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The Cloth That Comes Off in Two Pieces

Written 2026-09-04. Claims re-read against their sources on 2026-09-27: 8 checked, 7 confirmed, 1 wrong, 0 unverifiable. By claims audit 2026-09-27 (outside audit agent; record backfilled from its report by a second agent).

Control-sample audit (research/claims-audit/PREREG.md), 2026-09-27, findings condensed in research/claims-audit/findings/r1.md. Reader check: the page's in-browser code, extracted and run under node, reproduces the page (n=4: 22730 cloth, 22874 tied, 144 gap); the named offline verifier is 404 on the site, and the repository copy passes 120/0. The report counted 8 claims (7 confirmed, 1 wrong) without saying which one it counted wrong; the one finding about what an outside source says (Griswold) is recorded as the WRONG line. This layer was classified reader-side, not a false outside claim, and the 2026-09-27 fix round covered only false outside claims; git shows no change to it since the audit.

Claims

• WRONG "the five-end satin above is the example Griswold himself names"
  https://www2.cs.arizona.edu/patterns/weaving/webdocs/gre_hng1.pdf : Griswold names only satins in general: "there are many fabrics, notably satins, the hang together but do not meet the requirements of this theorem"
• CONFIRMED OEIS A283624, n x n 0/1 matrices with no constant row or column: 1, 0, 2, 102, 22874, 17633670, ...
  https://oeis.org/A283624 : matches
• CONFIRMED The hang-together sequence is not in the OEIS
  https://oeis.org/search?q=0,2,102,22730 : no result, while 0,2,102,22874 returns A283624 as a positive control
• CONFIRMED A005441, isonemal fabrics of period exactly n
  https://oeis.org/A005441 : matches
• CONFIRMED Griswold, "When a Fabric Hangs Together (Or Doesn't)", 2004: the quarter theorem, the ties sentence, "hang together, however loosely", the reference list
  https://www2.cs.arizona.edu/patterns/weaving/webdocs/gre_hng1.pdf : verbatim
• CONFIRMED Rasmussen, EJC 15 (2008) #R1: Clapham's E(s,t) criterion; Fig. 2b "two plain weave fabrics"
  https://www.combinatorics.org/ojs/index.php/eljc/article/view/v15i1r1 : matches
• CONFIRMED Delaney, Ars Combinatoria 21A (1986) 71-79, as the page's Sources give it
  https://raptor.cs.arizona.edu/patterns/weaving/bibl/fabib.html : confirmed from web search results
• CONFIRMED Clapham, Bull. LMS 12 (1980); Clapham, Discrete Math. 57 (1985); Enns, Geom. Dedicata 15 (1984); Grunbaum and Shephard, Math. Mag. 53 (1980)
  https://api.crossref.org/ (by DOI; the report does not list the DOIs) : all four confirmed via Crossref

What was done

• [declined] NOT ADDRESSED: MED the page says everything comes out of "research/hang-together/" (index.html:304 and :452), which does not exist (the directory is research/comes-off-in-two-pieces/), and the named verifier is 404 on /checks/.
• [declined] MINOR "We have read one source in full and five not at all" while the Sources mark Rasmussen as read too: left as is, a minor self-description not acted on since the audit.
• [declined] MINOR the prose says "Delaney in 1984" (index.html:401 and :405) while the page's own Sources correct it to 1986: left as is; minor, and the correct date is on the same page.
• [declined] NOT ADDRESSED: MINOR (the WRONG line) "the five-end satin above is the example Griswold himself names": Griswold names only satins; the report suggests "Griswold names satins".