72-upper-9.yml 9 9.0 9 9.0 square-packing-in-square-73-lower-sqrt73 square-packing-in-square-73 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-73-lower-sqrt73.yml \sqrt{73} 8.544004 ≈8.544004 square-packing-in-square-73-upper-9 square-packing-in-square-73 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-73-upper-9.yml 9 9.0 9 9.0 square-packing-in-square-74-lower-sqrt74 square-packing-in-square-74 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-74-lower-sqrt74.yml \sqrt{74} 8.602325 ≈8.602325 square-packing-in-square-74-upper-9 square-packing-in-square-74 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-74-upper-9.yml 9 9.0 9 9.0 square-packing-in-square-75-lower-sqrt75 square-packing-in-square-75 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-75-lower-sqrt75.yml \sqrt{75} 8.660254 ≈8.660254 square-packing-in-square-75-upper-9 square-packing-in-square-75 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-75-upper-9.yml 9 9.0 9 9.0 square-packing-in-square-76-lower-sqrt76 square-packing-in-square-76 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-76-lower-sqrt76.yml \sqrt{76} 8.717798 ≈8.717798 square-packing-in-square-76-upper-9 square-packing-in-square-76 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-76-upper-9.yml 9 9.0 9 9.0 square-packing-in-square-77-lower-sqrt77 square-packing-in-square-77 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-77-lower-sqrt77.yml \sqrt{77} 8.774964 ≈8.774964 square-packing-in-square-77-upper-9 square-packing-in-square-77 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-77-upper-9.yml 9 9.0 9 9.0 square-packing-in-square-78-lower-sqrt78 square-packing-in-square-78 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-78-lower-sqrt78.yml \sqrt{78} 8.831761 ≈8.831761 square-packing-in-square-78-upper-9 square-packing-in-square-78 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-78-upper-9.yml 9 9.0 9 9.0 square-packing-in-square-79-lower-sqrt79 square-packing-in-square-79 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-79-lower-sqrt79.yml \sqrt{79} 8.888194 ≈8.888194 9 9.0 square-packing-in-square-79-upper-9 square-packing-in-square-79 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-79-upper-9.yml 9 9.0 9 9.0 square-packing-in-square-8-lower-sqrt8 square-packing-in-square-8 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-8-lower-sqrt8.yml \sqrt{8} 2.828427 ≈2.828427 3 3.0 square-packing-in-square-8-upper-3 square-packing-in-square-8 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-8-upper-3.yml 3 3.0 3 3.0 square-packing-in-square-80-lower-sqrt80 square-packing-in-square-80 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-80-lower-sqrt80.yml \sqrt{80} 8.944272 ≈8.944272 9 9.0 square-packing-in-square-80-upper-9 square-packing-in-square-80 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-80-upper-9.yml 9 9.0 9 9.0 square-packing-in-square-81-lower-9 square-packing-in-square-81 square-packing lower lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-81-lower-9.yml 9 9.0 9 9.0 square-packing-in-square-81-upper-9 square-packing-in-square-81 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-81-upper-9.yml 9 9.0 9 9.0 square-packing-in-square-82-lower-sqrt82 square-packing-in-square-82 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-82-lower-sqrt82.yml \sqrt{82} 9.055385 ≈9.055385 {\approx}9.2667 9.2667 square-packing-in-square-82-upper-10 square-packing-in-square-82 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-82-upper-10.yml 10 10.0 6+\frac{5}{\sqrt{2}} 9.535534 ≈9.535534 square-packing-in-square-83-lower-sqrt83 square-packing-in-square-83 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-83-lower-sqrt83.yml \sqrt{83} 9.110434 ≈9.110434 {\approx}9.2667 9.2667 square-packing-in-square-83-upper-10 square-packing-in-square-83 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-83-upper-10.yml 10 10.0 {\approx}9.6348 9.6348 square-packing-in-square-84-lower-sqrt84 square-packing-in-square-84 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-84-lower-sqrt84.yml \sqrt{84} 9.165151 ≈9.165151 {\approx}9.2667 9.2667 square-packing-in-square-84-upper-10 square-packing-in-square-84 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-84-upper-10.yml 10 10.0 9+\frac{1}{\sqrt{2}} 9.707107 ≈9.707107 square-packing-in-square-85-lower-sqrt85 square-packing-in-square-85 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-85-lower-sqrt85.yml \sqrt{85} 9.219544 ≈9.219544 {\approx}9.2667 9.2667 square-packing-in-square-85-upper-10 square-packing-in-square-85 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-85-upper-10.yml 10 10.0 \frac{11}{2}+3\sqrt{2} 9.742641 ≈9.742641 square-packing-in-square-86-lower-sqrt86 square-packing-in-square-86 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-86-lower-sqrt86.yml \sqrt{86} 9.273618 ≈9.273618 square-packing-in-square-86-upper-10 square-packing-in-square-86 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-86-upper-10.yml 10 10.0 \frac{17+\sqrt{7}}{2} 9.822876 ≈9.822876 square-packing-in-square-87-lower-sqrt87 square-packing-in-square-87 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-87-lower-sqrt87.yml \sqrt{87} 9.327379 ≈9.327379 square-packing-in-square-87-upper-10 square-packing-in-square-87 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-87-upper-10.yml 10 10.0 {\approx}9.8388 9.8388 square-packing-in-square-88-lower-sqrt88 square-packing-in-square-88 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-88-lower-sqrt88.yml \sqrt{88} 9.380832 ≈9.380832 square-packing-in-square-88-upper-10 square-packing-in-square-88 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-88-upper-10.yml 10 10.0 {\approx}9.8882 9.8882 square-packing-in-square-89-lower-sqrt89 square-packing-in-square-89 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-89-lower-sqrt89.yml \sqrt{89} 9.433981 ≈9.433981 square-packing-in-square-89-upper-10 square-packing-in-square-89 square-packing upper lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-89-upper-10.yml 10 10.0 5+\frac{7}{\sqrt{2}} 9.949747 ≈9.949747 square-packing-in-square-9-lower-3 square-packing-in-square-9 square-packing lower lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-9-lower-3.yml 3 3.0 3 3.0 square-packing-in-square-9-upper-3 square-packing-in-square-9 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-9-upper-3.yml 3 3.0 3 3.0 square-packing-in-square-90-lower-sqrt90 square-packing-in-square-90 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-90-lower-sqrt90.yml \sqrt{90} 9.486833 ≈9.486833 square-packing-in-square-90-upper-10 square-packing-in-square-90 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-90-upper-10.yml 10 10.0 10 10.0 square-packing-in-square-91-lower-sqrt91 square-packing-in-square-91 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-91-lower-sqrt91.yml \sqrt{91} 9.539392 ≈9.539392 square-packing-in-square-91-upper-10 square-packing-in-square-91 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-91-upper-10.yml 10 10.0 10 10.0 square-packing-in-square-92-lower-sqrt92 square-packing-in-square-92 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-92-lower-sqrt92.yml \sqrt{92} 9.591663 ≈9.591663 square-packing-in-square-92-upper-10 square-packing-in-square-92 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-92-upper-10.yml 10 10.0 10 10.0 square-packing-in-square-93-lower-sqrt93 square-packing-in-square-93 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-93-lower-sqrt93.yml \sqrt{93} 9.643651 ≈9.643651 square-packing-in-square-93-upper-10 square-packing-in-square-93 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-93-upper-10.yml 10 10.0 10 10.0 square-packing-in-square-94-lower-sqrt94 square-packing-in-square-94 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-94-lower-sqrt94.yml \sqrt{94} 9.69536 ≈9.69536 square-packing-in-square-94-upper-10 square-packing-in-square-94 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-94-upper-10.yml 10 10.0 10 10.0 square-packing-in-square-95-lower-sqrt95 square-packing-in-square-95 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-95-lower-sqrt95.yml \sqrt{95} 9.746794 ≈9.746794 square-packing-in-square-95-upper-10 square-packing-in-square-95 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-95-upper-10.yml 10 10.0 10 10.0 square-packing-in-square-96-lower-sqrt96 square-packing-in-square-96 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-96-lower-sqrt96.yml \sqrt{96} 9.797959 ≈9.797959 square-packing-in-square-96-upper-10 square-packing-in-square-96 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-96-upper-10.yml 10 10.0 10 10.0 square-packing-in-square-97-lower-sqrt97 square-packing-in-square-97 square-packing lower lean daniel-munro 2026-10-30 True new certificates/square-packing/square-packing-in-square-97-lower-sqrt97.yml \sqrt{97} 9.848858 ≈9.848858 square-packing-in-square-97-upper-10 square-packing-in-square-97 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-97-upper-10.yml 10 10.0 10 10.0 square-packing-in-square-98-lower-sqrt98 square-packing-in-square-98 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-98-lower-sqrt98.yml \sqrt{98} 9.899495 ≈9.899495 10 10.0 square-packing-in-square-98-upper-10 square-packing-in-square-98 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-98-upper-10.yml 10 10.0 10 10.0 square-packing-in-square-99-lower-sqrt99 square-packing-in-square-99 square-packing lower lean daniel-munro 2026-10-30 True weaker certificates/square-packing/square-packing-in-square-99-lower-sqrt99.yml \sqrt{99} 9.949874 ≈9.949874 10 10.0 square-packing-in-square-99-upper-10 square-packing-in-square-99 square-packing upper lean daniel-munro 2026-10-30 True equal certificates/square-packing/square-packing-in-square-99-upper-10.yml 10 10.0 10 10.0 cage-10-10-lower-14762 cage-10-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-10-lower-14762.yml 14762 14762.0 14,762 cage-10-11-lower-73811 cage-10-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-11-lower-73811.yml 73811 73811.0 73,811 cage-10-12-lower-132860 cage-10-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-12-lower-132860.yml 132860 132860.0 132,860 cage-10-13-lower-664301 cage-10-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-13-lower-664301.yml 664301 664301.0 664,301 cage-10-14-lower-1195742 cage-10-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-14-lower-1195742.yml 1195742 1195742.0 1,195,742 cage-10-15-lower-5978711 cage-10-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-15-lower-5978711.yml 5978711 5978711.0 5,978,711 cage-10-16-lower-10761680 cage-10-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-16-lower-10761680.yml 10761680 10761680.0 10,761,680 cage-10-3-lower-11 cage-10-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-3-lower-11.yml 11 11.0 cage-10-4-lower-20 cage-10-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-4-lower-20.yml 20 20.0 cage-10-5-lower-101 cage-10-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-10-5-lower-101.yml 101 101.0 103 103.0 cage-10-6-lower-182 cage-10-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-10-6-lower-182.yml 182 182.0 182 182.0 cage-10-7-lower-911 cage-10-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-7-lower-911.yml 911 911.0 cage-10-8-lower-1640 cage-10-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-8-lower-1640.yml 1640 1640.0 cage-10-9-lower-8201 cage-10-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-10-9-lower-8201.yml 8201 8201.0 cage-11-10-lower-22222 cage-11-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-10-lower-22222.yml 22222 22222.0 22,222 cage-11-11-lower-122222 cage-11-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-11-lower-122222.yml 122222 122222.0 122,222 cage-11-12-lower-222222 cage-11-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-12-lower-222222.yml 222222 222222.0 222,222 cage-11-13-lower-1222222 cage-11-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-13-lower-1222222.yml 1222222 1222222.0 1,222,222 cage-11-14-lower-2222222 cage-11-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-14-lower-2222222.yml 2222222 2222222.0 2,222,222 cage-11-15-lower-12222222 cage-11-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-15-lower-12222222.yml 12222222 12222222.0 12,222,222 cage-11-16-lower-22222222 cage-11-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-16-lower-22222222.yml 22222222 22222222.0 22,222,222 cage-11-3-lower-12 cage-11-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-3-lower-12.yml 12 12.0 cage-11-4-lower-22 cage-11-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-4-lower-22.yml 22 22.0 cage-11-5-lower-122 cage-11-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-11-5-lower-122.yml 122 122.0 124 124.0 cage-11-6-lower-222 cage-11-6 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-11-6-lower-222.yml 222 222.0 224 224.0 cage-11-7-lower-1222 cage-11-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-7-lower-1222.yml 1222 1222.0 cage-11-8-lower-2222 cage-11-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-8-lower-2222.yml 2222 2222.0 cage-11-9-lower-12222 cage-11-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-11-9-lower-12222.yml 12222 12222.0 12,222 cage-12-10-lower-32210 cage-12-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-10-lower-32210.yml 32210 32210.0 32,210 cage-12-11-lower-193261 cage-12-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-11-lower-193261.yml 193261 193261.0 193,261 cage-12-12-lower-354312 cage-12-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-12-lower-354312.yml 354312 354312.0 354,312 cage-12-13-lower-2125873 cage-12-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-13-lower-2125873.yml 2125873 2125873.0 2,125,873 cage-12-14-lower-3897434 cage-12-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-14-lower-3897434.yml 3897434 3897434.0 3,897,434 cage-12-15-lower-23384605 cage-12-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-15-lower-23384605.yml 23384605 23384605.0 23,384,605 cage-12-16-lower-42871776 cage-12-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-16-lower-42871776.yml 42871776 42871776.0 42,871,776 cage-12-3-lower-13 cage-12-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-3-lower-13.yml 13 13.0 cage-12-4-lower-24 cage-12-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-4-lower-24.yml 24 24.0 cage-12-5-lower-145 cage-12-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-12-5-lower-145.yml 145 145.0 147 147.0 cage-12-6-lower-266 cage-12-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-12-6-lower-266.yml 266 266.0 266 266.0 cage-12-7-lower-1597 cage-12-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-7-lower-1597.yml 1597 1597.0 cage-12-8-lower-2928 cage-12-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-8-lower-2928.yml 2928 2928.0 cage-12-9-lower-17569 cage-12-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-12-9-lower-17569.yml 17569 17569.0 17,569 cage-13-10-lower-45242 cage-13-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-10-lower-45242.yml 45242 45242.0 45,242 cage-13-11-lower-294074 cage-13-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-11-lower-294074.yml 294074 294074.0 294,074 cage-13-12-lower-542906 cage-13-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-12-lower-542906.yml 542906 542906.0 542,906 cage-13-13-lower-3528890 cage-13-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-13-lower-3528890.yml 3528890 3528890.0 3,528,890 cage-13-14-lower-6514874 cage-13-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-14-lower-6514874.yml 6514874 6514874.0 6,514,874 cage-13-15-lower-42346682 cage-13-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-15-lower-42346682.yml 42346682 42346682.0 42,346,682 cage-13-16-lower-78178490 cage-13-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-16-lower-78178490.yml 78178490 78178490.0 78,178,490 cage-13-3-lower-14 cage-13-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-3-lower-14.yml 14 14.0 cage-13-4-lower-26 cage-13-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-4-lower-26.yml 26 26.0 cage-13-5-lower-170 cage-13-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-13-5-lower-170.yml 170 170.0 174 174.0 cage-13-6-lower-314 cage-13-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-13-6-lower-314.yml 314 314.0 314 314.0 cage-13-7-lower-2042 cage-13-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-7-lower-2042.yml 2042 2042.0 cage-13-8-lower-3770 cage-13-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-8-lower-3770.yml 3770 3770.0 cage-13-9-lower-24506 cage-13-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-13-9-lower-24506.yml 24506 24506.0 24,506 cage-14-10-lower-61882 cage-14-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-10-lower-61882.yml 61882 61882.0 61,882 cage-14-11-lower-433175 cage-14-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-11-lower-433175.yml 433175 433175.0 433,175 cage-14-12-lower-804468 cage-14-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-12-lower-804468.yml 804468 804468.0 804,468 cage-14-13-lower-5631277 cage-14-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-13-lower-5631277.yml 5631277 5631277.0 5,631,277 cage-14-14-lower-10458086 cage-14-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-14-lower-10458086.yml 10458086 10458086.0 10,458,086 cage-14-15-lower-73206603 cage-14-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-15-lower-73206603.yml 73206603 73206603.0 73,206,603 cage-14-16-lower-135955120 cage-14-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-16-lower-135955120.yml 135955120 135955120.0 135,955,120 cage-14-3-lower-15 cage-14-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-3-lower-15.yml 15 15.0 cage-14-4-lower-28 cage-14-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-4-lower-28.yml 28 28.0 cage-14-5-lower-197 cage-14-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-14-5-lower-197.yml 197 197.0 199 199.0 cage-14-6-lower-366 cage-14-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-14-6-lower-366.yml 366 366.0 366 366.0 cage-14-7-lower-2563 cage-14-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-7-lower-2563.yml 2563 2563.0 cage-14-8-lower-4760 cage-14-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-8-lower-4760.yml 4760 4760.0 cage-14-9-lower-33321 cage-14-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-14-9-lower-33321.yml 33321 33321.0 33,321 cage-15-10-lower-82742 cage-15-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-10-lower-82742.yml 82742 82742.0 82,742 cage-15-11-lower-620566 cage-15-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-11-lower-620566.yml 620566 620566.0 620,566 cage-15-12-lower-1158390 cage-15-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-12-lower-1158390.yml 1158390 1158390.0 1,158,390 cage-15-13-lower-8687926 cage-15-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-13-lower-8687926.yml 8687926 8687926.0 8,687,926 cage-15-14-lower-16217462 cage-15-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-14-lower-16217462.yml 16217462 16217462.0 16,217,462 cage-15-15-lower-121630966 cage-15-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-15-lower-121630966.yml 121630966 121630966.0 121,630,966 cage-15-16-lower-227044470 cage-15-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-16-lower-227044470.yml 227044470 227044470.0 227,044,470 cage-15-3-lower-16 cage-15-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-3-lower-16.yml 16 16.0 cage-15-4-lower-30 cage-15-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-4-lower-30.yml 30 30.0 cage-15-5-lower-226 cage-15-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-15-5-lower-226.yml 226 226.0 230 230.0 cage-15-6-lower-422 cage-15-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-15-6-lower-422.yml 422 422.0 422 422.0 cage-15-7-lower-3166 cage-15-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-7-lower-3166.yml 3166 3166.0 cage-15-8-lower-5910 cage-15-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-8-lower-5910.yml 5910 5910.0 cage-15-9-lower-44326 cage-15-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-15-9-lower-44326.yml 44326 44326.0 44,326 cage-16-10-lower-108482 cage-16-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-10-lower-108482.yml 108482 108482.0 108,482 cage-16-11-lower-867857 cage-16-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-11-lower-867857.yml 867857 867857.0 867,857 cage-16-12-lower-1627232 cage-16-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-12-lower-1627232.yml 1627232 1627232.0 1,627,232 cage-16-13-lower-13017857 cage-16-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-13-lower-13017857.yml 13017857 13017857.0 13,017,857 cage-16-14-lower-24408482 cage-16-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-14-lower-24408482.yml 24408482 24408482.0 24,408,482 cage-16-15-lower-195267857 cage-16-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-15-lower-195267857.yml 195267857 195267857.0 195,267,857 cage-16-16-lower-366127232 cage-16-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-16-lower-366127232.yml 366127232 366127232.0 366,127,232 cage-16-3-lower-17 cage-16-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-3-lower-17.yml 17 17.0 cage-16-4-lower-32 cage-16-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-4-lower-32.yml 32 32.0 cage-16-5-lower-257 cage-16-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-16-5-lower-257.yml 257 257.0 259 259.0 cage-16-6-lower-482 cage-16-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-16-6-lower-482.yml 482 482.0 482 482.0 cage-16-7-lower-3857 cage-16-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-7-lower-3857.yml 3857 3857.0 cage-16-8-lower-7232 cage-16-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-8-lower-7232.yml 7232 7232.0 cage-16-9-lower-57857 cage-16-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-16-9-lower-57857.yml 57857 57857.0 57,857 cage-17-10-lower-139810 cage-17-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-10-lower-139810.yml 139810 139810.0 139,810 cage-17-11-lower-1188386 cage-17-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-11-lower-1188386.yml 1188386 1188386.0 1,188,386 cage-17-12-lower-2236962 cage-17-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-12-lower-2236962.yml 2236962 2236962.0 2,236,962 cage-17-13-lower-19014178 cage-17-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-13-lower-19014178.yml 19014178 19014178.0 19,014,178 cage-17-14-lower-35791394 cage-17-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-14-lower-35791394.yml 35791394 35791394.0 35,791,394 cage-17-15-lower-304226850 cage-17-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-15-lower-304226850.yml 304226850 304226850.0 304,226,850 cage-17-16-lower-572662306 cage-17-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-16-lower-572662306.yml 572662306 572662306.0 572,662,306 cage-17-3-lower-18 cage-17-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-3-lower-18.yml 18 18.0 cage-17-4-lower-34 cage-17-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-4-lower-34.yml 34 34.0 cage-17-5-lower-290 cage-17-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-17-5-lower-290.yml 290 290.0 294 294.0 cage-17-6-lower-546 cage-17-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-17-6-lower-546.yml 546 546.0 546 546.0 cage-17-7-lower-4642 cage-17-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-7-lower-4642.yml 4642 4642.0 cage-17-8-lower-8738 cage-17-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-8-lower-8738.yml 8738 8738.0 cage-17-9-lower-74274 cage-17-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-17-9-lower-74274.yml 74274 74274.0 74,274 cage-18-10-lower-177482 cage-18-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-10-lower-177482.yml 177482 177482.0 177,482 cage-18-11-lower-1597339 cage-18-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-11-lower-1597339.yml 1597339 1597339.0 1,597,339 cage-18-12-lower-3017196 cage-18-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-12-lower-3017196.yml 3017196 3017196.0 3,017,196 cage-18-13-lower-27154765 cage-18-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-13-lower-27154765.yml 27154765 27154765.0 27,154,765 cage-18-14-lower-51292334 cage-18-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-14-lower-51292334.yml 51292334 51292334.0 51,292,334 cage-18-15-lower-461631007 cage-18-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-15-lower-461631007.yml 461631007 461631007.0 461,631,007 cage-18-16-lower-871969680 cage-18-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-16-lower-871969680.yml 871969680 871969680.0 871,969,680 cage-18-3-lower-19 cage-18-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-3-lower-19.yml 19 19.0 cage-18-4-lower-36 cage-18-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-4-lower-36.yml 36 36.0 cage-18-5-lower-325 cage-18-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-18-5-lower-325.yml 325 325.0 327 327.0 cage-18-6-lower-614 cage-18-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-18-6-lower-614.yml 614 614.0 614 614.0 cage-18-7-lower-5527 cage-18-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-7-lower-5527.yml 5527 5527.0 cage-18-8-lower-10440 cage-18-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-8-lower-10440.yml 10440 10440.0 10,440 cage-18-9-lower-93961 cage-18-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-18-9-lower-93961.yml 93961 93961.0 93,961 cage-19-10-lower-222302 cage-19-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-10-lower-222302.yml 222302 222302.0 222,302 cage-19-11-lower-2111870 cage-19-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-11-lower-2111870.yml 2111870 2111870.0 2,111,870 cage-19-12-lower-4001438 cage-19-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-12-lower-4001438.yml 4001438 4001438.0 4,001,438 cage-19-13-lower-38013662 cage-19-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-13-lower-38013662.yml 38013662 38013662.0 38,013,662 cage-19-14-lower-72025886 cage-19-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-14-lower-72025886.yml 72025886 72025886.0 72,025,886 cage-19-15-lower-684245918 cage-19-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-15-lower-684245918.yml 684245918 684245918.0 684,245,918 cage-19-16-lower-1296465950 cage-19-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-16-lower-1296465950.yml 1296465950 1296465950.0 1,296,465,950 cage-19-3-lower-20 cage-19-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-3-lower-20.yml 20 20.0 cage-19-4-lower-38 cage-19-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-4-lower-38.yml 38 38.0 cage-19-5-lower-362 cage-19-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-19-5-lower-362.yml 362 362.0 364 364.0 cage-19-6-lower-686 cage-19-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-19-6-lower-686.yml 686 686.0 686 686.0 cage-19-7-lower-6518 cage-19-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-7-lower-6518.yml 6518 6518.0 cage-19-8-lower-12350 cage-19-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-8-lower-12350.yml 12350 12350.0 12,350 cage-19-9-lower-117326 cage-19-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-19-9-lower-117326.yml 117326 117326.0 117,326 cage-20-10-lower-275122 cage-20-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-10-lower-275122.yml 275122 275122.0 275,122 cage-20-11-lower-2751221 cage-20-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-11-lower-2751221.yml 2751221 2751221.0 2,751,221 cage-20-12-lower-5227320 cage-20-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-12-lower-5227320.yml 5227320 5227320.0 5,227,320 cage-20-13-lower-52273201 cage-20-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-13-lower-52273201.yml 52273201 52273201.0 52,273,201 cage-20-14-lower-99319082 cage-20-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-14-lower-99319082.yml 99319082 99319082.0 99,319,082 cage-20-15-lower-993190821 cage-20-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-15-lower-993190821.yml 993190821 993190821.0 993,190,821 cage-20-16-lower-1887062560 cage-20-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-16-lower-1887062560.yml 1887062560 1887062560.0 1,887,062,560 cage-20-3-lower-21 cage-20-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-3-lower-21.yml 21 21.0 cage-20-4-lower-40 cage-20-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-4-lower-40.yml 40 40.0 cage-20-5-lower-401 cage-20-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-20-5-lower-401.yml 401 401.0 403 403.0 cage-20-6-lower-762 cage-20-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-20-6-lower-762.yml 762 762.0 762 762.0 cage-20-7-lower-7621 cage-20-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-7-lower-7621.yml 7621 7621.0 cage-20-8-lower-14480 cage-20-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-8-lower-14480.yml 14480 14480.0 14,480 cage-20-9-lower-144801 cage-20-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-20-9-lower-144801.yml 144801 144801.0 144,801 cage-3-10-lower-62 cage-3-10 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-3-10-lower-62.yml 62 62.0 70 70.0 cage-3-11-lower-94 cage-3-11 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-3-11-lower-94.yml 94 94.0 112 112.0 cage-3-12-lower-126 cage-3-12 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-3-12-lower-126.yml 126 126.0 126 126.0 cage-3-13-lower-190 cage-3-13 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-3-13-lower-190.yml 190 190.0 202 202.0 cage-3-14-lower-254 cage-3-14 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-3-14-lower-254.yml 254 254.0 258 258.0 cage-3-15-lower-382 cage-3-15 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-3-15-lower-382.yml 382 382.0 384 384.0 cage-3-16-lower-510 cage-3-16 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-3-16-lower-510.yml 510 510.0 512 512.0 cage-3-3-lower-4 cage-3-3 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-3-3-lower-4.yml 4 4.0 4 4.0 cage-3-4-lower-6 cage-3-4 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-3-4-lower-6.yml 6 6.0 6 6.0 cage-3-5-lower-10 cage-3-5 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-3-5-lower-10.yml 10 10.0 10 10.0 cage-3-6-lower-14 cage-3-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-3-6-lower-14.yml 14 14.0 14 14.0 cage-3-7-lower-22 cage-3-7 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-3-7-lower-22.yml 22 22.0 24 24.0 cage-3-8-lower-30 cage-3-8 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-3-8-lower-30.yml 30 30.0 30 30.0 cage-3-9-lower-46 cage-3-9 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-3-9-lower-46.yml 46 46.0 58 58.0 cage-4-10-lower-242 cage-4-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-4-10-lower-242.yml 242 242.0 cage-4-11-lower-485 cage-4-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-4-11-lower-485.yml 485 485.0 cage-4-12-lower-728 cage-4-12 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-4-12-lower-728.yml 728 728.0 728 728.0 cage-4-13-lower-1457 cage-4-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-4-13-lower-1457.yml 1457 1457.0 cage-4-14-lower-2186 cage-4-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-4-14-lower-2186.yml 2186 2186.0 cage-4-15-lower-4373 cage-4-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-4-15-lower-4373.yml 4373 4373.0 cage-4-16-lower-6560 cage-4-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-4-16-lower-6560.yml 6560 6560.0 cage-4-3-lower-5 cage-4-3 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-4-3-lower-5.yml 5 5.0 5 5.0 cage-4-4-lower-8 cage-4-4 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-4-4-lower-8.yml 8 8.0 8 8.0 cage-4-5-lower-17 cage-4-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-4-5-lower-17.yml 17 17.0 19 19.0 cage-4-6-lower-26 cage-4-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-4-6-lower-26.yml 26 26.0 26 26.0 cage-4-7-lower-53 cage-4-7 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-4-7-lower-53.yml 53 53.0 67 67.0 cage-4-8-lower-80 cage-4-8 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-4-8-lower-80.yml 80 80.0 80 80.0 cage-4-9-lower-161 cage-4-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-4-9-lower-161.yml 161 161.0 cage-5-10-lower-682 cage-5-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-5-10-lower-682.yml 682 682.0 cage-5-11-lower-1706 cage-5-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-5-11-lower-1706.yml 1706 1706.0 cage-5-12-lower-2730 cage-5-12 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-5-12-lower-2730.yml 2730 2730.0 2730 2730.0 cage-5-13-lower-6826 cage-5-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-5-13-lower-6826.yml 6826 6826.0 cage-5-14-lower-10922 cage-5-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-5-14-lower-10922.yml 10922 10922.0 10,922 cage-5-15-lower-27306 cage-5-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-5-15-lower-27306.yml 27306 27306.0 27,306 cage-5-16-lower-43690 cage-5-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-5-16-lower-43690.yml 43690 43690.0 43,690 cage-5-3-lower-6 cage-5-3 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-5-3-lower-6.yml 6 6.0 6 6.0 cage-5-4-lower-10 cage-5-4 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-5-4-lower-10.yml 10 10.0 10 10.0 cage-5-5-lower-26 cage-5-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-5-5-lower-26.yml 26 26.0 30 30.0 cage-5-6-lower-42 cage-5-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-5-6-lower-42.yml 42 42.0 42 42.0 cage-5-7-lower-106 cage-5-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-5-7-lower-106.yml 106 106.0 cage-5-8-lower-170 cage-5-8 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-5-8-lower-170.yml 170 170.0 170 170.0 cage-5-9-lower-426 cage-5-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-5-9-lower-426.yml 426 426.0 cage-6-10-lower-1562 cage-6-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-6-10-lower-1562.yml 1562 1562.0 cage-6-11-lower-4687 cage-6-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-6-11-lower-4687.yml 4687 4687.0 cage-6-12-lower-7812 cage-6-12 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-6-12-lower-7812.yml 7812 7812.0 7812 7812.0 cage-6-13-lower-23437 cage-6-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-6-13-lower-23437.yml 23437 23437.0 23,437 cage-6-14-lower-39062 cage-6-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-6-14-lower-39062.yml 39062 39062.0 39,062 cage-6-15-lower-117187 cage-6-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-6-15-lower-117187.yml 117187 117187.0 117,187 cage-6-16-lower-195312 cage-6-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-6-16-lower-195312.yml 195312 195312.0 195,312 cage-6-3-lower-7 cage-6-3 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-6-3-lower-7.yml 7 7.0 7 7.0 cage-6-4-lower-12 cage-6-4 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-6-4-lower-12.yml 12 12.0 12 12.0 cage-6-5-lower-37 cage-6-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-6-5-lower-37.yml 37 37.0 40 40.0 cage-6-6-lower-62 cage-6-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-6-6-lower-62.yml 62 62.0 62 62.0 cage-6-7-lower-187 cage-6-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-6-7-lower-187.yml 187 187.0 cage-6-8-lower-312 cage-6-8 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-6-8-lower-312.yml 312 312.0 312 312.0 cage-6-9-lower-937 cage-6-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-6-9-lower-937.yml 937 937.0 cage-7-10-lower-3110 cage-7-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-7-10-lower-3110.yml 3110 3110.0 cage-7-11-lower-10886 cage-7-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-7-11-lower-10886.yml 10886 10886.0 10,886 cage-7-12-lower-18662 cage-7-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-7-12-lower-18662.yml 18662 18662.0 18,662 cage-7-13-lower-65318 cage-7-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-7-13-lower-65318.yml 65318 65318.0 65,318 cage-7-14-lower-111974 cage-7-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-7-14-lower-111974.yml 111974 111974.0 111,974 cage-7-15-lower-391910 cage-7-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-7-15-lower-391910.yml 391910 391910.0 391,910 cage-7-16-lower-671846 cage-7-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-7-16-lower-671846.yml 671846 671846.0 671,846 cage-7-3-lower-8 cage-7-3 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-7-3-lower-8.yml 8 8.0 8 8.0 cage-7-4-lower-14 cage-7-4 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-7-4-lower-14.yml 14 14.0 14 14.0 cage-7-5-lower-50 cage-7-5 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-7-5-lower-50.yml 50 50.0 50 50.0 cage-7-6-lower-86 cage-7-6 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-7-6-lower-86.yml 86 86.0 90 90.0 cage-7-7-lower-302 cage-7-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-7-7-lower-302.yml 302 302.0 cage-7-8-lower-518 cage-7-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-7-8-lower-518.yml 518 518.0 cage-7-9-lower-1814 cage-7-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-7-9-lower-1814.yml 1814 1814.0 cage-8-10-lower-5602 cage-8-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-10-lower-5602.yml 5602 5602.0 cage-8-11-lower-22409 cage-8-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-11-lower-22409.yml 22409 22409.0 22,409 cage-8-12-lower-39216 cage-8-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-12-lower-39216.yml 39216 39216.0 39,216 cage-8-13-lower-156865 cage-8-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-13-lower-156865.yml 156865 156865.0 156,865 cage-8-14-lower-274514 cage-8-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-14-lower-274514.yml 274514 274514.0 274,514 cage-8-15-lower-1098057 cage-8-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-15-lower-1098057.yml 1098057 1098057.0 1,098,057 cage-8-16-lower-1921600 cage-8-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-16-lower-1921600.yml 1921600 1921600.0 1,921,600 cage-8-3-lower-9 cage-8-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-3-lower-9.yml 9 9.0 cage-8-4-lower-16 cage-8-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-4-lower-16.yml 16 16.0 cage-8-5-lower-65 cage-8-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-8-5-lower-65.yml 65 65.0 67 67.0 cage-8-6-lower-114 cage-8-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-8-6-lower-114.yml 114 114.0 114 114.0 cage-8-7-lower-457 cage-8-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-7-lower-457.yml 457 457.0 cage-8-8-lower-800 cage-8-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-8-lower-800.yml 800 800.0 cage-8-9-lower-3201 cage-8-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-8-9-lower-3201.yml 3201 3201.0 cage-9-10-lower-9362 cage-9-10 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-10-lower-9362.yml 9362 9362.0 cage-9-11-lower-42130 cage-9-11 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-11-lower-42130.yml 42130 42130.0 42,130 cage-9-12-lower-74898 cage-9-12 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-12-lower-74898.yml 74898 74898.0 74,898 cage-9-13-lower-337042 cage-9-13 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-13-lower-337042.yml 337042 337042.0 337,042 cage-9-14-lower-599186 cage-9-14 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-14-lower-599186.yml 599186 599186.0 599,186 cage-9-15-lower-2696338 cage-9-15 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-15-lower-2696338.yml 2696338 2696338.0 2,696,338 cage-9-16-lower-4793490 cage-9-16 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-16-lower-4793490.yml 4793490 4793490.0 4,793,490 cage-9-3-lower-10 cage-9-3 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-3-lower-10.yml 10 10.0 cage-9-4-lower-18 cage-9-4 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-4-lower-18.yml 18 18.0 cage-9-5-lower-82 cage-9-5 cage lower lean daniel-munro 2026-10-29 True weaker certificates/cage/cage-9-5-lower-82.yml 82 82.0 86 86.0 cage-9-6-lower-146 cage-9-6 cage lower lean daniel-munro 2026-10-29 True equal certificates/cage/cage-9-6-lower-146.yml 146 146.0 146 146.0 cage-9-7-lower-658 cage-9-7 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-7-lower-658.yml 658 658.0 cage-9-8-lower-1170 cage-9-8 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-8-lower-1170.yml 1170 1170.0 cage-9-9-lower-5266 cage-9-9 cage lower lean daniel-munro 2026-10-29 True new certificates/cage/cage-9-9-lower-5266.yml 5266 5266.0 cage-10-3-upper-11 cage-10-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-10-3-upper-11.yml 11 11.0 cage-10-4-upper-20 cage-10-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-10-4-upper-20.yml 20 20.0 cage-10-6-upper-182 cage-10-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-10-6-upper-182.yml 182 182.0 182 182.0 cage-11-3-upper-12 cage-11-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-11-3-upper-12.yml 12 12.0 cage-11-4-upper-22 cage-11-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-11-4-upper-22.yml 22 22.0 cage-12-3-upper-13 cage-12-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-12-3-upper-13.yml 13 13.0 cage-12-4-upper-24 cage-12-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-12-4-upper-24.yml 24 24.0 cage-12-6-upper-266 cage-12-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-12-6-upper-266.yml 266 266.0 266 266.0 cage-13-3-upper-14 cage-13-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-13-3-upper-14.yml 14 14.0 cage-13-4-upper-26 cage-13-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-13-4-upper-26.yml 26 26.0 cage-14-3-upper-15 cage-14-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-14-3-upper-15.yml 15 15.0 cage-14-4-upper-28 cage-14-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-14-4-upper-28.yml 28 28.0 cage-14-6-upper-366 cage-14-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-14-6-upper-366.yml 366 366.0 366 366.0 cage-15-3-upper-16 cage-15-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-15-3-upper-16.yml 16 16.0 cage-15-4-upper-30 cage-15-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-15-4-upper-30.yml 30 30.0 cage-16-3-upper-17 cage-16-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-16-3-upper-17.yml 17 17.0 cage-16-4-upper-32 cage-16-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-16-4-upper-32.yml 32 32.0 cage-17-3-upper-18 cage-17-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-17-3-upper-18.yml 18 18.0 cage-17-4-upper-34 cage-17-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-17-4-upper-34.yml 34 34.0 cage-17-6-upper-546 cage-17-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-17-6-upper-546.yml 546 546.0 546 546.0 cage-18-3-upper-19 cage-18-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-18-3-upper-19.yml 19 19.0 cage-18-4-upper-36 cage-18-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-18-4-upper-36.yml 36 36.0 cage-18-6-upper-614 cage-18-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-18-6-upper-614.yml 614 614.0 614 614.0 cage-19-3-upper-20 cage-19-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-19-3-upper-20.yml 20 20.0 cage-19-4-upper-38 cage-19-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-19-4-upper-38.yml 38 38.0 cage-20-3-upper-21 cage-20-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-20-3-upper-21.yml 21 21.0 cage-20-4-upper-40 cage-20-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-20-4-upper-40.yml 40 40.0 cage-20-6-upper-762 cage-20-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-20-6-upper-762.yml 762 762.0 762 762.0 cage-3-3-upper-4 cage-3-3 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-3-3-upper-4.yml 4 4.0 4 4.0 cage-3-4-upper-6 cage-3-4 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-3-4-upper-6.yml 6 6.0 6 6.0 cage-3-5-upper-10 cage-3-5 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-3-5-upper-10.yml 10 10.0 10 10.0 cage-3-6-upper-14 cage-3-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-3-6-upper-14.yml 14 14.0 14 14.0 cage-3-7-upper-24 cage-3-7 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-3-7-upper-24.yml 24 24.0 24 24.0 cage-3-8-upper-30 cage-3-8 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-3-8-upper-30.yml 30 30.0 30 30.0 cage-4-3-upper-5 cage-4-3 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-4-3-upper-5.yml 5 5.0 5 5.0 cage-4-4-upper-8 cage-4-4 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-4-4-upper-8.yml 8 8.0 8 8.0 cage-4-6-upper-26 cage-4-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-4-6-upper-26.yml 26 26.0 26 26.0 cage-4-8-upper-80 cage-4-8 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-4-8-upper-80.yml 80 80.0 80 80.0 cage-5-3-upper-6 cage-5-3 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-5-3-upper-6.yml 6 6.0 6 6.0 cage-5-4-upper-10 cage-5-4 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-5-4-upper-10.yml 10 10.0 10 10.0 cage-5-6-upper-42 cage-5-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-5-6-upper-42.yml 42 42.0 42 42.0 cage-5-8-upper-170 cage-5-8 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-5-8-upper-170.yml 170 170.0 170 170.0 cage-6-3-upper-7 cage-6-3 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-6-3-upper-7.yml 7 7.0 7 7.0 cage-6-4-upper-12 cage-6-4 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-6-4-upper-12.yml 12 12.0 12 12.0 cage-6-6-upper-62 cage-6-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-6-6-upper-62.yml 62 62.0 62 62.0 cage-6-8-upper-312 cage-6-8 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-6-8-upper-312.yml 312 312.0 312 312.0 cage-7-3-upper-8 cage-7-3 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-7-3-upper-8.yml 8 8.0 8 8.0 cage-7-4-upper-14 cage-7-4 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-7-4-upper-14.yml 14 14.0 14 14.0 cage-7-5-upper-50 cage-7-5 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-7-5-upper-50.yml 50 50.0 50 50.0 cage-8-3-upper-9 cage-8-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-8-3-upper-9.yml 9 9.0 cage-8-4-upper-16 cage-8-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-8-4-upper-16.yml 16 16.0 cage-8-6-upper-114 cage-8-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-8-6-upper-114.yml 114 114.0 114 114.0 cage-8-8-upper-800 cage-8-8 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-8-8-upper-800.yml 800 800.0 800 800.0 cage-9-3-upper-10 cage-9-3 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-9-3-upper-10.yml 10 10.0 cage-9-4-upper-18 cage-9-4 cage upper witness daniel-munro 2026-10-28 True new certificates/cage/cage-9-4-upper-18.yml 18 18.0 cage-9-6-upper-146 cage-9-6 cage upper witness daniel-munro 2026-10-28 True equal certificates/cage/cage-9-6-upper-146.yml 146 146.0 146 146.0 degree-diameter-10-2-lower-91 degree-diameter-10-2 degree-diameter lower witness daniel-munro 2026-10-28 True equal brown-1966 certificates/degree-diameter/degree-diameter-10-2-lower-91.yml 91 91.0 91 91.0 degree-diameter-12-2-lower-133 degree-diameter-12-2 degree-diameter lower witness daniel-munro 2026-10-28 True equal brown-1966 certificates/degree-diameter/degree-diameter-12-2-lower-133.yml 133 133.0 133 133.0 degree-diameter-14-2-lower-183 degree-diameter-14-2 degree-diameter lower witness daniel-munro 2026-10-28 True equal brown-1966 certificates/degree-diameter/degree-diameter-14-2-lower-183.yml 183 183.0 183 183.0 degree-diameter-18-2-lower-307 degree-diameter-18-2 degree-diameter lower witness daniel-munro 2026-10-28 True equal brown-1966 certificates/degree-diameter/degree-diameter-18-2-lower-307.yml 307 307.0 307 307.0 degree-diameter-20-2-lower-381 degree-diameter-20-2 degree-diameter lower witness daniel-munro 2026-10-28 True equal brown-1966 certificates/degree-diameter/degree-diameter-20-2-lower-381.yml 381 381.0 381 381.0 degree-diameter-3-2-lower-10 degree-diameter-3-2 degree-diameter lower witness daniel-munro 2026-10-28 True equal certificates/degree-diameter/degree-diameter-3-2-lower-10.yml 10 10.0 10 10.0 degree-diameter-7-2-lower-50 degree-diameter-7-2 degree-diameter lower witness daniel-munro 2026-10-28 True equal certificates/degree-diameter/degree-diameter-7-2-lower-50.yml 50 50.0 50 50.0 degree-diameter-8-2-lower-57 degree-diameter-8-2 degree-diameter lower witness daniel-munro 2026-10-28 True equal brown-1966 certificates/degree-diameter/degree-diameter-8-2-lower-57.yml 57 57.0 57 57.0 minimal-superpermutation-1-upper-1 minimal-superpermutation-1 minimal-superpermutation upper witness daniel-munro 2026-10-28 True equal egan-superpermutations certificates/minimal-superpermutation/minimal-superpermutation-1-upper-1.yml 1 1.0 1 1.0 minimal-superpermutation-2-upper-3 minimal-superpermutation-2 minimal-superpermutation upper witness daniel-munro 2026-10-28 True equal egan-superpermutations certificates/minimal-superpermutation/minimal-superpermutation-2-upper-3.yml 3 3.0 3 3.0 minimal-superpermutation-3-upper-9 minimal-superpermutation-3 minimal-superpermutation upper witness daniel-munro 2026-10-28 True equal egan-superpermutations certificates/minimal-superpermutation/minimal-superpermutation-3-upper-9.yml 9 9.0 9 9.0 minimal-superpermutation-4-upper-33 minimal-superpermutation-4 minimal-superpermutation upper witness daniel-munro 2026-10-28 True equal egan-superpermutations certificates/minimal-superpermutation/minimal-superpermutation-4-upper-33.yml 33 33.0 33 33.0 minimal-superpermutation-5-upper-153 minimal-superpermutation-5 minimal-superpermutation upper witness daniel-munro 2026-10-28 True equal egan-superpermutations certificates/minimal-superpermutation/minimal-superpermutation-5-upper-153.yml 153 153.0 153 153.0 minimal-superpermutation-6-upper-873 minimal-superpermutation-6 minimal-superpermutation upper witness daniel-munro 2026-10-28 True weaker egan-superpermutations certificates/minimal-superpermutation/minimal-superpermutation-6-upper-873.yml 873 873.0 872 872.0 minimal-superpermutation-7-upper-5913 minimal-superpermutation-7 minimal-superpermutation upper witness daniel-munro 2026-10-28 True weaker egan-superpermutations certificates/minimal-superpermutation/minimal-superpermutation-7-upper-5913.yml 5913 5913.0 5905 5905.0 van-der-waerden-2-3-lower-9 van-der-waerden-2-3 van-der-waerden lower witness daniel-munro 2026-10-28 True equal certificates/van-der-waerden/van-der-waerden-2-3-lower-9.yml 9 9.0 9 9.0 van-der-waerden-2-4-lower-35 van-der-waerden-2-4 van-der-waerden lower witness daniel-munro 2026-10-28 True equal certificates/van-der-waerden/van-der-waerden-2-4-lower-35.yml 35 35.0 35 35.0 van-der-waerden-3-3-lower-27 van-der-waerden-3-3 van-der-waerden lower witness daniel-munro 2026-10-28 True equal certificates/van-der-waerden/van-der-waerden-3-3-lower-27.yml 27 27.0 27 27.0 ramsey-3-3-lower-6 ramsey-3-3 ramsey lower lean daniel-munro 2026-10-22 True equal certificates/ramsey/ramsey-3-3-lower-6.yml 6 6.0 6 6.0 ramsey-3-3-upper-6 ramsey-3-3 ramsey upper lean daniel-munro 2026-10-22 True equal certificates/ramsey/ramsey-3-3-upper-6.yml 6 6.0 6 6.0 ramsey-3-4-lower-9 ramsey-3-4 ramsey lower witness daniel-munro 2026-10-22 True equal greenwood-gleason-1955 certificates/ramsey/ramsey-3-4-lower-9.yml 9 9.0 9 9.0 ramsey-3-5-lower-14 ramsey-3-5 ramsey lower witness daniel-munro 2026-10-22 True equal greenwood-gleason-1955 certificates/ramsey/ramsey-3-5-lower-14.yml 14 14.0 14 14.0 ramsey-4-4-lower-18 ramsey-4-4 ramsey lower witness daniel-munro 2026-10-22 True equal greenwood-gleason-1955 certificates/ramsey/ramsey-4-4-lower-18.yml 18 18.0 18 18.0 ramsey-5-5-lower-38 ramsey-5-5 ramsey lower witness daniel-munro 2026-10-22 False weaker certificates/ramsey/ramsey-5-5-lower-38.yml 38 38.0 43 43.0 ramsey-6-6-lower-102 ramsey-6-6 ramsey lower witness daniel-munro 2026-10-22 True equal kalbfleisch-1966 certificates/ramsey/ramsey-6-6-lower-102.yml 102 102.0 102 102.0