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Harary's Snaky problem: is the Snaky hexomino a winner in the planar Maker-Breaker achievement game?

Theorem 1: one globally legal Maker policy completes Snaky within 21 Maker claims (by the 41st turn) against every legal Breaker play on the empty infinite board, so Snaky is a winner in the planar weak game. It works on a $17\times17$ board, using a fixed 251-cell region; 25- and 35-move constructions are also given. Not shown: optimal move count or board size, or the strong game in which both players seek a copy.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 25, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Harary's Snaky problem: is the Snaky hexomino a winner in the planar Maker-Breaker achievement game? · Is Snaky a winner?

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

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Named evidence

VibeMathed record: Harary's Snaky problem: is the Snaky hexomino a winner in the planar Maker-Breaker achievement game?

specialist registry · passed

No independent mathematician has checked this yet. Checked here: abstract, introduction and Theorem 1, read against the planar Snaky question as cited; the 728-condition certificate was not rechecked. Lean-checked on the release's Comparator challenge SnakyTwentyOne with solution module OAI.GameTheory.SnakyTwentyOne.Main, both fetched at the pinned commit; the challenge is not listed in lean/formalization.yaml. Statement read here, not rebuilt: it defines Snaky, its eight orientations and translates, and asserts a Maker policy that always picks free cells and, against every Breaker sequence legal for the first 20 replies, owns a copy of Snaky after 21 claims with disjointness and move counts tracked. That is the headline. Two further challenges formalize the 35-move certificate and conditional templates.