---
slug: the-law-even-monkeys-obey
passed: 2026-10-14
by: the assay line (research/assay-line/cited-1014b/), Codex fixer directed by claude-assaying-boyle-1014; source record by Codex, checked by Codex
checked: 105
confirmed: 78
wrong: 23
unverifiable: 0
observed: 0
stale: 4
---

This was the directed correction pass for this layer at f5e5f84f34, following the 27 decisions in research/assay-line/cited-1014b/the-law-even-monkeys-obey/triage.json. The fixer re-read the evidence for each edited item, reproduced the browser arithmetic, corrected 11 WRONG findings, dated four STALE findings under the stated exceptions, and left the 12 listed MINOR findings unchanged. The subsequent repair pass fixed X3 in the corpus-fit wording and share-card source dek, leaving 11 listed MINOR findings unchanged. MINOR counts toward wrong here; changing a disposition does not change the 105-claim total. The CONFIRMED lines retain the N2 checker's source-read findings from N2-codex.md; their notes are explicitly attributed to that checker and their old entry numbers refer to N1-sources.json. They do not claim a new visual browser test or a new external-source read by this fixer for every retained claim.

## Claims

- WRONG | X1: "In 1949 the Harvard linguist George Kingsley Zipf noticed" | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf (p. 313, footnote 1) | Miller cites Zipf's 1935 treatment as well as the 1949 book. The page now dates the book, without asserting a first discovery date.
- MINOR | X2: "in city sizes, firm sizes, citation counts." | https://arxiv.org/pdf/cond-mat/0412004 (Table I and equation 4) | Newman gives citation-count alpha 3.04, implying rank exponent about 0.49, rather than about 1. MINOR scope qualification, listed per triage.
- MINOR | X3: "recomputing the fit in front of you." | public/strata/the-law-even-monkeys-obey/index.html (drawI1) | drawI1 reads stored corpus fits from DATA and calls no fitter. The repair pass corrected the corpus-fit wording in the page, markdown and metadata; the share image uses the opening of the dek.
- WRONG | X4: "it tends to overstate s" | https://arxiv.org/pdf/0706.1062 (Table 3.1); research/zipfs-law/data.json | CSN rank-frequency alpha estimates 2.570 and 2.4869 straddle true alpha 2.5. The inverse conversion reverses direction for s; no fixed upward direction follows. Stored Shakespeare OLS 1.109 is below its MLE-implied 1.243.
- MINOR | X5: "the discrepancy is the honest measure of how much the eye is being fooled by a tidy line" | public/strata/the-law-even-monkeys-obey/index.html (drawI1); research/zipfs-law/data.json | OLS uses ranks 10-1000; MLE uses count thresholds 8, 19 and 6. Differences mix fitting range and model mismatch with estimator effects. MINOR interpretation, listed per triage.
- MINOR | X6: "every character of the book randomly permuted" | research/zipfs-law/verify.mjs (letter-scramble block) | The verifier lowercases, strips boilerplate and prepares letters/spaces before permuting them. The page omits that normalization. MINOR precision, listed per triage.
- WRONG | X7: "So Zipf's law contains, provably, zero information about grammar." | https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf (section 3.4); research/zipfs-law/verify.mjs | The test preserves a fixed token bag, proving order invariance only. Piantadosi documents parameter differences across syntactic categories; no independence theorem follows.
- WRONG | X8: "That smoothness, and Mandelbrot's rounding constant b, are where the linguistics actually is." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf (p. 313, equation 8) | Miller equation 8 has offset 0.54 in a random-typing model. A nonzero shifted-rank constant is therefore not exclusive to language.
- WRONG | X9: "They agree." | public/strata/the-law-even-monkeys-obey/index.html (runI3); research/zipfs-law/verify-page.mjs | Re-executed the original page functions at M=26, p=0.18, seed 7, 600000 characters: rank OLS 0.906028, analytic 1.060910, class OLS 1.050405. The stored four-million-character experiment remains distinct.
- WRONG | X10: "fall onto the predicted line with no fitting at all." | public/strata/the-law-even-monkeys-obey/index.html (runI3); research/zipfs-law/verify-page.mjs | Original first class: rank 26, mean count 621.461538; old guide: 20.91. Model normalization N*p^2*q^L gives approximately 613.107692 at the full first-class rank, neglecting sample-edge effects. The class slope is explicitly a regression.
- WRONG | X11: "The exponent only sits near 1 for English-like word lengths" | public/strata/the-law-even-monkeys-obey/index.html (analyticS); research/zipfs-law/verify-page.mjs | Direct substitution gives s=1.0125294 at M=26, p=0.04 and expected nonempty length 25. At fixed M>1, s approaches 1 as p approaches zero; sparse samples may fit poorly.
- MINOR | X12: "the live instruments recompute the random-text cases from scratch." | public/strata/the-law-even-monkeys-obey/index.html (drawI2 and runI3) | drawI2 reads the scramble and overlay monkey from DATA; runI3 generates only the separate live monkey sample. MINOR live-checking overclaim, listed per triage.
- MINOR | X13: "it can't reproduce the empirical exponent" | https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf (section 4.1, PDF p. 14) | Piantadosi allows model modifications that could fit details of human language, while criticizing simple models. The categorical exponent wording is a MINOR scope qualification, listed per triage.
- WRONG | X14: "where the monkey has nothing to say." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf (p. 313, equation 8) | The final sentence included b among features unavailable to the monkey, contradicted by Miller equation 8. The revised interpretation requires an unexplained residual of a specified model.
- MINOR | X15: "is trained on exactly these word statistics" | https://arxiv.org/html/2005.14165v4 (abstract and introduction) | Brown et al. describes autoregressive, context-dependent sequence prediction. Marginal word frequencies are not the entire training objective. MINOR description, listed per triage.
- WRONG | X16: "OLS overstates s" | https://arxiv.org/pdf/0706.1062 (Table 3.1) | CSN Table 3.1 supports a bias warning without a universally upward rank-slope bias. Removed the direction claim from apparatus, relationship note and markdown body.
- MINOR | X17: "the scramble and monkey experiments recompute live in the browser." | public/strata/the-law-even-monkeys-obey/index.html (drawI2); src/content/strata/the-law-even-monkeys-obey.md | The scramble curve is precomputed and read from DATA. MINOR live-checking overclaim, listed per triage in apparatus and markdown.
- MINOR | X18: "All claims on this page are reproduced offline in research/zipfs-law/verify.mjs and recomputed live here." | public/strata/the-law-even-monkeys-obey/index.html (renderCheck); research/zipfs-law/verify.mjs | renderCheck formats stored results; the offline numerical verifier does not establish historical claims. MINOR checking-coverage overclaim, listed per triage.
- STALE | X19: "21/21 checks." | git show f5e5f84f34:memory/log.d/2026-06-14T2030Z-the-law-even-monkeys-obey.md; research/zipfs-law/verify.mjs | The June 14 log records 21/21; the August controls expanded the default suite to 24/24. Current count is updated, with one layer-wide Updated line dating the old observation.
- STALE | X20: "Last verified 14 June 2026, when it was written." | git show f5e5f84f34:memory/log.d/2026-08-10T0400Z-two-defects-and-three-new-doors.md; assay/records/the-law-even-monkeys-obey.md | Later August verification superseded the June placard date. Regenerated this layer's placard from the new October 14 record using the read-only shared generator output; the explicit placard exception adds no separate dated line.
- WRONG | X21: "mean word length ≈ 4.6" | public/strata/the-law-even-monkeys-obey/index.html (rankFreqFromText and runI3); research/zipfs-law/verify-page.mjs | The tokenizer counts only nonempty letter runs. Their expected length is 1/p=5.555556 at p=0.18; reproduced sample mean 5.527444. The former formula (1-p)/p includes empty gaps.
- WRONG | X22: "rank-freq ⊥ syntax" | research/zipfs-law/verify.mjs (word-order shuffle); https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf (section 3.4) | The verifier compares sorted frequencies before and after a permutation. Relabeled its assertion and page readout as word-order invariance; no assertion of syntax independence remains outside the correction account.
- MINOR | X23: "both random-text cases recompute in-page." | public/strata/the-law-even-monkeys-obey/index.html (drawI2); src/content/strata/the-law-even-monkeys-obey.md | The frontmatter promises live scrambling, but drawI2 reads DATA.scramble.curve. MINOR checking overclaim, listed per triage; its separate sentence is unchanged.
- STALE | X24: "The corpus curves are precomputed by the committed verifier (`research/zipfs-law/verify.mjs`, **21/21**);" | git show f5e5f84f34:memory/log.d/2026-06-14T2030Z-the-law-even-monkeys-obey.md; research/zipfs-law/verify.mjs | The markdown 21/21 count was the true June 14 observation, superseded by the August controls and the reproduced 24/24 suite. It shares X19's single Updated line.
- MINOR | X25: "eight coin-triples identical by frequency yet cyclically ordered head-to-head." | git show f5e5f84f34:src/content/strata/always-bet-second.md | The linked page describes four of eight triples in a ring. The relationship note compresses that distinction. MINOR scope ambiguity, listed per triage; no sibling layer was edited.
- STALE | X26: ""dateModified":"2026-06-14"" | git show f5e5f84f34:memory/log.d/2026-08-10T0400Z-two-defects-and-three-new-doors.md | The August log records substantive prose, dek and data changes. dateModified now records 2026-10-14; the explicit metadata exception needs no separate Updated line.
- MINOR | X27: (added) "recomputed in your browser" | public/strata/the-law-even-monkeys-obey/index.html (renderCheck) | renderCheck formats DATA, including stored analytic cases. MINOR live-checking overclaim, listed per triage; the heading retains its wording while its stale count is updated.
- CONFIRMED | "Count the words in a book and the most common one appears about twice as often as the second, three times as often as the third" [...] "frequency falls as one over rank." | https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf | N2 checker evidence: Piantadosi introduction, equation (1): "for α ≈ 1 (Zipf, 1936, 1949)" and the following rank-ratio paragraph. The record locator says section 4.1, but this excerpt is in the introduction. An approximate law, not an exact guarantee for each book.
- CONFIRMED | "It is one of the most reliable regularities in all of language." | https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf | N2 checker evidence: Section 4.1 says "Given the ubiquity and robustness of Zipf’s law". This supports the broad robustness claim.
- CONFIRMED | "a monkey hitting keys at random draws the same line." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller p.313 derives the random model and writes "monkeys typing at random manage to do it about as well as we do." The later page caveat about its staircase is necessary and present.
- CONFIRMED | "The most common word is about twice the second, three times the third." | https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf | N2 checker evidence: The introduction gives the first, second and third rank ratios with α approximately 1. The copied excerpt is real, but its locator should be Introduction, not section 4.1.
- CONFIRMED | "Sit a monkey at a typewriter" [...] "random keys, random spaces, no words at all" [...] "and it draws the same line, with an exponent we can derive in closed form." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller p.313: "d = 1 -" followed by log(0.82)/log(26), yielding 1.06. His equations (6)-(8) give the general random-typing exponent; the page labels the staircase approximation later.
- CONFIRMED | "The mere existence of the straight line is not evidence of deep linguistic structure." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller p.314 derives the rule "without appeal to least effort, least cost, maximal information". Random typing is a counterexample to treating a power law alone as proof of linguistic structure.
- CONFIRMED | "What is linguistic lives in the places the straight line is wrong." | https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf | N2 checker evidence: Piantadosi abstract: "human language has highly complex, reliable structure in the frequency distribution over and above this classic law". Read as the page's interpretation about informative deviations, not an exhaustive theorem about language.
- CONFIRMED | "Mandelbrot's correction f ∝ 1/(r+b)^s (Benoît Mandelbrot, 1953) bends to catch the flattened head, where the very commonest words are slightly less dominant than a pure 1/r would predict." | https://pdodds.w3.uvm.edu/files/papers/others/1953/mandelbrot1953a.pdf | N2 checker evidence: Mandelbrot p.486 gives "Pn = P(n + m)-B", with positive constants. Piantadosi equation (2) independently states the shifted-rank form. The fitted head is below the extrapolated pure power law.
- CONFIRMED | "So the readout also shows α, the maximum-likelihood exponent of the underlying frequency distribution p(f) ∝ f^(−α), and its implied rank exponent 1/(α−1) (the two exponents are tied by α = 1 + 1/s in the tail)." | git show f5e5f84f34:public/strata/the-law-even-monkeys-obey/index.html | N2 checker evidence: The readout prints "MLE   α" and "implied rank s = 1/(α−1)". Newman equation (4) gives cumulative frequency proportional to x raised to -(α-1), which implies the stated tail transformation.
- CONFIRMED | "The Cold Hand, where a trusted estimator quietly mis-measures." | git show f5e5f84f34:src/content/strata/the-cold-hand.md | N2 checker evidence: The linked layer says "This page reproduces that finite-sample selection bias from scratch (exactly, by recursion and by live coin-flipping)". This is a description of that page's subject.
- CONFIRMED | "Three curves on the same axes:" | git show f5e5f84f34:public/strata/the-law-even-monkeys-obey/index.html | N2 checker evidence: drawI2 uses "DATA.corpora['moby-dick'].curve", "DATA.scramble.curve", and "DATA.monkey.curve", then plots all three on P2. Executed with DOM/canvas stubs; no visual browser test asserted.
- CONFIRMED | "The difference is the language: the real curve is smooth and gently rounded at the head; the equiprobable monkey's, revealed, is a staircase" [...] "when every letter is equally likely, every word of a given length is exactly as likely as every other, so frequencies come in flat steps." | https://sfi-edu.s3.amazonaws.com/sfi-edu/production/uploads/sfi-com/dev/uploads/filer/a5/07/a507be1c-7232-422b-8657-d24dcf24a35d/91-03-016.pdf | N2 checker evidence: Li p.4: "all words with the same length have the same frequency of occurrence." The population probabilities form steps; finite samples fluctuate within them. The page explicitly restricts the staircase to equiprobable letters.
- CONFIRMED | "Give the letters their real, unequal frequencies" [...] "as the letter-scramble does" [...] "and the steps smear into a smoother curve; the staircase is a signature of the equiprobable model, not of randomness as such." | https://sfi-edu.s3.amazonaws.com/sfi-edu/production/uploads/sfi-com/dev/uploads/filer/a5/07/a507be1c-7232-422b-8657-d24dcf24a35d/91-03-016.pdf | N2 checker evidence: Li p.5: "The stepwise structure" can be removed by introducing unequal symbol probabilities. This supports the distinction between equiprobability and randomness.
- CONFIRMED | "The monkey's line is not a coincidence; it is forced, and the exponent is computable." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller equations (6)-(8) derive the exponent from the model rather than fit it; p.313 gives "d" equal to 1.06 for A=26 and p(space)=0.18.
- CONFIRMED | "Type M equiprobable letters with a space appearing with probability p." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller p.311 specifies the space probability and equiprobable letter sequences. His extra ban on consecutive spaces differs from the page's generator, but conditioning its independent-space model on nonempty words preserves the rank exponent.
- CONFIRMED | "A "word" is a run between spaces." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Li p.2 explicitly defines a word as a "non-blank" symbol string between blank spaces, whereas a string of spaces is not. The browser tokenizer agrees with this nonempty definition.
- CONFIRMED | "A specific word of length L has probability proportional to q^L with q = (1−p)/M" [...] "so longer words are exponentially rarer." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller equation (2) gives each word probability proportional to the length power of p(L)/A. With page notation this is q^L, q=(1-p)/M.
- CONFIRMED | "But there are exactly M^L distinct words of length L, exponentially many." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller p.311: "the number of different possible words of length i must be" A raised to i. Also follows by choosing independently among M letters at each position.
- CONFIRMED | "Rank them: the words of length L occupy a block of ranks ending near M^L, so rank r ≈ M^L means L ≈ logM r, and frequency q^L = q^(log_M r) = r^(ln q / ln M)." | https://sfi-edu.s3.amazonaws.com/sfi-edu/production/uploads/sfi-com/dev/uploads/filer/a5/07/a507be1c-7232-422b-8657-d24dcf24a35d/91-03-016.pdf | N2 checker evidence: Li equations (0.7)-(0.12) transform exponentially increasing word counts into a power law in rank. Cumulative ranks are proportional to M^L asymptotically; the page explicitly says "near" and explains the length-block approximation.
- CONFIRMED | "To leading order" [...] "treating each length-block as a single rank and ignoring the within-length degeneracy (the staircase, above)" [...] "the line falls out:" | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller p.312 assigns each word length an "average rank" and derives the shifted-rank form. The page explicitly acknowledges the within-length degeneracy.
- CONFIRMED | "s = 1 − ln(1−p) / ln(M)" | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller p.313 has "d = 1" minus log(0.82)/log(26), and the general exponent is 1-log(p(L))/log(A). This is the displayed formula after renaming variables.
- CONFIRMED | "The page generates fresh monkey text in your browser, fits the rank-frequency slope, and overlays the closed-form line." | git show f5e5f84f34:public/strata/the-law-even-monkeys-obey/index.html | N2 checker evidence: runI3 calls "monkeyText(i3M,i3p,600000,rng)" and olsLog on its generated ranks. Re-roll changes i3seed. The runtime call control records one monkey generation and one OLS fit.
- CONFIRMED | "Fewer spaces (small p) → longer words → gentler slope." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: From the confirmed closed form, ds/dp = 1/((1-p) ln M)>0. Decreasing p reduces s and increases the geometric word length. Miller's model supplies the formula.
- CONFIRMED | "A bigger alphabet → gentler slope too." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: For fixed p, ds/dM = ln(1-p)/(M(ln M)^2)<0. Thus a larger alphabet gives a smaller exponent.
- CONFIRMED | "popularized as "Miller's monkeys" (Miller 1957)" | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller's 1957 article starts "Imagine that a monkey hits the keys of a typewriter at random" and derives the rank law. The popular attribution is appropriate.
- CONFIRMED | "with the combinatorial argument in Mandelbrot (1953)" | https://pdodds.w3.uvm.edu/files/papers/others/1953/mandelbrot1953a.pdf | N2 checker evidence: The record's title-only excerpt does not establish the argument. Reading Mandelbrot pp.495-496 supplies the missing support: random elementary signs are grouped into words and yield the same probability form.
- CONFIRMED | "the modern random-text result formalized by Wentian Li (1992)" | https://sfi-edu.s3.amazonaws.com/sfi-edu/production/uploads/sfi-com/dev/uploads/filer/a5/07/a507be1c-7232-422b-8657-d24dcf24a35d/91-03-016.pdf | N2 checker evidence: The SFI document is explicitly "March 1991", and says its purpose is to prove random texts exhibit a Zipf-like distribution. The separate Crossref record confirms the 1992 journal publication. The source record correctly distinguishes them.
- CONFIRMED | "shows the bare power law is not, by itself, evidence of any optimization, any "principle of least effort," any deep property of meaning." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller p.314 says the rule follows "without appeal to least effort, least cost, maximal information". This supports the limited claim that the bare law is insufficient evidence for optimization.
- CONFIRMED | "But it does not show Zipf's law is meaningless." | https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf | N2 checker evidence: The published Piantadosi abstract says human language has reliable structure beyond the classic law; the critique of simple random typing supports retaining linguistic significance.
- CONFIRMED | "The debate over why real language is Zipfian" [...] "beyond the combinatorial floor a monkey already guarantees" [...] "is genuinely open." | https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf | N2 checker evidence: The quoted passage "No prior account straightforwardly explains all the basic facts" occurs in the abstract, not section 4.1 as the record says. The source presents multiple competing explanatory models.
- CONFIRMED | "Candidate mechanisms include Herbert Simon's preferential attachment (1955: rich-get-richer word reuse)" | https://snap.stanford.edu/class/cs224w-readings/Simon55Skewdistribution.pdf | N2 checker evidence: Simon p.427, Assumption I, makes reuse probability proportional to "the total number of occurrences" of words in a frequency class. This is the stated preferential-reuse mechanism.
- CONFIRMED | "least-effort optimization of a speaker-hearer tradeoff (Ferrer i Cancho & Solé, 2003)" | https://pmc.ncbi.nlm.nih.gov/articles/PMC298679/ | N2 checker evidence: The full primary abstract states "Simultaneous minimization in the effort of both hearer and speaker" and describes a communicative phase transition. The short record excerpt alone omits the tradeoff, but the full source supports it.
- CONFIRMED | "itself contested, with the claimed optimum sitting awkwardly near a phase transition and the derivation disputed" | https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf | N2 checker evidence: The primary paper says Zipf scaling appears at λ*=0.41, the transition. Piantadosi's communicative-accounts section challenges the assumptions and parameter sensitivity. "Contested" is supported, not a claim that the primary authors disowned their result.
- CONFIRMED | "the law is mostly a statistical inevitability." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: This is presented as one competing view. Miller p.314 derives the law from random spacing; Piantadosi section 4.1 explicitly describes the statistical-artifact interpretation.
- CONFIRMED | "the word-length/frequency relationship" | https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf | N2 checker evidence: The copied excerpt discusses "the number of word types of a given length", a different quantity from a word's frequency versus its length. The full review supplies relevant support in the paragraph saying a random model makes a word's frequency wholly determined by its components. The source record should use that passage instead.
- CONFIRMED | "or the structure below the word" | https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf | N2 checker evidence: The published review states that people "know whole words and do not emit subword components at random". This supports the criticism of the random subword mechanism.
- CONFIRMED | "And crucially, real word distributions are not a single clean power law: there is a well-documented two-regime break, the slope steepening past rank ≈ 10³–10⁴ (Ferrer i Cancho & Solé 2001; Gerlach & Altmann 2013)" | https://arxiv.org/html/1212.1362 | N2 checker evidence: Gerlach and Altmann report English break values b in [7*10^3,12*10^3], with steeper tail exponents, and discuss other languages. Ferrer and Sole's 2001 abstract explicitly gives approximately -1 and -2 regimes.
- CONFIRMED | "the single-s story this page fits is itself an idealization." | git show f5e5f84f34:research/zipfs-law/verify.mjs | N2 checker evidence: The page's verifier fits a restricted rank window; real-data residuals and the cited two-regime evidence show why a global single exponent is an idealization.
- CONFIRMED | "a beautiful aggregate regularity can be almost entirely upstream of meaning" | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: Miller's random-typing derivation supplies the counterexample. Read as an interpretive claim about a coarse aggregate, not a claim that every frequency distribution lacks semantic information.
- CONFIRMED | "Always Bet Second, whose closing turn is the same blade from the other side" [...] "that a sequence's load-bearing content is its dependence structure, not its marginal frequencies." | git show f5e5f84f34:src/content/strata/always-bet-second.md | N2 checker evidence: The linked layer explicitly identifies its closing subject as "the signal is in the dependence structure, not the marginals". This checks what the linked page argues.
- CONFIRMED | "Moby-Dick (Melville; Project Gutenberg #2701)" | https://www.gutenberg.org/ebooks/2701 | N2 checker evidence: Gutenberg #2701 lists "Melville, Herman, 1819-1891" and "Moby Dick; Or, The Whale".
- CONFIRMED | "Pride and Prejudice (Austen; #1342)" | https://www.gutenberg.org/ebooks/1342 | N2 checker evidence: Gutenberg #1342 lists "Austen, Jane, 1775-1817" and "Pride and Prejudice".
- CONFIRMED | "Corpora public domain (Project Gutenberg)." | https://www.gutenberg.org/ebooks/2701 | N2 checker evidence: Gutenberg #2701 says "Public domain in the USA." This confirms the named book's status; the footer attribution is shorthand for the corpus provenance described in the apparatus.
- CONFIRMED | "Moby-Dick (Melville; Project Gutenberg #2701), Pride and Prejudice (Austen; #1342), and a concatenation of Shakespeare (the "tinyshakespeare" file)" [...] "all public domain." | https://www.gutenberg.org/ebooks/1342 | N2 checker evidence: Gutenberg pages give both novels' public-domain status; the third corpus is the independently matched Shakespeare compilation. The Austen-only excerpt cannot establish all three by itself, but the combined sources do.
- CONFIRMED | "Gutenberg license boilerplate is stripped before counting." | git show f5e5f84f34:research/zipfs-law/verify.mjs | N2 checker evidence: stripGutenberg locates "START OF" and "END OF" markers and slices between them. The two pinned Gutenberg inputs contain the markers; independent tokenization reproduces the counts.
- CONFIRMED | "Tokenization is a deliberate free choice: lowercase, maximal runs of a–z with one optional internal apostrophe (so don't is one token, hyphenated compounds split)." | git show f5e5f84f34:research/zipfs-law/verify.mjs | N2 checker evidence: The exact regex is /[a-z]+(?:'[a-z]+)?/g and the input is lowercased. It admits one internal apostrophe and splits hyphens as stated.
- CONFIRMED | "The Zipf exponent is OLS of ln f on ln r over ranks 10–1000 (avoiding both the curved head and the singleton-dominated tail)." | git show f5e5f84f34:research/zipfs-law/verify.mjs | N2 checker evidence: The verifier sets "const RLO = 10, RHI = 1000" and olsZipf regresses log frequency on log rank over that inclusive interval.
- CONFIRMED | "Word counts are integers, so α here is the discrete maximum-likelihood estimator of Clauset–Shalizi–Newman 2009 §3.3 (the Hurwitz-zeta likelihood, maximised numerically), with xmin chosen by minimising a discrete Kolmogorov–Smirnov distance evaluated at each distinct count." | git show f5e5f84f34:research/zipfs-law/verify.mjs | N2 checker evidence: The implementation minimizes n*log(zeta(alpha,xmin))+alpha*sum(log counts), scans discrete xmin candidates, and computes empirical and fitted CDFs at distinct integer counts. The CSN anchor and seeded control reproduce the stated results.
- CONFIRMED | "Corrected here, and the verifier now carries two controls that go red if it ever comes back." | git show f5e5f84f34:research/zipfs-law/verify.mjs | N2 checker evidence: The pinned code includes the seeded planted-answer test and the optional "--csn-anchor" branch. The default run also shows the legacy estimator misses the planted xmin.
- CONFIRMED | "Mandelbrot's b is grid-searched; "fits better" means strictly lower sum-of-squared log-residuals over the same window." | git show f5e5f84f34:research/zipfs-law/verify.mjs | N2 checker evidence: fitMandelbrot scans "b = 0; b <= 40; b += 0.25" and compares sums of squared log residuals on the same window. The comparison means descriptive fit, not an independent model-selection test.
- CONFIRMED | "The monkey closed form is the asymptotic slope: for very small p (very long words) it only emerges far out in the tail, which is why the live check verifies it via the length-class steps rather than a fixed rank window." | git show f5e5f84f34:public/strata/the-law-even-monkeys-obey/index.html | N2 checker evidence: runI3 forms length classes, selects meanFreq>=3 and count>=2, and estimates their slope against cumulative rank. The closed form is asymptotic; the apparatus states the finite-vocabulary caveat. The incorrectly positioned displayed line is separately covered by entry 40.
- CONFIRMED | "Zipf, G.K. (1949), Human Behavior and the Principle of Least Effort." | https://iqla.org/wp-content/uploads/2025/05/Zipf_1949_Human_Behavior_and_the_Principle_of_Least_Effort.pdf | N2 checker evidence: Opened the scan and visually checked its title page: "HUMAN BEHAVIOR", "THE PRINCIPLE OF LEAST EFFORT", "GEORGE KINGSLEY ZIPF", "Harvard University", "1949". OCR misreads ZIPF as Z1PF, so its excerpt-search miss is not evidence against the record.
- CONFIRMED | "Mandelbrot, B. (1953), "An informational theory of the statistical structure of language" (symposium volume)." | https://pdodds.w3.uvm.edu/files/papers/others/1953/mandelbrot1953a.pdf | N2 checker evidence: The primary scan supplies the chapter title and "BENOIT MANDELBROT". Li reference [5] identifies Communication Theory, Willis Jackson, 1953. This confirms the year and symposium-volume attribution beyond the title-only excerpt.
- CONFIRMED | "Borel, É. (1913), the original "infinite monkey."" | https://hal.science/jpa-00241832/document | N2 checker evidence: Borel's primary article is dated 1913, pp.189-196; p.194 says "un million de singes" typing at random. The historical nickname is appropriate despite his finite-million example rather than the modern infinite formulation.
- CONFIRMED | "Miller, G.A. (1957), "Some effects of intermittent silence," Am. J. Psychol. 70:311–314 (the monkey argument; amplified in his 1965 introduction to Zipf's reprint)." | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | N2 checker evidence: JSTOR cover: "George A. Miller", June 1957, volume 70(2), pp.311-314. Li reference [4] separately identifies Miller's 1965 introduction. The online checker's A.-initial mismatch is a parser false alarm.
- CONFIRMED | "Li, W. (1992), "Random texts exhibit Zipf's-law-like word frequency distribution," IEEE Trans. Inf. Theory 38(6):1842–1845." | https://api.crossref.org/works/10.1109%2F18.165464 | N2 checker evidence: Crossref confirms W. Li, 1992, IEEE Transactions on Information Theory 38(6), pp.1842-1845, DOI 10.1109/18.165464 and the quoted title.
- CONFIRMED | "Simon, H.A. (1955), "On a class of skew distribution functions," Biometrika 42:425–440." | https://snap.stanford.edu/class/cs224w-readings/Simon55Skewdistribution.pdf | N2 checker evidence: The primary cover says "Herbert A. Simon", Biometrika 42(3/4), December 1955, pp.425-440. The online checker's A.-initial mismatch is a parser false alarm.
- CONFIRMED | "Ferrer i Cancho, R. & Solé, R.V. (2001), J. Quant. Linguistics 8:165 (the two-regime break); (2003), "Least effort and the origins of scaling in human language," PNAS 100:788–791." | https://pmc.ncbi.nlm.nih.gov/articles/PMC298679/ | N2 checker evidence: PMC gives Ferrer i Cancho and Sole, 2003, PNAS 100(3):788-791 and the title. The UPC institutional record independently confirms the 2001 Journal of Quantitative Linguistics 8(3):165-173 citation. The short title excerpt alone covers only the second paper.
- CONFIRMED | "Gerlach, M. & Altmann, E.G. (2013), Phys. Rev. X 3:021006." | https://api.crossref.org/works/10.1103%2FPhysRevX.3.021006 | N2 checker evidence: Crossref confirms Martin Gerlach, Eduardo G. Altmann, 2013, Physical Review X 3(2), article "021006".
- CONFIRMED | "Piantadosi, S.T. (2014), "Zipf's word frequency law in natural language: A critical review and future directions," Psychon. Bull. Rev. 21:1112–1130" | https://pubmed.ncbi.nlm.nih.gov/24664880/ | N2 checker evidence: PubMed returned a challenge response, so opened the full published article at PMC4176592 and Crossref DOI 10.3758/s13423-014-0585-6. They confirm Steven T. Piantadosi, 2014, volume 21, pp.1112-1130 and the title.
- CONFIRMED | "Clauset, A., Shalizi, C.R. & Newman, M.E.J. (2009), "Power-law distributions in empirical data," SIAM Review 51(4):661–703 (their method fits the frequency distribution; the bias caveat transfers to the rank exponent through α = 1 + 1/s)." | https://api.crossref.org/works/10.1137%2F070710111 | N2 checker evidence: Crossref confirms all three authors, 2009, SIAM Review 51(4):661-703, and the title. The full paper warns of least-squares bias; the tail exponent conversion is valid. A fixed direction of rank-slope bias is a separate erroneous claim in entries 15 and 78.
- CONFIRMED | "Ferrer i Cancho, R. & Solé, R.V. (2001), J. Quant. Linguistics 8:165 (the two-regime break)" | https://upcommons.upc.edu/entities/publication/3022e650-a374-44ba-8f2a-ea1ad69bfaf3 | N2 checker evidence: UPC institutional metadata gives "2001-08", authors Ferrer Cancho and Sole Vicente, and "vol. 8, num. 3, p. 165-173". Its abstract explicitly distinguishes the two exponents.
- CONFIRMED | "amplified in his 1965 introduction to Zipf's reprint" | https://sfi-edu.s3.amazonaws.com/sfi-edu/production/uploads/sfi-com/dev/uploads/filer/a5/07/a507be1c-7232-422b-8657-d24dcf24a35d/91-03-016.pdf | N2 checker evidence: Li p.1 credits Miller's preface; reference [4] specifies "Introduction" in The Psycho-biology of Language, MIT Press, 1965. This is the reprint actually meant, not the 1949 Human Behavior title.
- CONFIRMED | "No third-party requests beyond the site's one cookieless analytics beacon." | git show f5e5f84f34:public/strata/the-law-even-monkeys-obey/index.html | N2 checker evidence: Live HTML adds one Cloudflare beacon script and an internal /api/pulse request. The pinned page, its fonts, home-banner.js and plain-button.js otherwise reference site-local runtime resources. External source hyperlinks do not themselves make requests.
- CONFIRMED | "This layer's check works the answer out again from scratch, independently of this page." | git show f5e5f84f34:research/zipfs-law/verify.mjs | N2 checker evidence: The verifier reads corpus files and its data.json generation timestamp, not the page. The scratch run reproduces 24/24 independently of page HTML.
- CONFIRMED | "It can settle the finding; it cannot notice a figure that drifted on this page." | git show f5e5f84f34:research/zipfs-law/verify.mjs | N2 checker evidence: The verifier reads "CORP" inputs, not HTML or frontmatter. It therefore cannot detect changed page figures. The page explicitly discloses this limitation.
- CONFIRMED | "It is published to read." | git show f5e5f84f34:public/strata/the-law-even-monkeys-obey/index.html | N2 checker evidence: curl of https://artwaste.land/checks/research/zipfs-law/verify.mjs returned HTTP 200 and 22,880 nonzero bytes. It is published as claimed.
- CONFIRMED | "Running it needs the repository around it." | git show f5e5f84f34:research/zipfs-law/verify.mjs | N2 checker evidence: The downloaded script in an otherwise empty directory exits 1 with ENOENT for corpora/moby-dick.txt. Adding the pinned repository inputs in the separate scratch copy gives 24/24, a positive control for the stated repository requirement.
- CONFIRMED | "and check live in the browser." | git show f5e5f84f34:public/strata/the-law-even-monkeys-obey/index.html | N2 checker evidence: The browser script generates and checks a fresh monkey sample using analyticS and lengthClasses. Its mechanism slope at defaults is "1.050" versus analytic "1.061".
- CONFIRMED | "The Cold Hand shows a famous estimator (the streak statistic) is biased by the structure of finite sequences;" | git show f5e5f84f34:src/content/strata/the-cold-hand.md | N2 checker evidence: The linked layer explicitly describes "finite-sample selection bias". The relationship note accurately describes that topic.
- CONFIRMED | "The Farthest Point recomputes which mountain is farthest from Earth's centre from the WGS84 constants;" | git show f5e5f84f34:src/content/strata/the-farthest-point.md | N2 checker evidence: The linked layer says each radius is recomputed "from the WGS84 defining constants" and surveyed coordinates. This verifies the description of that page's operation.
- CONFIRMED | "the area of his namesake set" [...] "no closed form, estimated by descending bounds;" | git show f5e5f84f34:src/content/strata/how-big-is-the-mandelbrot-set.md | N2 checker evidence: The linked layer labels the area estimate numerical, states "Nobody knows its exact area", and describes descending rigorous partial-sum bounds. This checks the stated topic and distinction of methods, not every claim on the sibling page.
- CONFIRMED | "the Harvard linguist George Kingsley Zipf" | https://iqla.org/wp-content/uploads/2025/05/Zipf_1949_Human_Behavior_and_the_Principle_of_Least_Effort.pdf | N2 checker evidence: Visually checked Zipf's title page: "GEORGE KINGSLEY ZIPF, Ph.D." and "Harvard University". The book and its linguistic subject support the affiliation description.
- CONFIRMED | "the two exponents are tied by α = 1 + 1/s in the tail" | https://arxiv.org/pdf/cond-mat/0412004 | N2 checker evidence: Newman equation (4) gives cumulative frequency proportional to x^(-(alpha-1)); rank is proportional to the survival count, so s=1/(alpha-1). This is an asymptotic relation, as the page specifies.
- CONFIRMED | "Both pages separate the marginal from the relational and show the meaning is never in the marginal alone" [...] "the principle a sequence model itself runs on." | git show f5e5f84f34:public/strata/the-law-even-monkeys-obey/index.html | N2 checker evidence: This is the relationship note's interpretation of the two demonstrations, not a new measured universal. Both pages compare marginals with sequence structure; the narrower word-order invariance is demonstrable.
- CONFIRMED | "the uncertainties (tokenization choices; the asymptotic-regime caveat) are named in the apparatus rather than smoothed." | git show f5e5f84f34:public/strata/the-law-even-monkeys-obey/index.html | N2 checker evidence: The apparatus explicitly names "Tokenization" and calls the monkey slope "asymptotic". The stated caveats are present even though some surrounding stronger claims need repair.
- CONFIRMED | "on log-log axes, where a power law becomes a straight line." | https://iqla.org/wp-content/uploads/2025/05/Zipf_1949_Human_Behavior_and_the_Principle_of_Least_Effort.pdf | N2 checker evidence: OCR and the scanned p.24 give "will appear on doubly logarithmic chart paper as a succession of points" descending on a straight line. Algebra independently confirms log f=log C-s log r.
- CONFIRMED | (added) "Two 'laws' that are real and partly artefacts of how you count." | git show f5e5f84f34:src/content/strata/ask-a-random-friend.md | N2 checker evidence: The linked page gives the friend-weighted mean "μ + σ²/μ ≥ μ" and explains popularity-weighted sampling. Miller's random-typing calculation supports the Zipf comparison. This relationship sentence was omitted from the record.

## Findings

- [fixed] X1. Miller cites Zipf's 1935 treatment as well as the 1949 book. The page now dates the book, without asserting a first discovery date. The dated correction is on the page and mirrored at the end of the markdown body.
- [declined] X2 (MINOR only). Newman gives citation-count alpha 3.04, implying rank exponent about 0.49, rather than about 1. MINOR scope qualification, listed per triage. Triage reason: The checker distinguishes power laws in other domains from a rank exponent near 1: the cited citation-count exponent 3.04 implies rank exponent about 0.49. Accept this as a MINOR scope qualification in the broad comparison, rather than treating every use of power law as the same numerical exponent. Tier C lists it. This is a different sentence from the discovery-date sentence being fixed under X1.
- [fixed] X3 (MINOR). drawI1 reads stored corpus fits from DATA and calls no fitter. The page, markdown and metadata now describe computed or stored corpus fits. The false share-image subtitle comes from the dek: share card rebuilt at landing from the corrected dek. The generated plain card and thumbnail copies are left to landing; no image was regenerated in this repair pass.
- [fixed] X4. CSN rank-frequency alpha estimates 2.570 and 2.4869 straddle true alpha 2.5. The inverse conversion reverses direction for s; no fixed upward direction follows. Stored Shakespeare OLS 1.109 is below its MLE-implied 1.243. The dated correction is on the page and mirrored at the end of the markdown body.
- [declined] X5 (MINOR only). OLS uses ranks 10-1000; MLE uses count thresholds 8, 19 and 6. Differences mix fitting range and model mismatch with estimator effects. MINOR interpretation, listed per triage. Triage reason: I re-read index.html:310-311 and its embedded DATA. The OLS readout says "ranks 10–1000", while MLE uses a fitted count threshold, with x_min 8, 19 or 6 depending on corpus. Their difference is not an isolated measurement of estimator bias; fit range and model mismatch can contribute. Keep the MINOR interpretive qualification and list it for tier C. This is a separate sentence from the OLS direction claim fixed under X4, even though both appear in the same paragraph.
- [declined] X6 (MINOR only). The verifier lowercases, strips boilerplate and prepares letters/spaces before permuting them. The page omits that normalization. MINOR precision, listed per triage. Triage reason: I re-read research/zipfs-law/verify.mjs, the letter-scramble block: "stripGutenberg(raw).toLowerCase()" precedes the shuffle, and punctuation and whitespace are converted to spaces. The description omits that normalization; the experiment still permutes the resulting letters and spaces. Keep this as MINOR precision about the prepared input and list it for tier C. Its sentence is not being fixed for a WRONG finding.
- [fixed] X7. The test preserves a fixed token bag, proving order invariance only. Piantadosi documents parameter differences across syntactic categories; no independence theorem follows. The dated correction is on the page and mirrored at the end of the markdown body.
- [fixed] X8. Miller equation 8 has offset 0.54 in a random-typing model. A nonzero shifted-rank constant is therefore not exclusive to language. The dated correction is on the page and mirrored at the end of the markdown body.
- [fixed] X9. Re-executed the original page functions at M=26, p=0.18, seed 7, 600000 characters: rank OLS 0.906028, analytic 1.060910, class OLS 1.050405. The stored four-million-character experiment remains distinct. The dated correction is on the page and mirrored at the end of the markdown body.
- [fixed] X10. Original first class: rank 26, mean count 621.461538; old guide: 20.91. Model normalization N*p^2*q^L gives approximately 613.107692 at the full first-class rank, neglecting sample-edge effects. The class slope is explicitly a regression. The dated correction is on the page and mirrored at the end of the markdown body.
- [fixed] X11. Direct substitution gives s=1.0125294 at M=26, p=0.04 and expected nonempty length 25. At fixed M>1, s approaches 1 as p approaches zero; sparse samples may fit poorly. The dated correction is on the page and mirrored at the end of the markdown body.
- [declined] X12 (MINOR only). drawI2 reads the scramble and overlay monkey from DATA; runI3 generates only the separate live monkey sample. MINOR live-checking overclaim, listed per triage. Triage reason: I re-read index.html:330-343 and 358-366. Instrument II reads "const scram=DATA.scramble.curve" and a stored monkey curve; only Instrument III calls "monkeyText(i3M,i3p,600000,rng)". The scramble is not regenerated live. Reclassify WRONG as MINOR under the explicit rule for overclaims about the page's own live checking, and list it for tier C. X17 and X23 repeat the same error. This sentence is separate from the numerical claims being fixed elsewhere.
- [declined] X13 (MINOR only). Piantadosi allows model modifications that could fit details of human language, while criticizing simple models. The categorical exponent wording is a MINOR scope qualification, listed per triage. Triage reason: I re-read Piantadosi section 4.1, PDF p. 14 (https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf). After criticizing simple random-typing distributions, it allows that model modifications "might allow them to fit the details of human language". The page compresses a criticism of simple models into overly categorical wording about their exponent. Keep the checker's MINOR scope qualification and list it for tier C. This sentence is separate from the final sentence about the rounding constant being fixed under X14.
- [fixed] X14. The final sentence included b among features unavailable to the monkey, contradicted by Miller equation 8. The revised interpretation requires an unexplained residual of a specified model. The dated correction is on the page and mirrored at the end of the markdown body.
- [declined] X15 (MINOR only). Brown et al. describes autoregressive, context-dependent sequence prediction. Marginal word frequencies are not the entire training objective. MINOR description, listed per triage. Triage reason: Accept the checker's distinction: autoregressive language models learn conditional sequence prediction, which includes marginal frequency regularities but extends beyond them. The wording "exactly these word statistics" is a loose description of the training signal, rather than a measured result. Keep MINOR and list it for tier C; this sentence is not otherwise being fixed for a WRONG item.
- [fixed] X16. CSN Table 3.1 supports a bias warning without a universally upward rank-slope bias. Removed the direction claim from apparatus, relationship note and markdown body. The dated correction is on the page and mirrored at the end of the markdown body.
- [declined] X17 (MINOR only). The scramble curve is precomputed and read from DATA. MINOR live-checking overclaim, listed per triage in apparatus and markdown. Triage reason: I re-read index.html:221 and 330-343, plus src/content/strata/the-law-even-monkeys-obey.md:52-53. The display code uses "const scram=DATA.scramble.curve"; the separate live generator makes monkey text, not a fresh scramble. This repeats X12 and X23. Change WRONG to MINOR under the explicit live-checking-overclaim rule and list it for tier C. Its sentence is separate from the WRONG OLS sentence, although both are in the apparatus paragraph; the stale count in the frontmatter version does not trigger the WRONG-sentence exception.
- [declined] X18 (MINOR only). renderCheck formats stored results; the offline numerical verifier does not establish historical claims. MINOR checking-coverage overclaim, listed per triage. Triage reason: I re-read index.html:222 and 400-417. renderCheck starts with "const m=DATA.corpora" and formats stored corpus, scramble, monkey and mechanism results. It does not independently reproduce every claim in the browser; the verifier's numerical experiments also do not establish every historical claim. The finding is valid, but the explicit task rule makes overclaims about the page's own checking MINOR. Reclassify and list for tier C. X27 is the same stored-results-as-live claim in the panel heading. This sentence contains no separate WRONG finding.
- [dated] X19. The June 14 log records 21/21; the August controls expanded the default suite to 24/24. Current count is updated, with one layer-wide Updated line dating the old observation.
- [dated] X20. Later August verification superseded the June placard date. Regenerated this layer's placard from the new October 14 record using the read-only shared generator output; the explicit placard exception adds no separate dated line.
- [fixed] X21. The tokenizer counts only nonempty letter runs. Their expected length is 1/p=5.555556 at p=0.18; reproduced sample mean 5.527444. The former formula (1-p)/p includes empty gaps. The dated correction is on the page and mirrored at the end of the markdown body.
- [fixed] X22. The verifier compares sorted frequencies before and after a permutation. Relabeled its assertion and page readout as word-order invariance; no assertion of syntax independence remains outside the correction account. The dated correction is on the page and mirrored at the end of the markdown body.
- [declined] X23 (MINOR only). The frontmatter promises live scrambling, but drawI2 reads DATA.scramble.curve. MINOR checking overclaim, listed per triage; its separate sentence is unchanged. Triage reason: I re-read src/content/strata/the-law-even-monkeys-obey.md:4 and index.html:330-343: "const scram=DATA.scramble.curve" loads the precomputed scramble. Only the separate monkey dial generates a new sample. This is the frontmatter copy of X12 and X17. Reclassify WRONG to MINOR under the explicit rule for live-recomputation overclaims about the page's own checking, then list it for tier C. The earlier WRONG interpretation of the rounding constant is in another sentence, so it does not trigger the same-sentence fix exception.
- [dated] X24. The markdown 21/21 count was the true June 14 observation, superseded by the August controls and the reproduced 24/24 suite. It shares X19's single Updated line.
- [declined] X25 (MINOR only). The linked page describes four of eight triples in a ring. The relationship note compresses that distinction. MINOR scope ambiguity, listed per triage; no sibling layer was edited. Triage reason: I re-read src/content/strata/always-bet-second.md:5. It says "four of the eight triples sit in a ring" and describes all eight as equally likely in fixed windows. The relationship note compresses the distinction between the full set of eight and its nontransitive cycle. Keep this as a MINOR scope ambiguity: the comparison concerns a game with cyclic preferences, but should not suggest that every pattern belongs to one eight-pattern ring. Tier C lists it; this relationship sentence is separate from the OLS relationship sentence being fixed.
- [dated] X26. The August log records substantive prose, dek and data changes. dateModified now records 2026-10-14; the explicit metadata exception needs no separate Updated line.
- [declined] X27 (MINOR only). renderCheck formats DATA, including stored analytic cases. MINOR live-checking overclaim, listed per triage; the heading retains its wording while its stale count is updated. Triage reason: I re-read index.html:209 and the complete renderCheck function at 400-421. It begins "const m=DATA.corpora" and prints stored values, including "DATA.analytic.cases.map". Thus the table is not recomputed in the browser. Change WRONG to MINOR under the explicit rule for overstatements of the page's own live checking, and list it for tier C. This is the panel-heading copy of X18. The wrong grammar-independence label elsewhere in the table is a separate sentence, and the heading's stale count is not a WRONG finding.