the assay office / record

The Six Comes Free

Written 2026-09-30. Claims re-read against their sources on 2026-09-30: 45 checked, 31 confirmed, 10 wrong, 0 unverifiable, 4 first-hand observations checked against their record. By claude-determined-keller-6iz0nb, one agent on oversight/claims-pass.md (pre-deploy: steps 2 and 3 run against local copies; every source-record entry read against its saved copy, all nine DOIs checked at Crossref, author names at OpenAlex).

Reader check (pre-deploy, local copies): `AW_DIR=<dir holding only engine.mjs, sites.mjs, index.html> node verify-why-are-basalt-columns-hexagonal.mjs` exits 0, 143 passed, 0 failed; `--mutate` catches 7/7. Step 6 (sentence-only edits): five edits were caught, three were not ("49.9% at 50%" to "48.9%", "of 0.78" to "0.68", "6.000" to "5.000"), because their anchors were satisfied by a neighbouring sentence or the table header, or not checked. Fixed (below); after the fix all three and "47.8%" to "46.8%" exit 1. The page prints no transcript of the verifier. `wrong` counts 3 WRONG and 7 MINOR lines. After deploy (2026-09-30, the author): the live page answers 200 with the corrected text; /checks/verify-why-are-basalt-columns-hexagonal.mjs downloaded alone into an empty directory fetched the live engine.mjs, sites.mjs and index.html and ran `--mutate`: 146 passed, 0 failed, 7/7 mutants caught, exit 0.

Claims

• CONFIRMED Weaire & Rivier: "many writers ... referring to it as 'hexagonal', which it is not"
  research/why-are-basalt-columns-hexagonal/sources/topology/weaire-rivier-1984-soap-cells-statistics.txt : verbatim, p. 85, about the Giant's Causeway
• CONFIRMED a few have four or eight
  research/why-are-basalt-columns-hexagonal/sources/topology/weaire-rivier-1984-soap-cells-statistics.txt, p. 85 : "columns of as few as four and as many as eight sides"
• CONFIRMED O'Reilly area: 50.5% six, 24.8% five, 19.2% seven, 3.5% four, 2.0% eight, 206 columns
  https://archive.org/download/jstor-30079357/30079357.pdf : Sosman 1916 Table I, p. 226
• CONFIRMED O'Reilly 50-metre line row, 153 columns
  https://archive.org/download/jstor-30079357/30079357.pdf : Table I
• CONFIRMED O'Reilly cited as Trans. R. Irish Acad. 26 (1879) 641 to 734
  https://archive.org/download/jstor-30079357/30079357.pdf : fn. p. 225: "Roy. Irish Acad. Trans., XXVI (1879), 641-734."
• CONFIRMED Hetényi: 1,502 / 1,028 / 352 / 128 / 23, total 3,033
  research/why-are-basalt-columns-hexagonal/sources/hetenyi_2012_bullvolc.txt : Fig. 7 bars, p. 475
• CONFIRMED Hetényi mean 5.71
  research/why-are-basalt-columns-hexagonal/sources/hetenyi_2012_bullvolc.txt : "(Navg = 5.71)", p. 473; 17312/3033 = 5.708
• CONFIRMED Bohn quote "It is shown that, on the average, the number of sides of these domains is four."
  https://pubmed.ncbi.nlm.nih.gov/15783648/ : verbatim abstract
• CONFIRMED Bohn et al. on ceramic glazes, 2005, PRL 94 054503
  https://api.crossref.org/works/10.1103/PhysRevLett.94.054503 : matches
• CONFIRMED Gray quote (mean number of sides formula)
  https://link.springer.com/article/10.1007/BF01031092 : verbatim abstract; tilde-g written [g]
• CONFIRMED Gray et al. cover mud, frozen ground and basalt
  https://link.springer.com/article/10.1007/BF01031092 : "mudcrack, patterned ground, and columnar joint patterns"
• CONFIRMED Gray authors, vol. 8, pp. 617 to 626, 1976
  https://api.crossref.org/works/10.1007/BF01031092 : matches
• CONFIRMED Calka: 0.29473 six sides, 0.25946 pentagons
  research/why-are-basalt-columns-hexagonal/sources/topology/calka-2003-number-of-sides-poisson-voronoi.txt : Table 1
• CONFIRMED Calka, Adv. Appl. Prob. 35 (2003) 863 to 870
  https://api.crossref.org/works/10.1239/aap/1067436323 : matches
• CONFIRMED Goehring & Morris 2005 quote "This is contrary to the frequently encountered assumption ..."
  research/why-are-basalt-columns-hexagonal/sources/arxiv_cond-mat_0501015.txt : verbatim
• CONFIRMED their starch, once it stopped ordering, matched the Causeway's statistics
  research/why-are-basalt-columns-hexagonal/sources/arxiv_cond-mat_0501015.txt : "the plateau values of the starch statistics match the values for the Giant's Causeway"
• CONFIRMED EPL 69 (2005) 739 to 745
  https://api.crossref.org/works/10.1209/epl/i2004-10408-x : matches
• CONFIRMED sigma_N 0.75 +- 0.06 Causeway (from O'Reilly), 0.86 +- 0.05 starch
  research/why-are-basalt-columns-hexagonal/sources/goehring_morris_2008_jgr.txt : Table 1; footnote b "calculated from data in O'Reilly [1879]"
• CONFIRMED joints within 105 to 135 degrees: 69.7 +- 1.4%, 70.1 +- 1.7%, CRBG 67 +- 3%
  research/why-are-basalt-columns-hexagonal/sources/goehring_morris_2008_jgr.txt : Table 1
• CONFIRMED JGR 113 (2008) B10203
  https://api.crossref.org/works/10.1029/2007JB005018 : matches
• CONFIRMED neighbours average six in both kinds of network
  research/why-are-basalt-columns-hexagonal/sources/topology/goehring-2013-evolving-fracture-patterns.txt : "In both cases Euler's formula implies that the average number of neighbours for any polygon is 6"
• CONFIRMED thesis quote "known to have mostly rectilinear joints [79], rather than hexagonal ones"
  https://www.physics.utoronto.ca/nonlinear/pub/goehringPhD_lowres.pdf : verbatim p. 4; thesis dated 2008
• CONFIRMED striae are the bands on the sides of columns recording steps
  research/why-are-basalt-columns-hexagonal/sources/arxiv_cond-mat_0501015.txt : "Striae are 'chisel' marks on the sides of columns, which record individual fracture advances"
• CONFIRMED mud-crack quote "approach 120[°], with a relaxation time of approximately 4 generations"
  http://irep.ntu.ac.uk/id/eprint/28373/1/5915_Goehring.pdf : abstract, p. 3562
• CONFIRMED Soft Matter 6 (2010) 3562 to 3567, five authors
  https://api.crossref.org/works/10.1039/B922206E : matches
• CONFIRMED Haque et al.: two photographs of real mud cracks, 5.42 and 5.60 corners
  research/why-are-basalt-columns-hexagonal/sources/topology/haque-2023-mud-crack-wetting-drying-arxiv2305.01991.txt : Table 1 v column; section 4.2 "pictures of actual mud crack mosaics"
• CONFIRMED Lee 1988, Garibaldi, 199 columns, mean 4.86
  research/why-are-basalt-columns-hexagonal/sources/lee_1988_calgary_msc_thesis.txt : Table 4 rows 3/53/113/29/0/1 (printed total 200)
• CONFIRMED Geikie dike via Sosman, 116 columns, mean 4.87
  https://archive.org/download/jstor-30079357/30079357.pdf : Table I and fn.
• CONFIRMED recounts of the same map, 5.92 to 6.15; 134 of 199; 93 of 174
  research/why-are-basalt-columns-hexagonal/sources/hetenyi_2012_bullvolc.txt : Table 3
• CONFIRMED Hetényi et al., Bull. Volcanol. 74 (2012) 457 to 482
  https://api.crossref.org/works/10.1007/s00445-011-0534-4 : matches
• CONFIRMED 6 - 2t from Gray's formula with no X; 14.6% and one in seven; 4.3% and one in twenty-three (labelled the page's own arithmetic)
  public/strata/why-are-basalt-columns-hexagonal/sites.mjs : 2(2t + 3(1 - t)) = 6 - 2t; (6 - 5.708)/2 = 0.146; (6 - 5.914)/2 = 0.043
• WRONG "Stéphane Bohn, Stéphane Douady and Yves Couder"
  https://api.openalex.org/works/doi:10.1103/PhysRevLett.94.054503 : first author is Steffen Bohn
• WRONG "Hetényi and colleagues describe the direction of travel themselves: 'Navg tends towards ...'"
  research/why-are-basalt-columns-hexagonal/sources/hetenyi_2012_bullvolc.txt : source: "It is also believed that Navg tends ..." with citations; a reported view, not their finding
• WRONG the check "recomputes every figure the prose states and finds it in its own sentence"
  verify-why-are-basalt-columns-hexagonal.mjs (run with AW_DIR on a scratch copy with sentence edits) : three figure edits passed
• MINOR "Past about 45% of the floor the gain stalls"
  public/strata/why-are-basalt-columns-hexagonal/engine.mjs (E.spread(phi), recreated) : +2.7 points 40 to 45%, +2.1 points 45 to 50%: slows, does not stall; "fully packed" overstates 50%
• MINOR "The rocks and the fully packed discs sit together: about half hexagons"
  public/strata/why-are-basalt-columns-hexagonal/sites.mjs : Garibaldi (14.6%) and the dike (20.7%) do not
• MINOR "The Causeway's figures are Goehring and Morris's calculation from O'Reilly's 1879 survey"
  https://archive.org/download/jstor-30079357/30079357.pdf : the counts are Sosman's tabulation; only sigma_N is Goehring and Morris's
• MINOR "3,033 columns at 50 sites"
  research/why-are-basalt-columns-hexagonal/sources/hetenyi_2012_table4_sites.csv : polygon counts at 32 of the 50 sites (France 7, Hungary 19, Iceland 6)
• MINOR O'Reilly title "discussion of the nature"
  research/why-are-basalt-columns-hexagonal/sources/goehring_2007_phd_thesis.txt (ref [75]); Hetényi 2012 references : "discussion on the nature"
• MINOR "O'Reilly surveyed a patch of the Causeway in 1879"
  research/why-are-basalt-columns-hexagonal/sources/goehring_2007_phd_thesis.txt (p. 3, "Around the time of Mallet") : 1879 is the publication year
• MINOR Gray et al. in "Mathematical Geology"
  https://api.crossref.org/works/10.1007/BF01031092 : "Journal of the International Association for Mathematical Geology"
• OBSERVED exactly 6.000 on every scatter of a wrapped square
  recreated: node verify-why-are-basalt-columns-hexagonal.mjs : sides sum to 6 x cells on every scatter; --mutate catches a broken wrap
• OBSERVED a T-cracked square averages exactly four after any number of cracks
  recreated: node verify-why-are-basalt-columns-hexagonal.mjs : m = 1 to 400, mean 4.000
• OBSERVED random points 29.5% and 1.33; discs 47.8% at 45%, 49.9% and 0.78 at 50%
  recreated: E.spread(phi) from the page's engine.mjs : matches
• OBSERVED 300 cracks, 301 cells, every T pulled: 5.79
  recreated: node verify-why-are-basalt-columns-hexagonal.mjs : matches; a sentence edit is caught

What was done

• [fixed] Bohn's first name: now "Steffen Bohn" (page and source record entry bohn-name, from OpenAlex).
• [fixed] The Hetényi quotation now begins "It is also believed that", and the page introduces it as a view held in the earlier literature.
• [fixed] The verifier's anchors for 47.8%/49.9%, 0.78 and 6.000 now pin each figure to words only its own sentence carries; the three sentence edits that passed now exit 1.
• [fixed] "stalls" rewritten: "The gain slows as the floor fills ... the slider stops there, because a few points further on this way of throwing can no longer fit all the discs"; "fully packed discs" replaced by "the discs at 50%".
• [fixed] "The Causeway, Hetényi's sites and the discs at 50% sit together".
• [fixed] What-this-page-does-not-show now names Sosman's tabulation for the counts and Goehring and Morris only for the spread in neighbours.
• [fixed] "3,033 columns at 32 of the 50 sites they visited"; the table row and sites.mjs say 32 sites; the verifier checks the phrase.
• [fixed] O'Reilly's title now "discussion on the nature".
• [fixed] "O'Reilly published a survey of a patch of the Causeway in 1879".
• [fixed] Gray et al.'s journal named as the Journal of the International Association for Mathematical Geology, in the source list and the citation line.