Verified bounds
Verified bounds come with a certificate that is checked automatically: an explicit construction checked by a program, or a formal proof in Lean. Anyone can submit one, and each is credited to the GitHub account that submitted it, which may not be whoever found the bound. See the unverified bounds for bounds from the literature that still need one.
All certificates are also available as YAML, JSON, CSV or TSV.
Contributors
| Contributor | Certificates | Latest |
|---|---|---|
| daniel-munro | 834 | 2026-11-05 |
| darkhipo | 1 | 2026-11-04 |
Recent certificates
| Date | Contributor | Constant | Bound | Evidence | Compared with the literature |
|---|---|---|---|---|---|
| 2026-11-05 | daniel-munro | Cap set $r(1)$ | $\ge 2$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Cap set $r(2)$ | $\ge 4$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Cap set $r(3)$ | $\ge 9$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Cap set $r(4)$ | $\ge 20$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Cap set $r(5)$ | $\ge 45$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Cap set $r(6)$ | $\ge 112$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Cap set $r(7)$ | $\ge 236$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Cap set $r(8)$ | $\ge 512$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Isosceles set $i(1)$ | $\ge 3$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Isosceles set $i(10)$ | $\ge 56$ | Construction | No literature bound recorded |
| 2026-11-05 | daniel-munro | Isosceles set $i(11)$ | $\ge 67$ | Construction | No literature bound recorded |
| 2026-11-05 | daniel-munro | Isosceles set $i(12)$ | $\ge 79$ | Construction | No literature bound recorded |
| 2026-11-05 | daniel-munro | Isosceles set $i(2)$ | $\ge 6$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Isosceles set $i(3)$ | $\ge 8$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Isosceles set $i(4)$ | $\ge 11$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Isosceles set $i(5)$ | $\ge 17$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Isosceles set $i(6)$ | $\ge 28$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Isosceles set $i(7)$ | $\ge 30$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Isosceles set $i(8)$ | $\ge 45$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | Isosceles set $i(9)$ | $\ge 46$ | Construction | No literature bound recorded |
| 2026-11-05 | daniel-munro | No-three-in-line $D(1)$ | $\ge 1$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(10)$ | $\ge 20$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(11)$ | $\ge 22$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(12)$ | $\ge 24$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(13)$ | $\ge 26$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(14)$ | $\ge 28$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(15)$ | $\ge 30$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(16)$ | $\ge 32$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(17)$ | $\ge 34$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(18)$ | $\ge 36$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(19)$ | $\ge 38$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(2)$ | $\ge 4$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(20)$ | $\ge 40$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(21)$ | $\ge 42$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(22)$ | $\ge 44$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(23)$ | $\ge 46$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(24)$ | $\ge 48$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(25)$ | $\ge 50$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(26)$ | $\ge 52$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(27)$ | $\ge 54$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(28)$ | $\ge 56$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(29)$ | $\ge 58$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(3)$ | $\ge 6$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(30)$ | $\ge 60$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(31)$ | $\ge 62$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(32)$ | $\ge 64$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(33)$ | $\ge 66$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(34)$ | $\ge 68$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(35)$ | $\ge 70$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(36)$ | $\ge 72$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(37)$ | $\ge 74$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(38)$ | $\ge 76$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(39)$ | $\ge 78$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(4)$ | $\ge 8$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(40)$ | $\ge 80$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(41)$ | $\ge 82$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(42)$ | $\ge 84$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(43)$ | $\ge 86$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(44)$ | $\ge 88$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(45)$ | $\ge 90$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(46)$ | $\ge 92$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(47)$ | $\ge 94$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(48)$ | $\ge 96$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(49)$ | $\ge 98$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(5)$ | $\ge 10$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(50)$ | $\ge 100$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(51)$ | $\ge 102$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(52)$ | $\ge 104$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(53)$ | $\ge 106$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(54)$ | $\ge 108$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(55)$ | $\ge 110$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(56)$ | $\ge 112$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(57)$ | $\ge 114$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(58)$ | $\ge 116$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(59)$ | $\ge 118$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(6)$ | $\ge 12$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(60)$ | $\ge 120$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(61)$ | $\ge 122$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(62)$ | $\ge 124$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(63)$ | $\ge 126$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(64)$ | $\ge 128$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(65)$ | $\ge 130$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(66)$ | $\ge 132$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(67)$ | $\ge 134$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(68)$ | $\ge 136$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(69)$ | $\ge 138$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(7)$ | $\ge 14$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(70)$ | $\ge 140$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(71)$ | $\ge 142$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(72)$ | $\ge 144$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(73)$ | $\ge 146$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(74)$ | $\ge 148$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(75)$ | $\ge 148$ | Construction | No literature bound recorded |
| 2026-11-05 | daniel-munro | No-three-in-line $D(76)$ | $\ge 152$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(77)$ | $\ge 152$ | Construction | No literature bound recorded |
| 2026-11-05 | daniel-munro | No-three-in-line $D(78)$ | $\ge 156$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(8)$ | $\ge 16$ | Construction | Matches the literature |
| 2026-11-05 | daniel-munro | No-three-in-line $D(9)$ | $\ge 18$ | Construction | Matches the literature |
| 2026-11-04 | daniel-munro | Arrangements of $1$ lines in the affine plane | $\ge 1$ | Construction | Matches the literature |
| 2026-11-04 | daniel-munro | Arrangements of $2$ lines in the affine plane | $\ge 2$ | Construction | Matches the literature |
Showing the 100 most recent of 835 certificates. The downloads above have all of them.