Attempts
Every attempt, newest first. Each ran in its own sandbox and ended for a recorded reason.
Every attempt, newest first. Each ran in its own sandbox and ended for a recorded reason.
The attempt was to develop complement-factor syzygies for a 273-column pencil. The model call failed before producing a candidate, so no result reached the gate and the strategy was not tested.
openai/gpt-6.1-sol · 0 turnsThe attempt started with the strategy “Coupled interleaved syndromes with a redundant boundary equation.” The model call failed before producing a candidate, so no candidate reached the gate and there is no verified result. The attempt stopped before finishing.
openai/gpt-6.1-sol · 0 turnsThe attempt started on the strategy “Complement-factor syzygies for a 273-column pencil,” but the model call failed before any candidate was produced. No candidate reached the gate, so there is no verified result; the attempt stopped before finishing.
openai/gpt-6.1-sol · 0 turnsThe attempt began on the upper track with the strategy “Coupled interleaved syndromes with a redundant boundary equation.” The model call failed before producing a candidate, so no candidate reached the gate and there is no verified result.
openai/gpt-6.1-sol · 0 turnsThe attempt began exploring coupled interleaved syndromes with a redundant boundary equation, but the model call failed and could not be retried successfully. It stopped before finishing, and no candidate reached the gate, so the strategy was not evaluated.
openai/gpt-6.1-sol · 0 turnsThe attempt investigated the upper-track Lean submission and related orbit-pencil and prescribed-top files, then used Python calculations to explore complement-factor syzygies for the proposed 273-column pencil. It wrote a scratch Python script, but no candidate reached the gate, so no result was verified. The attempt stopped before finishing.
deepseek/deepseek-v4-pro-0813 · 20 turnsThe attempt explored coupled interleaved syndromes with a redundant boundary equation, first inspecting the existing upper-track formalization and benchmark, then prototyping the construction in Python and adding `SyndromePencil.lean`. Lean checks passed for that file, but no candidate reached the gate, so the proposed strategy was not verified as a solution. The attempt stopped before finishing.
openai/gpt-6.1-sol · 20 turnsThe attempt investigated whether complement-factor syzygies could create a rank defect for the 273-column pencil. Exact symbolic elimination and exhaustive 16×16 tests over F257 and F769 found no viable construction: with fourteen coordinates fixed, changing the fifteenth makes the quotient degree 256, above the allowed 255; slack terms and a third denominator factor introduce corresponding agreement or independent-value constraints. No candidate reached the gate, and the submission remained unchanged; the computation and analysis were saved in `scratch/complement_syzygy.py` and `scratch/complement_syzygy.md`.
openai/gpt-6.1-sol · 14 turnsThe attempt replaced monic subset-polynomial collisions with degree-one and degree-two Padé slack factors. An exact count showed that the models still have 15 residual top constraints: even before endpoint and collision losses, the available count is short of the required challenges by about 18.315 bits. Newton and low-order complement identities did not yield a structural saving, and no candidate reached the gate. The agent saved a symbolic audit and a Lean-checked conditional quotient bound, IRS degree bound, selected-column agreement, and core agreement; submission files were unchanged.
openai/gpt-6.1-sol · 11 turnsThe attempt explored an equivariant 1024-fibre pencil as a way to amplify challenges, inspecting the existing upper-bound Lean files and using Python calculations and `score_for_claim` queries to investigate candidate parameters.
deepseek/deepseek-v4-pro-0813 · 37 turnsThe attempt explored degree-one and degree-two Padé slack factors as an alternative to monic subset-polynomial collisions, but no candidate reached the gate. Exact symbolic counting found 15 residual top equations after eliminating the slack coefficients; even ignoring the endpoint constraint, the guaranteed fibre size was 843,420,585,443, below the required 274,980,728,111,395,088 challenges. The endpoint generally costs an additional base-field coordinate, and the low-order complement equations were unit-triangular, so no useful rank defect was found. The agent gave up without claiming an impossibility result; it left audit scripts, a report, and a Lean file that compiled, while leaving promoted files unchanged.
openai/gpt-6.1-sol · 27 turnsThe attempt tested a 1024-fibre equivariant pencil. The entropy bound passed by a factor of 1.903459, and the agent verified the 1008-point invariant core, the polynomial identity for R, and the stated agreement and degree values. It also compiled a Lean file proving transport and coordinate-permutation properties, but scalar actions leave the challenge parameter unchanged, while the tested faithful monomial twists were ruled out by an interpolation obstruction. No nontrivial challenge action was constructed, so no candidate reached the gate.
openai/gpt-6.1-sol · 27 turnsThe attempt explored replacing monic subset-polynomial collisions with Padé slack factors. After inspecting the upper-track Lean files and checking nearby score claims, it used Python calculations to analyze the existing OrbitPencil family; the notes found a promising entropy margin for one parameter choice, but no candidate was produced or submitted to the gate.
deepseek/deepseek-v4-pro-0813 · 21 turnsStopped at its limit.
openai/gpt-6.1-sol · 14 turnsThe attempt investigated whether Padé slack factors could improve the upper-track construction, using symbolic analysis of the existing rational pencil and its coefficient constraints. It found that agreement on an extra column forces a polynomial factor with that column as a root, adding a top-coefficient key coordinate; the resulting entropy ratio is about 2^-28 below the requirement of 2^58 winning challenges. Enlarging the core or adding generic auxiliary factors does not remove this deficit. No improved candidate was submitted, and the gate verified no result.
deepseek/deepseek-v4-pro-0813 · 39 turnsThe attempt explored a 1024-fibre equivariant pencil. Its prospective entropy bound passed by 0.9286 bits, and the invariant core had degree 1008, but the promoted rational words were fixed by the order-16 action, so the challenge action was identity. All 128 faithful monomial-character twist pairs failed the full-fibre construction: character projection yields a nonzero polynomial of degree at most 132095 with 139264 roots, contradicting the required nonzero, off-core parameter. No candidate reached the gate, and the hypothetical score was not verified; the obstruction applies to this search family, not to the strategy space generally. Scratch artifacts include the exact search and a compiled generic equivariance lemma preserving violation and agreement.
openai/gpt-6.1-sol · 24 turnsStopped at its limit.
openai/gpt-6.1-sol · 14 turnsThe attempt investigated the “Dihedral quotient pencil with exceptional half-sized fibres” strategy by reading the upper-track Lean submission and orbit-pencil files, then running several Python checks.
deepseek/deepseek-v4-pro-0813 · 21 turnsThe attempt explored higher-order pole pencils with compressed low-coefficient keys. It produced a kernel-checked `HigherPole.lean` proving divisibility, factorization, challenge separation, and root-agreement identities, and exact integer screens of sparse profiles found no improvement: best agreement remained 139,775, with ordinary keys providing 30.617 bits against 57.932 required. No candidate reached the gate, so the incumbent, score, and unsafe index were unchanged.
openai/gpt-6.1-sol · 26 turnsStopped at its limit.
openai/gpt-6.1-sol · 21 turnsThe attempt explored a mixed 256/512-point block strategy with an exact coefficient-profile search, inspecting the existing Lean submission and running several Python calculations. Score queries ranged from 11546 to 11613, but no candidate reached the gate, so none of those queries established a verified result.
deepseek/deepseek-v4-pro-0813 · 28 turnsThe attempt analyzed dihedral quotient pencils with exceptional half-sized fibres, using exact searches for degrees 64, 128, 256, and 512. Even with square-valued endpoint keys, the best calculated agreement was 139519, below the incumbent of 139775; the gate verified no candidate. The attempt ended without Lean formalization or submission changes, and the result rules out only the modeled profiles.
openai/gpt-6.1-sol · 13 turnsThe attempt pursued higher-order pole pencils with compressed low-coefficient keys, first inspecting the upper-track solution and related Lean files, then using several Python calls to investigate the approach.
deepseek/deepseek-v4-pro-0813 · 16 turnsThe attempt explored certifying an exceptional coefficient fibre via additive energy. It inspected the existing upper-submission files and Mathlib’s symmetric-polynomial and Newton-identity support, then built Python experiments and a Lean scratch file for fibre-counting arguments.
openai/gpt-6.1-sol · 28 turnsStopped at its limit.
openai/gpt-6.1-sol · 14 turnsthe agent process stopped during this attempt
deepseek/deepseek-v4-pro-0813 · 36 turnsThe attempt searched mixed 256/512-point block strategies using an exact coefficient-profile analysis. It evaluated 183,123 profiles across cores 255, 511, 767, and 1023, varying block degrees, singleton counts, exclusion patterns, and key constructions; none met the required threshold. The best mixed profile had 272 pairs and one singleton, but its guaranteed K was 880,067,499 versus the required 274,980,728,111,395,088, so no candidate reached the gate and the submission remained unchanged.
openai/gpt-6.1-sol · 16 turnsThe attempt explored the “higher-order pole pencils with compressed low-coefficient keys” strategy by inspecting the upper-track Lean submission and running several Python experiments. An initial score query failed because the unsafe index was supplied as a fraction rather than an integer; querying index 122369 returned 11613.
deepseek/deepseek-v4-pro-0813 · 16 turnsthe agent process stopped during this attempt
deepseek/deepseek-v4-pro-0813 · 5 turnsThe attempt sought an unusually large coefficient fibre by bounding additive energy for 273 columns and 15 coefficients. Exact rational counting showed that diagonal pairs and the analyzed direct whole-coset replacement pairs with dimension d ≥ 4 contribute E/N < 2^19; the d ≥ 16 contribution beyond the diagonal is below 2^-40. These estimates cover only those structured pair classes, not the full energy, and did not certify a fibre meeting the density-only requirement of 274980728111395088 challenges, with about 2^27.31465 concentration still missing. The agent gave up without reaching the gate or changing the promoted submission; it left Python analysis and a Lean file that compiled, proving second-moment bounds and a conditional triangular Newton-key equivalence.
openai/gpt-6.1-sol · 25 turns