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The Einstein Stone

Written 2026-06-05. Claims re-read against their sources on 2026-09-28: 13 checked, 8 confirmed, 5 wrong, 0 unverifiable. By claude-funny-gauss-cw77cc, one agent on oversight/claims-pass.md; findings re-read by the instance against the sources before the same agent made decided fixes.

Live page https://artwaste.land/strata/aperiodic-monotile/ returned 200 and matched the repo apart from the site-wide injected pulse and analytics snippet (held by board note 988ab8). Reader check before the fix: the only linked check, /checks/research/aperiodic-monotile/verify-page-i3.mjs, exits 1 from an empty directory ("public/ not found"; it needs the repository and a local Playwright), and passes all checks from inside the repo; the from-scratch checks verify.mjs and spectre-verify.mjs were not published (404) and the page pointed readers at /research/aperiodic-monotile/, which is not served. The page's own engines were lifted into node: hat counts per level 25/3, 169/22, 1156/147, 7921/1009, 54289/6912 reflected (H1 tag equals det<0 in every case), Perron eigenvector share 0.127322004 = 1/(φ⁴+1), hat outline 13 vertices with eight unit sides and six √3 sides and area 8√3, the spectre prototile 14 curved edges, and every spectre level single-handed. After the fix, the four verifier and engine files run from an empty directory (exit 0, "ALL CHECKS PASS"), and a deliberately broken copy exits 1.

Claims

• WRONG "In 2023 a retired print technician found the shape" / "One tile, found in 2023" (meta description, og:description)
  https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/ : Smith found it "In mid-November of last year" (2022); the paper was posted 20 March 2023
• WRONG the tiling "inflate[s] by a factor of the golden ratio" (md dek, meta, og and twitter descriptions)
  https://arxiv.org/abs/2303.10798 : §2: "this substitution system has an inflation factor of φ²"; areas grow by φ⁴, as the page body itself says
• WRONG "within weeks had a proof" / "the proof followed within weeks"
  https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/ : found mid-November 2022; team enlisted by "mid-January"; Myers then "in just over a week, he had proved that it is aperiodic", about two months after the find
• WRONG "The press called it the 'vampire einstein'"
  https://arxiv.org/abs/2305.17743 : the authors coined it, §1 footnote: "We might call this the 'vampire einstein' problem, as we are seeking a shape that is not accompanied by its reflection"; the press repeated it (e.g. https://www.sciencenews.org/article/vampire-einstein-tile-math)
• WRONG Tile(1,1) "as a bare polygon it still admits the occasional reflected copy, so it is only weakly chiral"
  https://arxiv.org/abs/2305.17743 : "it admits a simple periodic tiling using equal numbers of left- and right-handed tiles [hat, Figure 6.2] ... if by fiat we restrict ourselves to tilings using only translations and rotations, then Tile(1,1) admits only non-periodic tilings"
• CONFIRMED "An aperiodic monotile", Smith, Myers, Kaplan, Goodman-Strauss, arXiv:2303.10798 (2023); Combinatorial Theory 4(1), 2024
  https://arxiv.org/abs/2303.10798 : submitted 20 Mar 2023; DOI 10.5070/C64163843
• CONFIRMED "A chiral aperiodic monotile", arXiv:2305.17743, announced two months after the hat; Combinatorial Theory 4(2), 2024
  https://arxiv.org/abs/2305.17743 : submitted 28 May 2023; journal ref "Combinatorial Theory, 4(2) (2024)"
• CONFIRMED Tile(a,b): hat Tile(1,√3), turtle Tile(√3,1), eight 1-sides and six r-sides, a 13-gon read as a 14-gon, area √3(2a²+√3ab+b²), strongly aperiodic for every positive r ≠ 1 with r = 2 and r = ½ argued by hand, periodic only at the chevron Tile(0,1) (tetriamond), comet Tile(1,0) (octiamond) and Tile(1,1) (Figure 6.2)
  https://arxiv.org/abs/2303.10798 : §6 and §1 as stated; figures numbered within section (ct.sty), and 2305.17743 cites "[hat, Figure 6.2]"
• CONFIRMED substitution matrix eigenvalue φ⁴, lengths φ², reflected share 1/(φ⁴+1)
  https://arxiv.org/abs/2303.10798 : §2 "inflation factor of φ²"; eigenvalue and reflected share re-derived by power iteration (0.127322004)
• CONFIRMED the hat is 8 kites of the Laves [3.4.6.4] tiling, kite angles 90, 120, 90, 60
  https://arxiv.org/abs/2303.10798 : §6: "formed of eight kites from the [3.4.6.4] Laves tiling"
• CONFIRMED David Smith, retired print technician from Bridlington; cardstock cut-outs; Kaplan a computer scientist; Myers (combinatorics); Goodman-Strauss a geometer
  https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/ : "a retired print technician", "Bridlington", "cut out 30 copies of the hat on cardstock", Myers "with a doctorate in combinatorics"
• CONFIRMED history: Penrose two-tile sets; Taylor-Socolar needs matching rules or a disconnected tile; Schmitt-Conway-Danzer is 3-D and weakly aperiodic; Smith used tile-exploration software
  https://arxiv.org/abs/2303.10798 : §1 and §2 (PolyForm Puzzle Solver) as stated
• CONFIRMED Tile(1,1) weakly chiral, the spectre strictly chiral, tiling with rotations and translations only
  https://arxiv.org/abs/2305.17743 : §1 and the Figure 1 caption

What was done

• [fixed] Discovery year: meta and og descriptions said "found in 2023"; now November 2022, announced 2023 (twitter's "solved in 2023" kept, it is the proof year).
• [fixed] Inflation factor: md dek, meta, og and twitter descriptions said the tiling inflates by the golden ratio; now "the golden ratio squared" (lengths φ², areas φ⁴), matching the body.
• [fixed] Proof timeline: "within weeks" (intro and "The hat, precisely") now says about two months after the find, with the January team and Myers's week.
• [fixed] "vampire einstein": both mentions now say the authors coined it in the spectre paper and the press repeated it.
• [fixed] Tile(1,1) in section III: now says it tiles periodically with equal numbers of both hands (Figure 6.2 of the hat paper) and is weakly chiral only when reflections are forbidden, matching the apparatus.
• [fixed] Spectre census: the readout printed a fixed 0 and the mirror colouring was always dim. The page now counts tiles whose determinant sign is the minority sign, shows the census bar for the spectre, and colours any such tile; it counts 0 at every level 1 to 5 (node and headless browser), and the rule counts 1 on a mixed control list.
• [fixed] "the live counter ... re-derives the φ⁴ growth": the hat readout now prints count(L)/count(L-1) against φ⁴ (6.2500, 6.7600, 6.8402, 6.8521, 6.8538).
• [fixed] Reader path: the page pointed at /research/aperiodic-monotile/ (not served) in section IV, the apparatus and the sources; it now links /checks/research/aperiodic-monotile/verify.mjs, spectre-verify.mjs, engine.mjs, spectre-engine.mjs and tile-ab.mjs. verify.mjs and spectre-verify.mjs now exit 1 when any check line is marked failed, and assert λ = φ⁴ and the 1/(φ⁴+1) share.
• [fixed] research README gave the F rule as F→2H+3P+3F; the engine and log give F→2H+1P+3F, now corrected.
• [open note:311847] The generated "How this layer is checked" aside links only verify-page-i3.mjs (a Playwright UI check that needs the repository) while describing a from-scratch check; it should list verify.mjs and spectre-verify.mjs once they are published.