CATALOGUE 187
Snaky in 21 Maker moves
Official catalogue 187 contains one manuscript in Combinatorics. It proves a win from the empty board by composing conditions that survive every legal reply and bounding the height of a finite certificate. “21” is an upper bound on actual Maker moves, not an optimality assertion.
1. Manuscripts in official order
These summaries give the principal scope; consult the cited original results for the complete hypotheses and statements.
Page counts include references. On narrow screens, scroll the table sideways.
| # | Manuscript and overview | Principal claim | Role and available overview |
|---|---|---|---|
| 01 | Snaky in 21 Maker moves →Short name: Snaky in 21 Maker movesSeptember 25, 2026 · 84 pagesOriginal paper (GitHub) ↗ | From the empty infinite grid, Maker wins within 21 actual moves against every legal Breaker continuation; the strategy also works on a 251-cell board and a 17×17 board. Theorem 1 · p. 1; Corollary 6 · p. 8 ↗ | Compose ownership and exclusion conditions; a finite certificate yields an empty requirement and height 21. Owning the common intersection preserves a continuation after every reply. Read the proof overview → |
2. Reading route
Begin with the main proof overview: composition of conditions, an empty requirement, then a single policy. The composition lemma explains coverage of every reply; the finite certificate explains the number 21. The article's main-results section states the board, move order and target shape.
A one-paper catalogue does not need inter-paper categories or a relation diagram. Branching and merging within the proof appear in the article's overview and composition diagrams; the intersection details appear in a table. Direct dependencies, consequences, alternative proofs and generalizations involving other catalogues remain uninvestigated, rather than being declared absent.
3. Sources and checking scope
OpenAI Research Catalog · Catalogue 187; Combinatorics · p. 20
The field name and ordering follow the official overview. Combinatorics is the seventh subject heading (subject ID 13), spanning catalogue numbers 155–192 and PDF pp. 17–21; this entry is on p. 20. The reference is the October 6, 2026 overview in official repository snapshot 1581d4cbdd69a0faf34b2089614fe2a814316a6a.
Astra wrote the new draft from the original sources and self-checked the game quantifiers, both turn conventions in composition, the final intersection, policy extraction, actual-move accounting and finite-board restriction. Two author-provided reconstructors were freshly rerun; the dedicated local-reply suite and Lean compilation were not run. See the article's source section for the full scope and remaining limitations.
This guide and the article are AI-generated explanations. They do not replace the original or guarantee mathematical correctness; consult the linked manuscript, proofs and data before using the results in research.