Snaky 21-Move Cards

An interactive viewer for the 728 cards of the 21-move Snaky certificate from “Snaky in 21 Maker moves” (OpenAI, 2026), Appendix D. The live page is linked in this repository's About panel.

Each card is drawn on square cells: X marks a required cell, gray is the pivot, and white is the rest of the envelope. The card's child conditions are drawn in the same coordinates. Hover a cell to place a Breaker reply and see which children survive; click a child to follow it down the proof.

Link to a specific card with #c<number>, for example #c727.

How the page checks itself

On every load the page recomputes all 728 cards from the combination rule (Lemma 3, equation (2)), checks that each of the 37,042 Breaker reply classes leaves a child alive, and compares the certificate's SHA-256 with the value printed in the paper.

Rebuild

index.html is generated. Edit template.html or engine.js, then run:

python3 build.py              # writes index.html
python3 build.py --artifact   # writes the variant used as a Claude artifact

build.py stops if certificate.txt differs from the paper's file.

Cross-check against the paper's own reconstruction

In a clone of https://github.com/openai/math, from the folder preprints/Snaky-in-21-Maker-moves-September-25-2026:

python3 verification/supporting/route21/primary.py --output reference.json

Then, in this repository:

node test_engine.js certificate.txt path/to/reference.json

This compares all 728 cards and all 1,620 combination nodes, inline ones included, and checks the counts in Section 6 of the paper.

Files

File	Contents
index.html	The page that GitHub Pages serves (generated)
template.html	Layout, styles and interaction
engine.js	Certificate parser and combination rule; runs in the browser and in Node
certificate.txt	Appendix D, byte-identical to the paper's verification/certificate.txt
build.py	Inlines the engine, certificate and license text into index.html
test_engine.js	Cross-check against the paper's reconstruction

License and credits

This project is licensed under the Apache License 2.0; see LICENSE.

certificate.txt is the certificate from “Snaky in 21 Maker moves” (OpenAI, 2026), copied unchanged from https://github.com/openai/math/tree/main/preprints/Snaky-in-21-Maker-moves-September-25-2026, where it is distributed under the Apache License 2.0. See NOTICE.

This project is independent and is not affiliated with or endorsed by OpenAI.

To cite the paper, its repository gives:

@misc{OAI:Snaky-in-21-Maker-moves-September-25-2026,
  author = {{OpenAI}},
  title = {{Snaky in 21 Maker moves}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Snaky-in-21-Maker-moves-September-25-2026/article.pdf}{OAI:Snaky-in-21-Maker-moves-September-25-2026}},
  year = {2026}
}