Applied the exact one-cell AnswerBench v2 correction, compared it with commit-pinned v1/v2 sources, and validated it through independent semantic-CSV and raw-byte encodings.

Candidate — review needed

Corrected imo-bench-geometry-004 from 45752 to the quoted CSV field 4, 5. Pinned v1, the official Sharygin solution, a complete semantic comparison, a separate byte checker, four negative controls, and a clean-upstream patch replay all agree. number_theory-048 and every unrelated byte remain unchanged.

Candidate for review — not a solution claim

Independent statement checking, criticism, literature review, and verification remain required.

Strategy and discriminator

hash-bound one-cell dataset correction

Full-file semantic identity outside one approved CSV cell, independently reinforced by a unique context-bound byte replacement.

Hypothesis: The candidate differs from pinned AnswerBench v2 only by changing imo-bench-geometry-004 Short Answer from 45752 to the quoted field 4, 5, agrees with v1 and the official solution, preserves the released schema profile, and leaves imo-bench-number_theory-048 unchanged.

Test: Parse pinned v1, pinned v2, and candidate v2 with Python's standard CSV reader, compare every parsed cell and row arity, then independently require exact byte-stream equality after one unique replacement.

Rationale

The official solution explicitly gives n=4 or n=5. The candidate has exactly one semantic-cell delta and is byte-for-byte the pinned baseline after that unique replacement. Independent encodings and adversarial controls make the result eligible for isolated human review.

Claims requiring scrutiny

Against upstream commit 96fa6c4cc3a9bb7450ee7b6773b659d3a030dace, the candidate changes exactly imo-bench-geometry-004 column 3 from 45752 to 4, 5.
The corrected geometry-004 record parses into exactly six fields.
imo-bench-number_theory-048 and all other records are unchanged.
The candidate SHA-256 is a56cee7c31412a6d851af03263d305b65baa173f455bd092837c476c5a975cdc.
The review patch applies cleanly to the pinned upstream commit and produces the same candidate hash.

Evidence and scope

python3 checkers/verify_answerbench_geometry_004.py V1.csv BASELINE_V2.csv imobench/answerbench_v2.csv: PASS
python3 checkers/check_exact_geometry_004_patch_bytes.py BASELINE_V2.csv imobench/answerbench_v2.csv: PASS
python3 checkers/test_geometry_004_checkers.py V1.csv BASELINE_V2.csv imobench/answerbench_v2.csv: candidate accepted and four adversarial controls rejected
git apply --check artifacts/answerbench-v2-geometry-004.patch in a clean upstream checkout: PASS
Clean-checkout application produced a one-file, one-insertion/one-deletion diff and candidate SHA-256 a56cee7c31412a6d851af03263d305b65baa173f455bd092837c476c5a975cdc.

Computational experiments

.proof-experiments/20260722-191953-1b9235: candidate accepted and four adversarial variants rejected in 0.076 seconds.
.proof-experiments/20260722-192003-88bf3d: semantic CSV checker passed in 0.083 seconds.
.proof-experiments/20260722-192003-1006c6: independent byte checker passed in 0.082 seconds.

Independent checker

checkers/check_exact_geometry_004_patch_bytes.py is a separately written, parser-independent encoding. It requires exact full-file byte equality after one unique context-bound replacement and passed against the pinned baseline.

Contribution gate

candidate_eligible

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome: candidate
Public classification: candidate

Cross-domain transfers tested

None recorded.

Established facts

The official 2009 Sharygin final-round solution gives n=4 or n=5.
https://geometry.ru/olimp/2009/finseng.pdf, PDF page 10. · The source problem represented by imo-bench-geometry-004. · proved
Pinned AnswerBench v1 stores geometry-004 Short Answer as 4, 5.
Standards-compliant parse of SHA-256 37aeca686ce677f93580821cfe16a0c0e45872479a502df43272e099da37d8fa. · Upstream commit 96fa6c4cc3a9bb7450ee7b6773b659d3a030dace. · computed
Pinned AnswerBench v2 stores the corrupted answer 45752.
Standards-compliant parse of SHA-256 275877a9d988d85278fad3a5f8a41d7f83393a60bf259531ec0a5161e6b21cf9. · Upstream commit 96fa6c4cc3a9bb7450ee7b6773b659d3a030dace. · computed
The candidate differs from pinned v2 only by the approved geometry-004 answer replacement.
Semantic and byte checkers plus clean-checkout patch replay. · All 400 records and all candidate bytes. · computed

Ruled out in this epoch

Change imo-bench-number_theory-048 as part of issue 14.
This dataset-correction patch. · The task's independent derivation confirms the v2 answer; the scoped correction explicitly protects it. · Semantic checker and exact byte checker preserve the row. · A separate rigorous derivation finding an error in the current v2 value and an independently scoped correction request.
Normalize every v2 record to six fields.
The geometry-004 correction. · That would alter unrelated pre-existing algebra-036 data and violate the one-cell repair contract. · Pinned v2 and candidate each have exactly one five-field record, imo-bench-algebra-036. · A separately sourced request to repair algebra-036.
Use an unquoted replacement 4, 5.
The target CSV field. · It parses as two fields and corrupts target-row arity. · The malformed-comma adversarial control was rejected. · None; standards-compliant CSV requires quoting.

Open leads

Submit the clean one-cell patch upstream.
All technical acceptance criteria are satisfied; maintainer review is the remaining path to external usefulness. · Refetch current main and replay the two checkers before submission. · high · open

Continuation checkpoint

Objective: Convert the validated local candidate into an upstream-reviewed correction.

First action: Fetch current google-deepmind/superhuman main, compare its commit and target row with 96fa6c4cc3a9bb7450ee7b6773b659d3a030dace, then replay the patch and checkers.

Stop condition: Stop if the correction is already present; otherwise stop the technical phase after a one-cell pull request is prepared for authorized submission.

Next moves

Obtain human approval to submit externally.
Refetch upstream main and confirm issue 14 remains unresolved.
Apply artifacts/answerbench-v2-geometry-004.patch in a clean upstream checkout and replay both checkers.
Open a one-cell pull request referencing issue 14, explicitly stating that number_theory-048 was not changed.
Complete Google's CLA and maintainer-review process.

Citations

Tool disclosure

GPT-5.6 Sol served as principal investigator. A GPT-5.6 Terra delegate supplied bounded source reconnaissance; Sol independently rechecked every relied-on claim against the live issue, pinned Git object, and official olympiad solution. Python 3.12.3 standard-library CSV parsing, Git 2.43.0, deterministic Python checkers, curl, and the Proof Factory experiment recorder were used. No CAS, solver, proof assistant, lab compute, system-package installation, external publication, or repository-remote change was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 775.2s
Review state: needs isolated skeptic review
Attempt ID: deepmind-superhuman-14-geometry-answer-20260722-192533-af3889

Human review ledger

accept · Charlie Krug · 2026-07-22 20:31 UTC
I reviewed the evidence packet and approve this candidate for the next external contribution step.