Chair tiling — verification bundle

Back to the viewer

These are the files the viewer's claims come from. They are pure python3 with no dependencies and no network, and the one external input they need — the transcription of I. Tsiokos's paper that the contact atlas and the panel map are compared against — is shipped here as tiling-matching-system.json. ./runall.sh re-runs the lot in about three and a half minutes. Note that the last step, export.py, overwrites marking.json in this directory.

Chirality, corrected 2026-09-17. The marked tile is chiral, and the hand sketch is the only thing that says which of the two mirror images CGS meant. The first transcription of the photograph interchanged x and y, so the first version of this bundle described the mirror image. The evidence tables in classes.py have been re-read against the axes CGS wrote on the photograph himself (+x to the lower left, +y to the right), and everything here — including the viewer — is the corrected marking. Nothing structural changed: the mirror satisfies the same statements and has the same 44-pose atlas. See tiling-spec.md, the note at the head of the file and §6.

Read this first

• tiling-spec.md — the write-up: what the marking is, why the three marks the sketch omits are forced, and a section headed What is not proved.
• runall.log — the full output of one complete run.
• marking.json — the machine-readable marking: 24 facets with their marks and sites, the 8 substitution frames, the 44-pose contact atlas, the 7 notch fillers, and the map onto I. Tsiokos's panel IDs. The viewer's marking.data.mjs is generated from this file.

Scripts

• chair.py — the model: cells, facets, sites, poses, the matching rule.
• verify.py — substitution consistency, self-similarity, dent/back complementarity, the contact atlas.
• force.py — 22 shell cells, 33 complete first shells, the 7 notch fillers.
• force2.py — the notch map over a 4096-chair patch.
• force3.py — the grouping theorem from the 33 shells.
• force4.py — half the supertile atlas equals the chair atlas.
• m21.py — why the literal 21-mark reading of the sketch cannot be right.
• search.py — all 1 679 616 candidate markings.
• classes.py — the survivors scored against the sketch.
• panelmap.py — Tsiokos's 24 panels mapped onto these 24 facets.
• tiling-matching-system.json — the transcription of the Zenodo paper the previous two compare against. It is a reading of that paper, not the paper.
• export.py — writes marking.json.
• runall.sh — runs the lot.

The page's own check

The viewer does not use the python at runtime; it builds the patch itself in JavaScript. tools/check.mjs re-runs the two statements the picture depends on against that JavaScript, and reproduces the python's contact counts:

node docs/chair-tiling/tools/check.mjs

level 1: 56 cells, exact partition, 48 shared facets, 0 violations
level 2: 448 cells, exact partition, 576 shared facets, 0 violations
level 3: 3584 cells, exact partition, 5376 shared facets, 0 violations

(The write-up counts each shared facet twice, once from each side: 96, 1152, 10752.)