General (non-CSS) stabilizer codes, verified and ranked apart from the CSS board. Back to the CSS board.
A general stabilizer code has one binary symplectic check matrix S = (A | B): generator i acts as X on Ai and Z on Bi, Y where both. A CSS code is the special case where every row is pure X or pure Z; here every code has at least one mixed generator, and stays mixed under every single-qubit Clifford (a code that is CSS up to a Hadamard or an S on some qubits is rejected in favor of its CSS image, which belongs on the CSS board). These codes are ranked on their own board because the quantities the CSS board reads per side have no side here:
| CSS board | this board | |
|---|---|---|
| checks | H_X, H_Z | S = (A | B), isotropic: A Bᵀ + B Aᵀ = 0 |
| k | n − rank H_X − rank H_Z | n − rank S |
| distance | d = min(d_X, d_Z), one witness per side | one d: the minimum Pauli weight of a nontrivial logical operator (Y counts once); one Pauli-operator witness |
| check weight w | row weight | |Ai ∪ Bi| |
| kd²/n, g, tracks | unchanged; the primary-track cells are computed the same way, but carry the code type, so a record here is never a record there | |
| certificate | MILP per side | not built yet: every entry stands as d ≤ |
| circuit tier | memory circuits per basis | not accepted yet: syndrome extraction needs a general stabilizer-measurement schedule |
Symplectic doubling maps any [[n, k, d]] stabilizer code to a CSS code [[2n, 2k, d′]] with d ≤ d′ ≤ 2d, so the two boards are linked; halving that map is how the highest-rate entries here were built. See the schema, tracks, and how to submit a stabilizer code (bring S, or A and B, as an .npz).
10 contributors · 193 codes submitted through the challenge6 of 10 contributors have a verified layout and d ≥ 3 (their own code, or a layout they contributed)165 of 193 codes submitted through the challenge currently sit on a track frontier
Computed grid of locality × check weight, derived from H and the layout, not self-declared. Each cell lists its Pareto frontier, ranked by the selected score (kd²/n, or geometric efficiency g for codes with a verified layout); codes tied on the score rank by the lowest (n, k) pair. The code count filters the table below to that cell. Membership nests: a tighter cell’s codes also compete in the looser ones. In the g view, the seeded surface/toric tilings are not raced; they set the ceiling g is normalized to (surface code = 1) and appear dimmed below the ranking.
Type terms (all must match): a family, author, or a comparison like k>=10 d>8 eff>=5 g>=0.1 swaps<=50; ler<=0.005; record keeps only frontier rows and ler-record only the (n, k, LER) frontier; literature / submitted filter by origin; with-layout / no-layout filter by layout status; exact / upper-bound filter by whether the distance is proved; with-circuit (alias circuit) / no-circuit filter by whether the entry ships verified memory circuits; modular keeps the entries whose layout assigns every qubit to a module.
| code | type | n | k | d | kd²/n | g | w | swaps | girth | diam | authors | model | date | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ★ | [[662,122,95]] | other | 662 | 122 | d ≤ 95 | 1663.218 | · | 32 | · | 4 | · | @vprusso | GPT-6 | 2026-10-11 |
| ★ | [[452,115,18]] | pair-partition CPM | 452 | 115 | d ≤ 18 | 82.434 | · | 8 | · | 4 | · | @MicheldeMessieres | Claude Opus 5.5 (Claude Code) | 2026-10-09 |
| ★ | [[200,43,19]] | other | 200 | 43 | d ≤ 19 | 77.615 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-13 |
| ★ | [[220,47,18]] | other | 220 | 47 | d ≤ 18 | 69.218 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[240,51,18]] | other | 240 | 51 | d ≤ 18 | 68.85 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[185,40,17]] | other | 185 | 40 | d ≤ 17 | 62.486 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[512,54,24]] | other | 512 | 54 | d ≤ 24 | 60.75 | · | 32 | · | 4 | · | @MathysRennela | MiMo-V2.6-Flash | 2026-10-13 |
| ★ | [[186,65,13]] | other | 186 | 65 | d ≤ 13 | 59.059 | · | 12 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[160,35,16]] | other | 160 | 35 | d ≤ 16 | 56.0 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[170,37,16]] | other | 170 | 37 | d ≤ 16 | 55.718 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[180,39,16]] | other | 180 | 39 | d ≤ 16 | 55.467 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[168,59,12]] | other | 168 | 59 | d ≤ 12 | 50.571 | · | 12 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[140,31,14]] | other | 140 | 31 | d ≤ 14 | 43.4 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-13 |
| ★ | [[150,33,14]] | other | 150 | 33 | d ≤ 14 | 43.12 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[150,53,11]] | other | 150 | 53 | d ≤ 11 | 42.753 | · | 12 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| [[576,42,24]] | other | 576 | 42 | d ≤ 24 | 42.0 | · | 32 | · | 4 | · | @MathysRennela | MiMo-V2.6-Flash | 2026-10-13 | |
| ★ | [[130,29,13]] | other | 130 | 29 | d ≤ 13 | 37.7 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[672,28,30]] | other | 672 | 28 | d ≤ 30 | 37.5 | · | 24 | · | 4 | · | @MathysRennela | MiMo-V2.6-Flash | 2026-10-13 |
| ★ | [[120,43,10]] | other | 120 | 43 | d ≤ 10 | 35.833 | · | 12 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[66,12,14]] | other2D-local bilayer | 66 | 12 | d ≤ 14 | 35.636 | 0.0527 | 32 | 18 | 4 | 6.08 | @MathysRennela | MiMo v2.6 Flash | 2026-09-28 |
| ★ | [[132,47,10]] | other | 132 | 47 | d ≤ 10 | 35.606 | · | 12 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[210,86,9]] | other | 210 | 86 | d ≤ 9 | 33.171 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[110,25,12]] | other | 110 | 25 | d ≤ 12 | 32.727 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[120,27,12]] | other | 120 | 27 | d ≤ 12 | 32.4 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[480,12,36]] | 2BGA coset | 480 | 12 | d ≤ 36 | 32.4 | · | 6 | · | 4 | · | @jacksongquera | Claude Opus 5.5 (Claude Code) | 2026-10-21 |
| ★ | [[62,20,10]] | other2D-local bilayer | 62 | 20 | d ≤ 10 | 32.258 | 0.0236 | 32 | 8 | 4 | 7.28 | @MathysRennela | MiMo v2.6 Flash | 2026-09-28 |
| ★ | [[95,22,11]] | other | 95 | 22 | d ≤ 11 | 28.021 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-13 |
| ★ | [[100,23,11]] | other | 100 | 23 | d ≤ 11 | 27.83 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[80,33,8]] | other | 80 | 33 | d ≤ 8 | 26.4 | · | 16 | · | 4 | · | @hirobumii | GPT-6 Astra +1 | 2026-10-18 |
| ★ | [[170,70,8]] | other | 170 | 70 | d ≤ 8 | 26.353 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[148,39,10]] | other | 148 | 39 | d ≤ 10 | 26.351 | · | 8 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[190,78,8]] | other | 190 | 78 | d ≤ 8 | 26.274 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[160,42,10]] | other | 160 | 42 | d ≤ 10 | 26.25 | · | 8 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[230,94,8]] | other | 230 | 94 | d ≤ 8 | 26.157 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[235,96,8]] | pair-partition CPM | 235 | 96 | d ≤ 8 | 26.145 | · | 10 | · | 4 | · | @MathysRennela | Space Bunny Alpha 1.0 | 2026-10-01 |
| ★ | [[64,24,8]] | other | 64 | 24 | d ≤ 8 | 24.0 | · | 14 | · | 4 | · | @hirobumii | GPT-6 Astra +1 | 2026-10-18 |
| ★ | [[90,21,10]] | other | 90 | 21 | d ≤ 10 | 23.333 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-13 |
| ★ | [[336,10,28]] | 2BGA coset | 336 | 10 | d ≤ 28 | 23.333 | · | 6 | · | 4 | · | @MicheldeMessieres | Claude Opus 5.5 (Claude Code) | 2026-10-11 |
| ★ | [[73,46,6]] | other | 73 | 46 | d ≤ 6 | 22.685 | · | 28 | · | 4 | · | @hirobumii | GPT-6 Astra +1 | 2026-10-18 |
| ★ | [[73,44,6]] | other | 73 | 44 | d ≤ 6 | 21.699 | · | 24 | · | 4 | · | @hirobumii | GPT-6 Astra +1 | 2026-10-18 |
| ★ | [[120,32,9]] | other | 120 | 32 | d ≤ 9 | 21.6 | · | 8 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[329,190,6]] | pair-partition CPM | 329 | 190 | d ≤ 6 | 20.79 | · | 14 | · | 4 | · | @MathysRennela | Space Bunny Alpha 1.0 | 2026-10-01 |
| ★ | [[155,6,23]] | other2D-local bilayer | 155 | 6 | d ≤ 23 | 20.477 | 0.0085 | 8 | 981 | 4 | 10.3 | @mrvee-qC-bee | GPT-6 Astra | 2026-10-01 |
| ★ | [[150,62,7]] | other | 150 | 62 | d ≤ 7 | 20.253 | · | 10 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[56,16,8]] | other | 56 | 16 | d ≤ 8 | 18.286 | · | 16 | · | 4 | · | @hirobumii | GPT-6 Astra +1 | 2026-10-18 |
| ★ | [[282,143,6]] | pair-partition CPM | 282 | 143 | d ≤ 6 | 18.255 | · | 12 | · | 4 | · | @MathysRennela | Space Bunny Alpha 1.0 | 2026-10-01 |
| ★ | [[144,10,16]]known params | other | 144 | 10 | d ≤ 16 | 17.778 | · | 8 | · | 4 | · | @mrvee-qC-bee | GPT-6 Astra | 2026-10-01 |
| ★ | [[92,25,8]]known params | pair-partition CPM2D-local bilayer | 92 | 25 | d ≤ 8 | 17.391 | 0.0086 | 8 | 455 | 4 | 5.66 | @mrvee-qC-bee | GPT-6 Astra | 2026-10-01 |
| [[155,6,21]] | other2D-local bilayer | 155 | 6 | d ≤ 21 | 17.071 | 0.0084 | 8 | 833 | 4 | 9.49 | @mrvee-qC-bee | GPT-6 Astra | 2026-10-01 | |
| ★ | [[93,32,7]] | other | 93 | 32 | d ≤ 7 | 16.86 | · | 13 | · | 4 | · | @hirobumii | GPT-6 Astra +1 | 2026-10-18 |
| ★ | [[96,10,12]]known params | other2D-local bilayer | 96 | 10 | d ≤ 12 | 15.0 | 0.0094 | 8 | 569 | 4 | 7.81 | @mrvee-qC-bee | GPT-6 Astra | 2026-10-01 |
| ★ | [[48,11,8]] | other | 48 | 11 | d ≤ 8 | 14.667 | · | 14 | · | 4 | · | @hirobumii | GPT-6 Astra +1 | 2026-10-18 |
| ★ | [[355,144,6]] | pair-partition CPM | 355 | 144 | d ≤ 6 | 14.603 | · | 10 | · | 4 | · | @MathysRennela | Space Bunny Alpha 1.0 | 2026-10-01 |
| ★ | [[52,15,7]]known params | pair-partition CPM2D-local bilayer | 52 | 15 | d ≤ 7 | 14.135 | 0.0109 | 8 | 142 | 4 | 5.39 | @mrvee-qC-bee | GPT-6 Astra | 2026-10-01 |
| ★ | [[88,24,7]] | other | 88 | 24 | d ≤ 7 | 13.364 | · | 8 | · | 4 | · | @vprusso | Claude Fable 5.1 | 2026-10-15 |
| ★ | [[360,12,20]] | bivariate bicycle | 360 | 12 | d ≤ 20 | 13.333 | · | 8 | · | 4 | · | @cbjuan | Claude Opus 4.6 +2 | 2026-10-07 |
| ★ | [[93,6,14]] | other2D-local bilayer | 93 | 6 | d ≤ 14 | 12.645 | 0.0092 | 8 | 454 | 4 | 7.28 | @mrvee-qC-bee | GPT-6 Astra | 2026-10-01 |
| ★ | [[144,12,12]] | bivariate bicycle | 144 | 12 | d ≤ 12 | 12.0 | · | 8 | · | 4 | · | @cbjuan | Claude Opus 4.6 +2 | 2026-10-07 |
| ★ | [[48,29,4]] | other | 48 | 29 | d ≤ 4 | 9.667 | · | 14 | · | 4 | · | @hirobumii | GPT-6 Astra +1 | 2026-10-18 |
| ★ | [[188,49,6]] | pair-partition CPM | 188 | 49 | d ≤ 6 | 9.383 | · | 8 | · | 4 | · | @MathysRennela | Space Bunny Alpha 1.0 | 2026-10-01 |
| ★ | [[75,7,10]] | other2D-local bilayer | 75 | 7 | d ≤ 10 | 9.333 | 0.0072 | 8 | 302 | 4 | 5.66 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| [[187,27,8]] | other | 187 | 27 | d ≤ 8 | 9.241 | · | 8 | · | 4 | · | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| [[99,17,7]] | other2D-local bilayer | 99 | 17 | d ≤ 7 | 8.414 | 0.0135 | 8 | 238 | 4 | 4.12 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| ★ | [[40,9,6]] | other2D-local bilayer | 40 | 9 | d ≤ 6 | 8.1 | 0.028 | 8 | 82 | 4 | 5 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| [[117,19,7]] | other2D-local bilayer | 117 | 19 | d ≤ 7 | 7.957 | 0.0118 | 8 | 324 | 4 | 4.47 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| ★ | [[145,32,6]] | pair-partition CPM2D-local bilayer | 145 | 32 | d ≤ 6 | 7.945 | 0.0047 | 10 | 510 | 4 | 5.1 | @MathysRennela | Mimo-V2.6-Flash | 2026-09-28 |
| [[143,23,7]] | other2D-local bilayer | 143 | 23 | d ≤ 7 | 7.881 | 0.0033 | 8 | 815 | 4 | 4.47 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| [[169,13,10]] | other | 169 | 13 | d ≤ 10 | 7.692 | · | 8 | · | 4 | · | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| ★ | [[65,5,10]] | other2D-local bilayer | 65 | 5 | d ≤ 10 | 7.692 | 0.0114 | 8 | 241 | 4 | 5.83 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[50,6,8]] | other2D-local bilayer | 50 | 6 | d ≤ 8 | 7.68 | 0.0266 | 8 | 96 | 4 | 4.12 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[85,8,9]]known params | other2D-local bilayer | 85 | 8 | d ≤ 9 | 7.624 | 0.0113 | 6 | 275 | 4 | 7.21 | @mrvee-qC-bee et al. | GPT-6 Astra | 2026-10-01 |
| ★ | [[91,19,6]] | other2D-local bilayer | 91 | 19 | d ≤ 6 | 7.516 | 0.0055 | 8 | 458 | 4 | 5.1 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[40,12,5]] | other2D-local bilayer | 40 | 12 | d ≤ 5 | 7.5 | 0.0231 | 8 | 101 | 4 | 3.61 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| [[63,13,6]] | other2D-local bilayer | 63 | 13 | d ≤ 6 | 7.429 | 0.0054 | 8 | 255 | 4 | 3.61 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| ★ | [[66,6,9]] | other2D-local bilayer | 66 | 6 | d ≤ 9 | 7.364 | 0.0109 | 8 | 268 | 4 | 5.83 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[66,4,11]] | other2D-local bilayer | 66 | 4 | d ≤ 11 | 7.333 | 0.0057 | 8 | 277 | 4 | 6.08 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| [[105,21,6]] | other2D-local bilayer | 105 | 21 | d ≤ 6 | 7.2 | 0.007 | 8 | 502 | 4 | 8.25 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| [[171,25,7]] | other2D-local bilayer | 171 | 25 | d ≤ 7 | 7.164 | 0.0106 | 8 | 473 | 4 | 4.24 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| ★ | [[48,7,7]] | other2D-local bilayer | 48 | 7 | d ≤ 7 | 7.146 | 0.0247 | 8 | 92 | 4 | 3.16 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[81,9,8]] | other2D-local bilayer | 81 | 9 | d ≤ 8 | 7.111 | 0.0105 | 8 | 234 | 4 | 5.1 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[45,5,8]] | other2D-local bilayer | 45 | 5 | d ≤ 8 | 7.111 | 0.0105 | 8 | 145 | 4 | 5 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[36,4,8]] | other2D-local bilayer | 36 | 4 | d ≤ 8 | 7.111 | 0.0105 | 8 | 82 | 4 | 5.1 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| [[91,13,7]] | other2D-local bilayer | 91 | 13 | d ≤ 7 | 7.0 | 0.0242 | 8 | 129 | 4 | 2.24 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| [[77,11,7]] | other2D-local bilayer | 77 | 11 | d ≤ 7 | 7.0 | 0.0175 | 8 | 186 | 4 | 2.83 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| [[63,9,7]] | other2D-local bilayer | 63 | 9 | d ≤ 7 | 7.0 | 0.0112 | 8 | 178 | 4 | 5 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| [[56,8,7]] | other2D-local bilayer | 56 | 8 | d ≤ 7 | 7.0 | 0.0083 | 8 | 206 | 4 | 6.08 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| ★ | [[36,7,6]] | other2D-local bilayer | 36 | 7 | d ≤ 6 | 7.0 | 0.0104 | 8 | 81 | 4 | 4.12 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[42,6,7]] | other2D-local bilayer | 42 | 6 | d ≤ 7 | 7.0 | 0.0083 | 8 | 112 | 4 | 4.47 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[35,5,7]] | other2D-local bilayer | 35 | 5 | d ≤ 7 | 7.0 | 0.0104 | 8 | 79 | 4 | 4.47 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| [[119,23,6]] | other2D-local bilayer | 119 | 23 | d ≤ 6 | 6.958 | 0.0029 | 8 | 682 | 4 | 5.39 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| ★ | [[56,24,4]] | other | 56 | 24 | d ≤ 4 | 6.857 | · | 8 | · | 4 | · | @hirobumii | GPT-6 Astra | 2026-10-17 |
| [[55,15,5]] | other2D-local bilayer | 55 | 15 | d ≤ 5 | 6.818 | 0.021 | 8 | 95 | 4 | 2 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| [[133,25,6]] | other2D-local bilayer | 133 | 25 | d ≤ 6 | 6.767 | 0.0042 | 8 | 699 | 4 | 5.83 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| ★ | [[87,3,14]] | other2D-local bilayer | 87 | 3 | d ≤ 14 | 6.759 | 0.0049 | 8 | 475 | 4 | 7.28 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[88,36,4]] | other | 88 | 36 | d ≤ 4 | 6.545 | · | 8 | · | 4 | · | @hirobumii | GPT-6 Astra | 2026-10-17 |
| ★ | [[65,17,5]] | other2D-local bilayer | 65 | 17 | d ≤ 5 | 6.538 | 0.0097 | 8 | 229 | 4 | 2.83 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| [[360,4,24]] | bivariate bicycle | 360 | 4 | d ≤ 24 | 6.4 | · | 8 | · | 4 | · | @cbjuan | Claude Opus 4.6 +2 | 2026-10-07 | |
| ★ | [[32,4,7]] | other2D-local bilayer | 32 | 4 | d ≤ 7 | 6.125 | 0.0362 | 8 | 64 | 4 | 3.61 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[36,6,6]]known params | other | 36 | 6 | d ≤ 6 | 6.0 | · | 6 | · | 4 | · | @MathysRennela | Space Bunny Alpha 1.0 | 2026-10-15 |
| ★ | [[36,6,6]] | other2D-local bilayer | 36 | 6 | d ≤ 6 | 6.0 | 0.0234 | 6 | 76 | 4 | 2.24 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| [[105,25,5]] | other2D-local bilayer | 105 | 25 | d ≤ 5 | 5.952 | 0.0071 | 8 | 381 | 4 | 2.24 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| ★ | [[51,3,10]] | other2D-local bilayer | 51 | 3 | d ≤ 10 | 5.882 | 0.0087 | 8 | 158 | 4 | 6.08 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[30,7,5]] | other2D-local bilayer | 30 | 7 | d ≤ 5 | 5.833 | 0.0202 | 8 | 42 | 4 | 2.83 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| [[143,13,8]] | other2D-local bilayer | 143 | 13 | d ≤ 8 | 5.818 | 0.0045 | 8 | 632 | 4 | 7 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| [[121,11,8]] | other2D-local bilayer | 121 | 11 | d ≤ 8 | 5.818 | 0.0042 | 8 | 550 | 4 | 6.08 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| ★ | [[33,3,8]] | other2D-local bilayer | 33 | 3 | d ≤ 8 | 5.818 | 0.0093 | 8 | 60 | 4 | 4.12 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[27,3,7]] | other2D-local bilayer | 27 | 3 | d ≤ 7 | 5.444 | 0.0042 | 8 | 60 | 4 | 6.08 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[12,4,4]] | other2D-local single | 12 | 4 | d ≤ 4 | 5.333 | 0.213 | 8 | 0 | 4 | 3.61 | @MathysRennela | MiMo v2.6 Flash | 2026-09-28 |
| ★ | [[95,5,10]] | other2D-local bilayer | 95 | 5 | d ≤ 10 | 5.263 | 0.0078 | 6 | 384 | 4 | 6.4 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[38,2,10]] | other2D-local bilayer | 38 | 2 | d ≤ 10 | 5.263 | 0.0182 | 8 | 93 | 4 | 4.47 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[46,2,11]] | other2D-local bilayer | 46 | 2 | d ≤ 11 | 5.261 | 0.0078 | 8 | 141 | 4 | 5.83 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[189,27,6]] | other2D-local bilayer | 189 | 27 | d ≤ 6 | 5.143 | 0.0082 | 6 | 529 | 4 | 3.61 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[161,23,6]] | other2D-local bilayer | 161 | 23 | d ≤ 6 | 5.143 | 0.0178 | 6 | 247 | 4 | 2.83 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[147,21,6]] | other2D-local bilayer | 147 | 21 | d ≤ 6 | 5.143 | 0.0178 | 6 | 235 | 4 | 3.61 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[133,19,6]] | other2D-local bilayer | 133 | 19 | d ≤ 6 | 5.143 | 0.0304 | 6 | 199 | 4 | 2.83 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[119,17,6]] | other2D-local bilayer | 119 | 17 | d ≤ 6 | 5.143 | 0.0304 | 6 | 109 | 4 | 2.24 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[91,13,6]] | other2D-local bilayer | 91 | 13 | d ≤ 6 | 5.143 | 0.0304 | 6 | 140 | 4 | 3.16 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[77,11,6]] | other2D-local bilayer | 77 | 11 | d ≤ 6 | 5.143 | 0.0514 | 6 | 74 | 4 | 3.16 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[63,9,6]] | other2D-local bilayer | 63 | 9 | d ≤ 6 | 5.143 | 0.0514 | 6 | 58 | 4 | 3.16 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[49,7,6]] | other2D-local bilayer | 49 | 7 | d ≤ 6 | 5.143 | 0.0201 | 6 | 76 | 4 | 3.16 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[35,5,6]] | other2D-local bilayer | 35 | 5 | d ≤ 6 | 5.143 | 0.0304 | 6 | 53 | 4 | 3.16 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[28,4,6]] | other2D-local bilayer | 28 | 4 | d ≤ 6 | 5.143 | 0.004 | 8 | 52 | 4 | 5.1 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[21,3,6]] | other2D-local bilayer | 21 | 3 | d ≤ 6 | 5.143 | 0.0304 | 8 | 20 | 4 | 3.61 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[25,5,5]] | other2D-local bilayer | 25 | 5 | d ≤ 5 | 5.0 | 0.0074 | 8 | 28 | 4 | 3.16 | @davidplu | GPT-6 | 2026-09-30 |
| ★ | [[20,4,5]] | other2D-local bilayer | 20 | 4 | d ≤ 5 | 5.0 | 0.0173 | 8 | 15 | 4 | 3.16 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[169,13,8]] | other2D-local bilayer | 169 | 13 | d ≤ 8 | 4.923 | 0.0079 | 6 | 468 | 4 | 3.61 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| [[91,7,8]] | other2D-local bilayer | 91 | 7 | d ≤ 8 | 4.923 | 0.017 | 6 | 211 | 4 | 4.12 | @FarLab | Claude Fable 5.1 | 2026-10-01 | |
| ★ | [[65,5,8]] | other2D-local bilayer | 65 | 5 | d ≤ 8 | 4.923 | 0.0123 | 6 | 224 | 4 | 4.47 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[39,3,8]] | other2D-local bilayer | 39 | 3 | d ≤ 8 | 4.923 | 0.017 | 6 | 103 | 4 | 4.12 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[26,2,8]] | other2D-local bilayer | 26 | 2 | d ≤ 8 | 4.923 | 0.0038 | 8 | 33 | 4 | 5.1 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[123,3,14]] | other2D-local bilayer | 123 | 3 | d ≤ 14 | 4.78 | 0.0071 | 6 | 422 | 4 | 8.25 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[82,2,14]] | other2D-local bilayer | 82 | 2 | d ≤ 14 | 4.78 | 0.012 | 6 | 269 | 4 | 6.4 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[34,2,9]] | other2D-local bilayer | 34 | 2 | d ≤ 9 | 4.765 | 0.0076 | 8 | 73 | 4 | 5.1 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[93,3,12]] | other2D-local bilayer | 93 | 3 | d ≤ 12 | 4.645 | 0.0074 | 6 | 298 | 4 | 5 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[62,2,12]] | other2D-local bilayer | 62 | 2 | d ≤ 12 | 4.645 | 0.0069 | 6 | 209 | 4 | 6.71 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[74,2,13]] | other2D-local bilayer | 74 | 2 | d ≤ 13 | 4.568 | 0.0068 | 6 | 301 | 4 | 6.71 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[142,2,18]] | other2D-local bilayer | 142 | 2 | d ≤ 18 | 4.563 | 0.0054 | 6 | 558 | 4 | 8.06 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[188,95,3]] | pair-partition CPM2D-local bilayer | 188 | 95 | d ≤ 3 | 4.548 | 0.0019 | 8 | 617 | 4 | 3.61 | @MathysRennela | Space Bunny Alpha 1.0 | 2026-10-01 |
| ★ | [[188,95,3]] | pair-partition CPM2D-local bilayer | 188 | 95 | d ≤ 3 | 4.548 | 0.0019 | 8 | 512 | 4 | 1.41 | @MathysRennela | Space Bunny Alpha 1.0 | 2026-10-01 |
| ★ | [[178,2,20]] | other2D-local bilayer | 178 | 2 | d ≤ 20 | 4.494 | 0.0033 | 6 | 913 | 4 | 11.4 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[69,3,10]] | other2D-local bilayer | 69 | 3 | d ≤ 10 | 4.348 | 0.007 | 6 | 241 | 4 | 5 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[46,2,10]] | other2D-local bilayer | 46 | 2 | d ≤ 10 | 4.348 | 0.015 | 6 | 128 | 4 | 5 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[177,3,16]] | other2D-local bilayer | 177 | 3 | d ≤ 16 | 4.339 | 0.0032 | 6 | 802 | 4 | 7.81 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[134,2,17]] | other2D-local bilayer | 134 | 2 | d ≤ 17 | 4.313 | 0.0064 | 6 | 495 | 4 | 8.54 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[57,3,9]] | other2D-local bilayer | 57 | 3 | d ≤ 9 | 4.263 | 0.0148 | 6 | 139 | 4 | 5.83 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[58,2,11]] | other2D-local bilayer | 58 | 2 | d ≤ 11 | 4.172 | 0.0129 | 6 | 156 | 4 | 5.39 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| [[94,2,14]] | other2D-local bilayer | 94 | 2 | d ≤ 14 | 4.17 | 0.0062 | 6 | 375 | 4 | 5.66 | @FarLab | Claude Fable 5.1 | 2026-09-30 | |
| ★ | [[18,3,5]] | other2D-local bilayer | 18 | 3 | d ≤ 5 | 4.167 | 0.0651 | 8 | 7 | 4 | 2.24 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[11,5,3]] | other2D-local single | 11 | 5 | d ≤ 3 | 4.091 | 0.202 | 8 | 0 | 4 | 2.24 | @MathysRennela | MiMo v2.6 Flash | 2026-09-28 |
| ★ | [[256,16,8]]known params | topological | 256 | 16 | d ≤ 8 | 4.0 | 0.0015 | 6 | 768 | 4 | 7.07 | Chamon, Claudio | Claude Fable 5.1 | 2005 |
| [[108,12,6]]known params | topological | 108 | 12 | d ≤ 6 | 4.0 | 0.0053 | 6 | 216 | 4 | 5.1 | Chamon, Claudio | Claude Fable 5.1 | 2005 | |
| ★ | [[16,4,4]] | other | 16 | 4 | d ≤ 4 | 4.0 | · | 5 | · | 4 | · | @MicheldeMessieres | Claude Opus 5.5 (Claude Code) | 2026-10-12 |
| ★ | [[155,5,11]] | other2D-local bilayer | 155 | 5 | d ≤ 11 | 3.903 | 0.0029 | 6 | 640 | 4 | 4.47 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| [[111,3,12]] | other2D-local bilayer | 111 | 3 | d ≤ 12 | 3.892 | 0.0097 | 6 | 297 | 4 | 3.16 | @FarLab | Claude Fable 5.1 | 2026-10-01 | |
| ★ | [[33,2,8]] | other2D-local bilayer | 33 | 2 | d ≤ 8 | 3.879 | 0.0152 | 7 | 38 | 4 | 4.47 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[28,3,6]] | other2D-local bilayer | 28 | 3 | d ≤ 6 | 3.857 | 0.0057 | 6 | 47 | 4 | 5.1 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[20,3,5]] | other2D-local single | 20 | 3 | d ≤ 5 | 3.75 | 0.0586 | 6 | 65 | 4 | 2.83 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[44,2,9]] | other | 44 | 2 | d ≤ 9 | 3.682 | · | 6 | · | 4 | · | @davidplu | GPT-6 | 2026-10-03 |
| ★ | [[20,2,6]] | other2D-local single | 20 | 2 | d ≤ 6 | 3.6 | 0.0563 | 6 | 65 | 4 | 4.24 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[8,3,3]] | other2D-local single | 8 | 3 | d ≤ 3 | 3.375 | 0.135 | 6 | 1 | 4 | 1.41 | @MathysRennela | MiMo v2.6 Flash | 2026-09-28 |
| ★ | [[38,2,8]] | other2D-local bilayer | 38 | 2 | d ≤ 8 | 3.368 | 0.0337 | 6 | 58 | 4 | 4.24 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[75,10,5]] | other2D-local bilayer | 75 | 10 | d ≤ 5 | 3.333 | 0.0049 | 7 | 287 | 4 | 7.21 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[10,2,4]] | other2D-local single | 10 | 2 | d ≤ 4 | 3.2 | 0.128 | 6 | 4 | 4 | 4 | @MathysRennela | MiMo v2.6 Flash | 2026-09-28 |
| ★ | [[53,1,13]] | other2D-local bilayer | 53 | 1 | d ≤ 13 | 3.189 | 0.0047 | 8 | 183 | 4 | 6.32 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[16,2,5]] | other | 16 | 2 | d ≤ 5 | 3.125 | · | 6 | · | 4 | · | @hirobumii | GPT-6 Astra | 2026-10-17 |
| ★ | [[173,1,23]] | other2D-local bilayer | 173 | 1 | d ≤ 23 | 3.058 | 0.0019 | 6 | 862 | 4 | 10.8 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[151,1,21]] | other2D-local bilayer | 151 | 1 | d ≤ 21 | 2.921 | 0.0018 | 6 | 749 | 4 | 10.4 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[34,2,7]] | other2D-local bilayer | 34 | 2 | d ≤ 7 | 2.882 | 0.0046 | 6 | 67 | 4 | 4.12 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[17,1,7]]known params | other2D-local bilayer | 17 | 1 | d ≤ 7 | 2.882 | 0.045 | 8 | 12 | 4 | 2.83 | @FarLab | Claude Fable 5.1 | 2026-09-30 |
| ★ | [[127,1,19]] | other2D-local bilayer | 127 | 1 | d ≤ 19 | 2.843 | 0.0034 | 6 | 525 | 4 | 7.21 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[29,1,9]] | other2D-local bilayer | 29 | 1 | d ≤ 9 | 2.793 | 0.0097 | 8 | 51 | 4 | 3.61 | @davidplu | GPT-6 | 2026-09-30 |
| [[27,3,5]] | other2D-local bilayer | 27 | 3 | d ≤ 5 | 2.778 | 0.0044 | 6 | 47 | 4 | 4 | @davidplu | GPT-6 | 2026-09-30 | |
| ★ | [[18,2,5]] | other2D-local single | 18 | 2 | d ≤ 5 | 2.778 | 0.0434 | 5 | 47 | 4 | 3.61 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[27,2,6]] | other2D-local bilayer | 27 | 2 | d ≤ 6 | 2.667 | 0.0043 | 5 | 53 | 4 | 4.12 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[31,1,9]] | other2D-local bilayer | 31 | 1 | d ≤ 9 | 2.613 | 0.0261 | 6 | 56 | 4 | 4.24 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[47,1,11]] | other | 47 | 1 | d ≤ 11 | 2.574 | · | 6 | · | 4 | · | @davidplu | GPT-6 | 2026-10-03 |
| ★ | [[113,1,17]] | other2D-local bilayer | 113 | 1 | d ≤ 17 | 2.558 | 0.0038 | 6 | 458 | 4 | 8.94 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[89,1,15]] | other2D-local bilayer | 89 | 1 | d ≤ 15 | 2.528 | 0.0037 | 6 | 300 | 4 | 8.94 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[39,2,7]] | other2D-local bilayer | 39 | 2 | d ≤ 7 | 2.513 | 0.0251 | 5 | 70 | 4 | 2.83 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[21,1,7]] | other2D-local bilayer | 21 | 1 | d ≤ 7 | 2.333 | 0.0233 | 6 | 24 | 4 | 3 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[12,3,3]] | other | 12 | 3 | d ≤ 3 | 2.25 | · | 4 | · | 4 | · | @MicheldeMessieres | Claude Opus 5.5 (Claude Code) | 2026-10-13 |
| ★ | [[8,2,3]]known params | other2D-local single | 8 | 2 | d ≤ 3 | 2.25 | 0.36 | 4 | 3 | 4 | 1.41 | Cross et al. | Claude Opus 5.5 (Claude Code) | 2026-10-09 |
| [[23,1,7]] | other2D-local bilayer | 23 | 1 | d ≤ 7 | 2.13 | 0.0213 | 6 | 32 | 4 | 3.61 | @davidplu | GPT-6 | 2026-09-30 | |
| [[137,1,17]] | other2D-local bilayer | 137 | 1 | d ≤ 17 | 2.109 | 0.0025 | 6 | 581 | 4 | 7.21 | @FarLab | Claude Fable 5.1 | 2026-10-01 | |
| ★ | [[18,1,6]] | other2D-local single | 18 | 1 | d ≤ 6 | 2.0 | 0.0312 | 6 | 45 | 4 | 4 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[761,1,39]]known params | topological | 761 | 1 | d ≤ 39 | 1.999 | · | 4 | · | 4 | · | @mrvee-qC-bee | GPT-6 Astra | 2026-10-01 |
| ★ | [[25,1,7]] | other2D-local single | 25 | 1 | d ≤ 7 | 1.96 | 0.0968 | 4 | 55 | 4 | 4.24 | @FarLab | Claude Fable 5.1 | 2026-10-01 |
| ★ | [[14,3,3]] | topological2D-local single | 14 | 3 | d ≤ 3 | 1.929 | 0.0301 | 4 | 18 | 4 | 2.24 | @MathysRennela | Mimo-V2.6-Flash | 2026-09-27 |
| ★ | [[13,1,5]] | topological2D-local single | 13 | 1 | d ≤ 5 | 1.923 | 0.0769 | 4 | 17 | 4 | 3.61 | @MathysRennela | Mimo-V2.6-Flash | 2026-09-27 |
| ★ | [[216,4,10]] | bivariate bicycle | 216 | 4 | d ≤ 10 | 1.852 | · | 5 | · | 4 | · | @cbjuan | Claude Opus 5 +1 | 2026-10-07 |
| ★ | [[25,5,3]] | other2D-local bilayer | 25 | 5 | d ≤ 3 | 1.8 | 0.0062 | 6 | 46 | 4 | 1.41 | @davidplu | GPT-6 | 2026-09-30 |
| ★ | [[5,1,3]] | other2D-local single | 5 | 1 | d ≤ 3 | 1.8 | 0.0281 | 4 | 2 | 4 | 2 | @MathysRennela | Mimo-V2.6-Flash | 2026-09-27 |
| ★ | [[144,4,8]] | bivariate bicycle | 144 | 4 | d ≤ 8 | 1.778 | · | 5 | · | 4 | · | @cbjuan | Claude Opus 5 +1 | 2026-10-07 |
| ★ | [[360,4,12]] | bivariate bicycle | 360 | 4 | d ≤ 12 | 1.6 | · | 5 | · | 4 | · | @cbjuan | Claude Opus 5 +1 | 2026-10-07 |
| ★ | [[180,2,11]] | bivariate bicycle | 180 | 2 | d ≤ 11 | 1.344 | · | 5 | · | 4 | · | @cbjuan | Claude Opus 5 +1 | 2026-10-07 |
| [[48,4,4]] | bivariate bicycle | 48 | 4 | d ≤ 4 | 1.333 | · | 5 | · | 4 | · | @cbjuan | Claude Opus 5 +1 | 2026-10-07 |