What was already known
Earlier planar results gave a Maker win with a one-stone handicap, while the ordinary empty-board planar case remained unresolved in the cited literature.
AI involvement
OpenAI says its internal frontier model produced this mathematics release and credits OpenAI as manuscript author. The source does not detail the individual human mathematical input for this result.
OpenAI says its internal frontier model produced this release and credits OpenAI as the paper author. The source does not establish a more precise individual autonomy claim.
- Supporting source (openai.com) — Release provenance
Importance
An explicit strategy settles the ordinary planar Snaky achievement question and gives a 21 move upper bound.
Limitations
The 21 move theorem does not claim the minimum move count or a strategy for the strong game. The Lean scope note checks the infinite-board strategy but not the paper’s separate 17×17-board restriction. No named human reconstruction or independent proof review is documented.
Technical verification
The pinned repository note states that its Lean theorem covers the selected statement, with a named Comparator theorem and source file. This is source-reported machine checking; repository review is unchecked and no independent run is recorded here.
Formal checking
The pinned scope note identifies a Lean proof of the selected statement and links the comparator theorem.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- In the initially empty infinite square-board weak Maker–Breaker game, Maker can complete a translated, rotated or reflected Snaky hexomino within 21 legal Maker claims against every legal Breaker play.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. The manuscript explains the proof, but OpenAI is its credited author and no named human reconstruction of the central argument is documented. Few is the evidence default, not a finding that people cannot understand it.
Correction and publication history
Primary manuscript, prior-work and pinned formalization review of one OpenAI-authored contribution; historical non-notifying inclusion.
Read this published revision