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Benefit Ledger · provisional · Mathematics

GPT-5.6 Sol / Codex produces shorter superpermutations for n=8, 9, and 10

On 26 July 2026 Epoch recorded new superpermutation constructions for n=8, 9, and 10 that beat prior upper bounds, accepted by an exact verifier, from a GPT-5.6 Sol / Codex session.

26 Jul 2026Tier 2 NotableMethodology 0.1

Current score

+0.38

3 base · Notable (tier 2 of 5, 3 pts)
× 0.6500 attribution · Critical contribution
× 0.5000 evidence · External expert evaluation
× 0.7000 realization · Independently validated or deployed
× 0.5500 durability
Event-level product before credit split: 0.38

Improved explicit superpermutation lengths are notable constructions (tier 2), not a closed theory. Sol/Codex co-developed them (0.65). Evidence is an exact verifier (0.50). Realization is finite accepted sequences (0.70).

What happened

A superpermutation on n symbols contains every permutation as a contiguous block. Minimal lengths for n≥8 are a long-running computational problem. Epoch’s FrontierMath open-problem page marks the improved sequences Solved (AI) with an exact verifier. Credit is the named Sol release used via Codex, not Astra.

Model attribution

+0.38

GPT-5.6

Named Sol release, used in a Codex session, that produced the shorter n=8,9,10 superpermutations Epoch accepted.

Epoch and the compiled sheet credit a GPT-5.6 Sol / Codex session, not Astra.

Attribution 0.6500 · Credit share 100% · OpenAI

Claims

  • New superpermutation sequences for n=8, 9, and 10 beat prior upper bounds and were accepted by Epoch’s exact verifier.

    outcome · supported

Sources

primary sources

Secondary domains: Computer Science

Revision history

  • 13 Sep 2026 · 0.00 → 0.38

    Imported events under methodology 0.1.

GPT-5.6 Sol / Codex produces shorter superpermutations for n=8, 9, and 10 · NetGoodIndex