---
slug: luria-delbruck
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; Codex repair re-read the fix-check findings and all dated correction lines
checked: 98
confirmed: 50
wrong: 46
unverifiable: 2
observed: 0
stale: 0
---

This was the directed correction pass for the luria-delbruck layer read at f5e5f84f34: the fixer re-read the evidence for all 46 triage items, repaired the authored page, its inline captions, markdown, source record and verifier wording, and retained the 50 CONFIRMED source claims from Codex N2's re-reads with that provenance named on each line. Of the 46 findings counted under wrong, 15 are WRONG and 31 are MINOR; 23 repair evidence metadata only. The source record retains the pinned pre-fix claims, while its repaired evidence summaries are explicitly distinguished from quotations. The claims here do not certify other layers or shared files.

The repair pass completed X17 by removing its remaining unqualified dismissal of jackpots, and removed the unsupported universal about Luria's predecessors from both authored copies. N2 entries 050 and 120 are recorded below as UNVERIFIABLE with [fixed] outcomes: the cited account does not establish the universal, but does not disprove it. All 12 dated corrections were re-read against the record and evidence and retained. The final count is 50 CONFIRMED + 15 WRONG + 31 MINOR + 2 UNVERIFIABLE = 98.

## Claims

- MINOR | [X1] "You cannot tell by counting one culture." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained.
- MINOR | [X2] "many cultures disagree" | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained.
- MINOR | [X3] "the variance is far larger than the mean." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained. Changed kind from quote to paraphrase and removed the false verbatim-quote field.
- MINOR | [X4] "Genetics 28, 1943" | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The original title page, p. 491, confirms authors, Genetics 28 and November 1943. Replaced control counts with a title-page evidence summary; retained the paraphrase attribution.
- WRONG | [X5] "Bloomington, Indiana, January 1943." | https://mdpi-res.com/d_attachment/axioms/axioms-12-00280/article_deploy/axioms-12-00280.pdf | The autobiographical passage reproduced by Robeva and Jungck, section 2.1, p. 4, dates the dance to February 1943. January changed to February.
- MINOR | [X6] "an Italian refugee three years off the boat," | https://news.mit.edu/2022/honoring-longtime-mit-professor-salvador-luria-1118; https://ki.mit.edu/news/2019/golden-anniversary-for-lurias-gold-medal | MIT News confirms flight from Italy and Nazi Europe; the Koch Institute dates US immigration to 1940. Added both located sources; retained the approximate three-calendar-year wording.
- MINOR | [X7] "Luria stops dancing." | https://mdpi-res.com/d_attachment/axioms/axioms-12-00280/article_deploy/axioms-12-00280.pdf | The autobiographical passage places Luria near the machine during a pause in the music, before the jackpot. Replaced the unsupported stops-dancing sequence with pause, observation and thought.
- MINOR | [X8] "A single number cannot separate them." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained.
- MINOR | [X9] "the spread between parallel cultures can" | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained.
- WRONG | [X10] "Same average. Watch the spread." | git show f5e5f84f34:public/strata/luria-delbruck/index.html | The actual code has induced mean m and spontaneous mean m*G*2^(G-1)/(2^G-1). With G=22 and m=2 these are 2 and 22.0000052452. Replayed sample means are 2.266667 and 14.416667. Corrected prose and generated caption; distinguished the finite simulation mean from the ideal infinite mean.
- WRONG | [X11] "Each click runs a fresh experiment of 100 parallel spontaneous cultures" | git show f5e5f84f34:public/strata/luria-delbruck/index.html | The registered estimator click handler calls estRun(40), each iteration generating 100 cultures. Callback replay increased the experiment count from 40 to 80. Corrected the prose to 40 experiments per click.
- MINOR | [X12] "The spread alone decides the case" | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 Discussion, p. 509, and Summary, p. 510, support resistance mutations independent of virus action in the stated experimental case. Replaced the Burnet excerpt with a located summary of that conclusion.
- MINOR | [X13] "independent cultures fluctuate enormously." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained.
- WRONG | [X14] "six years after the 1943 paper, D. E. Lea and C. A. Coulson wrote it down in closed form." | https://link.springer.com/article/10.1007/BF02986080 | Coulson's publisher note says the manuscript and calculations had been completed just before Lea's June 1947 death; the issue date is December 1949. Changed writing date to completion in 1947 and publication in 1949, specifying a probability generating function.
- WRONG | [X15] "a mutation is equally likely at any moment of exponential growth" | https://arxiv.org/pdf/1203.3422 | Hamon and Ycart, p. 3, point 2, places most divisions late in exponential growth. Replaced uniform clock time with constant probability per division and more late opportunities; kept the equal-fitness clone law.
- MINOR | [X16] "the fraction of cultures with zero resistant colonies." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 Mutation Rate subsection, p. 507, uses 29 empty cultures out of 87 to estimate m about 1.10, then normalizes with cell count. Replaced the unrelated count-of-one excerpt with this located evidence summary.
- MINOR | [X17] "the information about the mutation rate lives in the low counts and the empties, not in the jackpots." | https://pmc.ncbi.nlm.nih.gov/articles/PMC2041832/ | Foster's analysis section says MSS uses all results; the 1943 paper, p. 507, calls zero-only estimation inefficient. Narrowed the summary to the p0 estimator ignoring jackpot sizes and being useful at small m. The repair pass also removed the remaining unqualified dismissal of jackpots from the end of the paragraph.
- MINOR | [X18] "The fluctuation test was the first quantitative proof" | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 introduction, pp. 491-492, distinguishes prior proposals from rigorous demonstration; the Summary, p. 510, gives the result. Replaced the Burnet excerpt with those locators, retaining the claim in its experimental scope.
- MINOR | [X19] "shared the 1969 Nobel Prize." | https://www.paijournal.com/index.php/paijournal/article/download/763/836 | PAI p. 16 completes the Andrew Murray passage with the 1969 prize shared with Hershey. Replaced the cut-off excerpt with a located summary of the complete assessment.
- MINOR | [X20] "What it did not prove is that all mutation is blind" | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 Discussion, p. 509, explicitly restricts the proof to the experimental case and leaves generality open. Replaced the culture-volume excerpt with this scope locator and evidence summary.
- MINOR | [X21] "the targeted machinery of CRISPR-Cas immunity" | https://www.nature.com/articles/335142a0; https://www.paijournal.com/index.php/paijournal/article/download/763/836 | Read the original 1988 abstract and PAI p. 15. The former concerns proposed mutation choice; the latter supplies the CRISPR-Cas comparison. Added the CRISPR source and locator, retaining the qualified page comparison.
- WRONG | [X22] "a refusal to trust the average at all" | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 496-498 and 507-508, models a finite mean and describes both zero-culture and average-based rate estimators. Removed the exclusive refusal story from prose, metadata, JSON-LD, dek and relates note. The ideal limiting law remains infinite-mean.
- MINOR | [X23] "the coastline's length scale-free." | https://courses.physics.ucsd.edu/2019/Spring/physics235/BTW-PRA.pdf; https://gis.humboldt.edu/olm/courses/gsp_510/Articles/Mandelbrot1967.pdf; https://arxiv.org/pdf/1203.3422 | Read Bak, Tang and Wiesenfeld's abstract, Mandelbrot p. 636 and Hamon and Ycart p. 7. Added separate coastline and clone-law sources and locators to the sandpile-only evidence. The analogy concerns scaling, not identical exponents.
- MINOR | [X24] "E. coli strain B and a bacteriophage (designated α)." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The original Material and Methods, p. 501, identifies Escherichia coli B and virus alpha. Replaced the unrelated powers-of-two excerpt with the correct materials locator and summary.
- MINOR | [X25] "independent cultures show variance ≫ mean" | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained.
- WRONG | [X26] "reproduce the offline figures." | git show f5e5f84f34:research/luria-delbruck/verify.mjs | The offline run uses seed 424242 and 4000 spontaneous cultures before induced draws; the page uses seed 13579 and 60 interleaved cultures. Their spontaneous variance/mean values are 608.5712 and 102.9371. Corrected the reproduction promise, including the live-check heading and README.
- WRONG | [X27] "and that count is honest Poisson." | https://pmc.ncbi.nlm.nih.gov/articles/PMC2041832/ | Foster, Confidence Limits for p0, identifies the zero fraction as a binomial parameter. Across C independent cultures the empty count is Binomial(C,exp(-m)); mutation events within a culture are Poisson(m). Corrected the displayed comment.
- MINOR | [X28] "The Jackpot shows mutation is blind" | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 Discussion, p. 509, and Summary, p. 510, support resistance mutations independent of virus action in the stated experimental case. Replaced the Burnet excerpt with a located summary of that conclusion.
- MINOR | [X29] "Every number checked three ways." | git show f5e5f84f34:research/luria-delbruck/verify.mjs | The exact convolution uses c_k=1/[k(k+1)]; the growth simulator uses powers-of-two clones. At m=2 the two laws give P(2)=0.1127794 and 0.1353353. Changed the checking claim to two exact calculations plus a separate growth simulation, including README and verifier comments.
- WRONG | [X30] "Two rows of parallel bacterial cultures" | git show f5e5f84f34:public/og/default.png | Viewed public/og/default.png and verified that this is the image selected in metadata. It is a site title card with text and a stack of bars. Replaced the nonexistent-cultures description without changing the image.
- MINOR | [X31] "You cannot tell from one culture." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained.
- MINOR | [X32] "the variance explodes." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained.
- WRONG | [X33] "the clone tail falls only as m/n² […] and not from the useless average." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf; https://arxiv.org/pdf/1203.3422 | The 1943 paper, pp. 496-498 and 507-508, models a finite mean and describes both zero-culture and average-based rate estimators. Removed the exclusive refusal story from prose, metadata, JSON-LD, dek and relates note. The ideal limiting law remains infinite-mean. Hamon and Ycart p. 7 gives the single-clone law 1/[k(k+1)], independent of m. Changed the dek's m/n² attribution to total mutant counts.
- MINOR | [X34] "Every number checked three independent ways" | git show f5e5f84f34:research/luria-delbruck/verify.mjs | The exact convolution uses c_k=1/[k(k+1)]; the growth simulator uses powers-of-two clones. At m=2 the two laws give P(2)=0.1127794 and 0.1353353. Changed the checking claim to two exact calculations plus a separate growth simulation, including README and verifier comments.
- WRONG | [X35] "which is why they counted the empty cultures instead." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 496-498 and 507-508, models a finite mean and describes both zero-culture and average-based rate estimators. Removed the exclusive refusal story from prose, metadata, JSON-LD, dek and relates note. The ideal limiting law remains infinite-mean.
- MINOR | [X36] "Every number checked three ways." | git show f5e5f84f34:research/luria-delbruck/verify.mjs | The exact convolution uses c_k=1/[k(k+1)]; the growth simulator uses powers-of-two clones. At m=2 the two laws give P(2)=0.1127794 and 0.1353353. Changed the checking claim to two exact calculations plus a separate growth simulation, including README and verifier comments. This duplicates X29's social-description claim.
- WRONG | [X37] "Same mean, by construction (m = 2)." | git show f5e5f84f34:public/strata/luria-delbruck/index.html | The actual code has induced mean m and spontaneous mean m*G*2^(G-1)/(2^G-1). With G=22 and m=2 these are 2 and 22.0000052452. Replayed sample means are 2.266667 and 14.416667. Corrected prose and generated caption; distinguished the finite simulation mean from the ideal infinite mean.
- WRONG | [X38] "mostly empty, rare towering jackpots" | git show f5e5f84f34:public/strata/luria-delbruck/index.html | For the model, P(empty)=exp(-m); at m=2 this is 0.135335. Replaying the actual default code gives only 6 empty spontaneous cultures out of 60. Changed the generated label to mostly small counts.
- WRONG | [X39] "the spontaneous one only grows" | git show f5e5f84f34:public/strata/luria-delbruck/index.html | The actual accumulated-sample ratio falls from 113.600595 at 180 cultures to 97.965989 at 240. Replaced monotone-growth wording in the generated caption and the prose with fluctuations and occasional jackpot jumps.
- MINOR | [X40] "a published statistic too CLEAN to be honest" | https://pmc.ncbi.nlm.nih.gov/articles/PMC9706470/ | Read Mendel: From genes to genome, Mendel's ratios section. It attributes the suspicion to Fisher and describes disagreement among later researchers. Attributed the concern to Fisher and called it disputed, in this layer's relates note and cousin card.
- MINOR | [X41] "There the mean is fine and the spread is the lie" | https://pmc.ncbi.nlm.nih.gov/articles/PMC9706470/ | The same Mendel review documents dispute over the too-close fit. Replaced spread-is-the-lie wording with an attributed, disputed suspicion; preserved the limited comparison with the ideal infinite-mean law.
- MINOR | [X42] "the Luria–Delbrück distribution's mean is infinite" | https://courses.physics.ucsd.edu/2019/Spring/physics235/BTW-PRA.pdf; https://gis.humboldt.edu/olm/courses/gsp_510/Articles/Mandelbrot1967.pdf; https://arxiv.org/pdf/1203.3422 | Hamon and Ycart p. 7 gives the equal-fitness clone law 1/[k(k+1)], whose mean diverges harmonically. Added the clone-law source and locator to the sandpile-only evidence; retained the ideal-law infinite mean.
- WRONG | [X43] "has no finite target at all, so Luria and Delbrück reached for p₀ = e^(−m)" | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 496-498 and 507-508, models a finite mean and describes both zero-culture and average-based rate estimators. Removed the exclusive refusal story from prose, metadata, JSON-LD, dek and relates note. The ideal limiting law remains infinite-mean.
- MINOR | [X44] "the experiment that first proved bacterial mutations" | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 introduction, pp. 491-492, distinguishes prior proposals from rigorous demonstration; the Summary, p. 510, gives the result. Replaced the Burnet excerpt with those locators, retaining the claim in its experimental scope.
- MINOR | [X45] "jackpots make the variance across cultures dwarf the mean." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained.
- MINOR | [X46] "the mutation rate read off the fraction of *empty* cultures" | https://arxiv.org/pdf/1203.3422 | Hamon and Ycart, p. 4, distinguishes expected event count from per-cell mutation probability. Changed the markdown to expected mutation count and stated normalization by final cell count in the large-population approximation.
- CONFIRMED | "is at a faculty dance, watching a colleague feed a slot machine and lose, lose, lose" [...] "and then hit a jackpot." | https://mdpi-res.com/d_attachment/axioms/axioms-12-00280/article_deploy/axioms-12-00280.pdf | Codex N2 source re-read: [007 dance-jackpot] Read the entire autobiographical passage in section 2.1. It says "February 1943", "faculty dance at Indiana University", and "During the pause in the music". The next lines complete the truncated jackpot account.
- CONFIRMED | "He has been stuck for months on a question about bacteria, and the slot machine has just handed him the answer." | https://mdpi-res.com/d_attachment/axioms/axioms-12-00280/article_deploy/axioms-12-00280.pdf | Codex N2 source re-read: [009 months-and-insight] Read the entire autobiographical passage in section 2.1. It says "February 1943", "faculty dance at Indiana University", and "During the pause in the music". The next lines complete the truncated jackpot account.
- CONFIRMED | "The question was old and looked unanswerable." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Codex N2 source re-read: [010 old-question] The introduction, p. 494, describes the authors realizing that fluctuations "were not due to any uncontrolled conditions of our experiments" and could test the mutation hypothesis.
- CONFIRMED | "Pour a billion E. coli onto a plate seeded with a virus" [...] "a bacteriophage that kills them on contact" [...] "and almost all die. But a few colonies grow: resistant bacteria." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Codex N2 source re-read: [011 phage-kills] Read p. 492 beyond the truncated excerpt: plating with excess virus leaves a small surviving fraction that forms resistant colonies. The billion-cell setup is illustrative; loss of reproductive viability is distinguished from instantaneous physical lysis.
- CONFIRMED | "Contact with the phage causes a few cells to acquire resistance" [...] "an adaptation, like a callus forming under friction. Each cell, on meeting the virus, has some small independent chance of converting. The Lamarckian story: the environment writes the trait." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Codex N2 source re-read: [012 prose-4] Read pp. 494-495 beyond the cut-off excerpt. The acquired-immunity hypothesis gives independent rare survival events, a binomial distribution with the Poisson rare-event limit. Its Poisson mean and variance coincide.
- CONFIRMED | "Resistance arises by random mutation during the ordinary growth of the culture, days before any virus appears. The phage doesn't create resistance; it merely reveals the mutants that were already swimming in the broth. The Darwinian story: variation comes first, selection only sorts." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Codex N2 source re-read: [013 prose-5] The supplied p. 510 passage concerns Burnet and is not the Summary paragraph. The actual Summary immediately below it, and Discussion p. 509, support resistance mutations independent of virus action. Read in the explicitly stated experimental scope.
- CONFIRMED | "Here is the engine of the whole proof. Under hypothesis A, every cell independently rolls the same long-odds die at the moment of plating, so the number of survivors per culture is a sum of independent rare events" [...] "a Poisson count. A Poisson distribution has a signature so exact it is almost a fingerprint: its variance equals its mean. All the cultures cluster tightly around the same value." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Codex N2 source re-read: [015 prose-7] Read pp. 494-495 beyond the cut-off excerpt. The acquired-immunity hypothesis gives independent rare survival events, a binomial distribution with the Poisson rare-event limit. Its Poisson mean and variance coincide.
- CONFIRMED | "Under hypothesis B, a mutation can strike at any moment during the days of growth. If it strikes late, the mutant has time to make only a handful of resistant descendants before plating. If it strikes early" [...] "while the culture is still small" [...] "that one mutant and all its progeny double, and double, and double, until by plating day there are thousands of resistant cells from a single ancestral accident. A jackpot. Most cultures get no early mutation and show few or zero survivors; a rare few hit the jackpot and show enormous counts. The cultures disagree violently. The variance dwarfs the mean." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Codex N2 source re-read: [016 prose-8] The p. 497 account explains early mutations, clone multiplication and rare high counts. Its comparison with a slot machine and its high-variance conclusion support the claim.
- CONFIRMED | "That gap, two or three orders of magnitude wide, is what Luria and Delbrück saw in 1943, and it is not subtle." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Codex N2 source re-read: [022 historical-ratio-gap] Recomputed Table 3: 6270/10.12 = 619.57 and 6431/28.6 = 224.86. These independent-culture examples support the stated orders of magnitude; Table 1 controls have variance close to mean.
- CONFIRMED | "Discretised, a clone has size k with probability 1/(k(k+1))." | https://arxiv.org/pdf/1203.3422 | Codex N2 source re-read: [027 clone-distribution] At equal growth rates, rho*B(rho+1,k) at rho=1 equals 1/[k(k+1)]. This is the stochastic clone law, not the powers-of-two law used by Instrument I.
- CONFIRMED | "The mutant count is the sum of a Poisson number of such clones, and its probabilities follow the Ma–Sandri–Sarkar recursion:" | https://arxiv.org/pdf/1203.3422 | Codex N2 source re-read: [028 compound-poisson-recursion] Hamon and Ycart section 3 gives the Yule clone probability rho*B(rho+1,k). At equal fitness rho=1 this is 1/[k(k+1)]. The compound-Poisson construction and harmonic divergence follow directly.
- CONFIRMED | "Note the shape: a tall spike at zero (those are the … of cultures that never mutated), then a long, fat tail that falls off as m/n²" [...] "slowly enough that the rare jackpots out at n = 100 or 1000 still carry real probability." | https://rcpcm.ru/science/wp-content/uploads/2017/11/MSS-1992.pdf | Codex N2 source re-read: [030 distribution-shape] The default m=2 has p0=0.135335 and the asymptotic total-count tail m/n^2. The input retains an ellipsis in place of the rendered 14%; that omitted number is added separately.
- CONFIRMED | "The expected clone size is Σ k·(1/(k(k+1))) = Σ 1/(k+1)" [...] "the harmonic series, which diverges." | https://arxiv.org/pdf/1203.3422 | Codex N2 source re-read: [032 harmonic-clone-mean] Direct arithmetic: k/[k(k+1)]=1/(k+1); partial sums diverge. The missing k=1 term of the standard harmonic series does not alter divergence.
- CONFIRMED | "So the mean of the Luria–Delbrück distribution is infinite. Not large: infinite." | https://rcpcm.ru/science/wp-content/uploads/2017/11/MSS-1992.pdf | Codex N2 source re-read: [033 infinite-mean] Read MSS pp. 261-263 and the clone law in Hamon and Ycart. Sum k/[k(k+1)] diverges. At a finite cap the expectation is finite and grows logarithmically; statements about an infinite mean concern the ideal limiting distribution.
- CONFIRMED | "In any real culture the clone is capped at the final population N, so the mean is finite but grows like m·ln N and never settles to a fixed value" [...] "it depends on how big you grew the cultures, which is no property of the mutation rate at all." | https://rcpcm.ru/science/wp-content/uploads/2017/11/MSS-1992.pdf | Codex N2 source re-read: [034 finite-culture-mean] Read MSS pp. 261-263 and the clone law in Hamon and Ycart. Sum k/[k(k+1)] diverges. At a finite cap the expectation is finite and grows logarithmically; statements about an infinite mean concern the ideal limiting distribution.
- CONFIRMED | "You cannot estimate m from the average. The average has no stable target. The jackpots are heavy enough to drag it wherever the largest one happens to land." | https://rcpcm.ru/science/wp-content/uploads/2017/11/MSS-1992.pdf | Codex N2 source re-read: [035 mean-estimator] Confirmed for the ideal infinite-mean law discussed immediately above and the naive sample mean used as m itself. Foster also states that methods based on the mean are invalid in standard fluctuation analysis. This does not justify the separate historical claim that Luria and Delbruck never used a mean-based method.
- CONFIRMED | "A culture is empty exactly when no mutation occurred at all, and mutational events are Poisson(m), so" | https://arxiv.org/pdf/1203.3422 | Codex N2 source re-read: [037 empty-equivalence] Under the stated no-death, fully plated model, every mutation has a positive clone size. Hence a zero mutant count is exactly the event of zero mutation events.
- CONFIRMED | "The p₀ method has a known weakness" [...] "if m is large, almost no culture is empty and there is nothing to count" | https://arxiv.org/pdf/1203.3422 | Codex N2 source re-read: [038 p0-large-m] Hamon and Ycart p. 4 gives the no-mutant probability exp(-alpha), its small-alpha limitation and conversion of expected event count to mutation probability by dividing by final cell count. Algebra gives -ln(p0).
- CONFIRMED | "and the modern “gold standard” is the Ma–Sandri–Sarkar maximum-likelihood fit that uses the whole distribution from Instrument II." | https://pmc.ncbi.nlm.nih.gov/articles/2041832/ | Codex N2 source re-read: [039 mss-gold-standard] Foster, Method 5, explicitly calls the MSS likelihood method the "gold standard" because it uses all experimental results. This is the conventional equal-fitness fluctuation-analysis method.
- CONFIRMED | "In 1952 Joshua and Esther Lederberg closed the case visually with replica plating: resistant colonies can be lifted off a plate that never met the phage, proving the mutants pre-existed." | https://lenski.mmg.msu.edu/lenski/pdf/1995%2C%20ARES%2C%20Sniegowski%20%26%20Lenski.pdf; https://pubmed.ncbi.nlm.nih.gov/14927572/ | Codex N2 source re-read: [043 replica-1952] The Lenski-hosted PDF URL now redirects to a profile. Its indexed text was retrieved by web search and matches the supplied passage on pure resistant cultures without selective exposure. The 1952 primary citation was checked through ASM, PubMed and Crossref.
- CONFIRMED | "There is a small irony the modern literature enjoys: the E. coli strain B that Luria and Delbrück happened to use lacks a working CRISPR-Cas system" [...] "had they picked a strain with one, they would have been studying a genuine case of heritable, environment-directed resistance, and the experiment might have read very differently." | https://www.paijournal.com/index.php/paijournal/article/download/763/836 | Codex N2 source re-read: [046 crispr-strain-counterfactual] Read past the excerpt in PAI p. 15: the selected E. coli strain "lacked an operative CRISPR-Cas mechanism". The counterfactual is conditional on a functioning resistance pathway for the particular phage. This is an explicitly hypothetical historical comparison, not an observed rerun on another strain.
- CONFIRMED | "The test was right about its phage and its strain; the universe kept a subtler card in reserve." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Codex N2 source re-read: [047 test-strain] The supplied passage concerns mutation-rate comparisons, not experimental scope. The explicit restriction is in Discussion p. 509: the result concerns their case, and generality remains open.
- CONFIRMED | "When a distribution's mean is infinite, the average stops meaning anything" [...] "a lesson this page shares with them." | https://rcpcm.ru/science/wp-content/uploads/2017/11/MSS-1992.pdf | Codex N2 source re-read: [052 average-no-meaning] The sample mean lacks a finite population-mean target under the ideal law. Read the rhetorical phrase as lack of a stable mean summary, not as denial of all possible statistical information.
- CONFIRMED | "Luria, S. E., & Delbrück, M. (1943). Mutations of Bacteria from Virus Sensitivity to Virus Resistance. Genetics 28(6): 491–511." | https://pmc.ncbi.nlm.nih.gov/articles/1209226/ | Codex N2 source re-read: [053 citation-25] Checked original 1943 PDF title, authors, journal, volume and pages, and the DOI metadata. Citation matches.
- CONFIRMED | "Lea, D. E., & Coulson, C. A. (1949). The distribution of the numbers of mutants in bacterial populations. Journal of Genetics 49(3): 264–285." | https://link.springer.com/article/10.1007/BF02986080 | Codex N2 source re-read: [054 citation-26] Springer gives D. E. Lea, C. A. Coulson, volume 49, pages 264-285, December 1949. Its additional note dates completion of the manuscript and calculations to June 1947.
- CONFIRMED | "Ma, W. T., Sandri, G. vH., & Sarkar, S. (1992). Analysis of the Luria–Delbrück distribution using discrete convolution powers. Journal of Applied Probability 29(2): 255–267." | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3CF16F78A88372E56AA1BE234D479BAD/S0021900200043023a.pdf/analysis-of-the-luria-delbruck-distribution-using-discrete-convolution-powers.pdf | Codex N2 source re-read: [055 citation-27] The original MSS PDF title page and Cambridge metadata agree on the three authors, 1992, volume 29(2), pages 255-267. The archival DOI resolves to the same work.
- CONFIRMED | "Lederberg, J., & Lederberg, E. M. (1952). Replica plating and indirect selection of bacterial mutants. Journal of Bacteriology 63(3): 399–406." | https://journals.asm.org/doi/10.1128/jb.63.3.399-406.1952 | Codex N2 source re-read: [056 citation-28] ASM, PubMed 14927572 and Crossref agree: Joshua Lederberg and Esther M. Lederberg, March 1952, 63(3):399-406. The checker DOI MISMATCH is a repeated-surname/initial-matching false alarm.
- CONFIRMED | "Zheng, Q. (1999). Progress of a half century in the study of the Luria–Delbrück distribution. Mathematical Biosciences 162(1–2): 1–32." | https://pubmed.ncbi.nlm.nih.gov/10616278/ | Codex N2 source re-read: [057 citation-29] PubMed 10616278 and DOI metadata agree: Q. Zheng, 1999 Nov-Dec, Mathematical Biosciences 162(1-2):1-32.
- CONFIRMED | "The first closed-form probability generating function for the mutant distribution, parameterised by the single quantity m." | https://rcpcm.ru/science/wp-content/uploads/2017/11/MSS-1992.pdf | Codex N2 source re-read: [060 lea-first-pgf] MSS p. 256 explicitly credits Lea and Coulson with the generating function, and Springer dates publication to 1949. The claim specifies the PGF and is distinct from entry 25's date-of-writing problem.
- CONFIRMED | "The recursion used on this page: p₀ = e^−m, pₙ = (m/n)Σ pᵢ/(n−i+1); and the asymptotic pₙ ∼ c/n²." | https://rcpcm.ru/science/wp-content/uploads/2017/11/MSS-1992.pdf | Codex N2 source re-read: [061 mss-recursion-asymptotic] Equation (21) gives the displayed recursion; p. 263 gives p_n asymptotic c/n^2. The page does not falsely claim that MSS wrote the constant there as m.
- CONFIRMED | "The visual confirmation: resistant colonies recovered from plates never exposed to the selective agent" [...] "the mutants pre-existed." | https://lenski.mmg.msu.edu/lenski/pdf/1995%2C%20ARES%2C%20Sniegowski%20%26%20Lenski.pdf; https://pubmed.ncbi.nlm.nih.gov/14927572/ | Codex N2 source re-read: [063 replica-source-description] The Lenski-hosted PDF URL now redirects to a profile. Its indexed text was retrieved by web search and matches the supplied passage on pure resistant cultures without selective exposure. The 1952 primary citation was checked through ASM, PubMed and Crossref.
- CONFIRMED | "The standard modern review of the distribution, its estimators, and the infinite-mean fact." | https://pubmed.ncbi.nlm.nih.gov/10616278/ | Codex N2 source re-read: [064 zheng-source-description] PubMed abstract explicitly says the review discusses generating functions, moments, computational methods, asymptotics and "new explanations of divergent moments".
- CONFIRMED | "Luria, S. E. (1984). A Slot Machine, a Broken Test Tube: An Autobiography. Harper & Row." | https://www.nobelprize.org/prizes/medicine/1969/luria/biographical/ | Codex N2 source re-read: [065 citation-autobiography] The Nobel biography lists A Slot Machine, a Broken Test Tube: an Autobiography, Harper & Row, New York, 1984.
- CONFIRMED | "Luria's own account of the slot-machine epiphany at the Indiana faculty dance, winter 1943." | https://mdpi-res.com/d_attachment/axioms/axioms-12-00280/article_deploy/axioms-12-00280.pdf | Codex N2 source re-read: [066 autobiography-description] Read the entire autobiographical passage in section 2.1. It says "February 1943", "faculty dance at Indiana University", and "During the pause in the music". The next lines complete the truncated jackpot account.
- CONFIRMED | "Nobel Prize in Physiology or Medicine 1969" [...] "Delbrück, Hershey & Luria, “for their discoveries concerning the replication mechanism and the genetic structure of viruses.”" | https://www.nobelprize.org/prizes/medicine/1969/summary/ | Codex N2 source re-read: [067 nobel-citation] The official Nobel summary names Delbruck, Hershey and Luria jointly and reproduces the motivation. The checker quote warning is final-punctuation handling, not a substantive misquotation.
- CONFIRMED | "for their discoveries concerning the replication mechanism and the genetic structure of viruses." | https://www.nobelprize.org/prizes/medicine/1969/summary/ | Codex N2 source re-read: [068 nobel-quote] The official motivation matches the words. The terminal sentence period triggers the strict offline test but does not alter the quotation's meaning or attribution; no punctuation finding is reported.
- CONFIRMED | "p₀ = e^(−m) pₙ = (m / n) · Σ[i=0..n−1] pᵢ / (n − i + 1)" | https://rcpcm.ru/science/wp-content/uploads/2017/11/MSS-1992.pdf | Codex N2 source re-read: [072 recursion-formula] MSS equations (17)-(22) match each symbol and index. Recreated at m=1: p1=0.1839397206 and p2=0.1072981703.
- CONFIRMED | "p = Σ[j] e^(−m) mʲ/j! · c^(*j), c_k = 1/(k(k+1))" | https://arxiv.org/pdf/1203.3422 | Codex N2 source re-read: [073 compound-formula] Conditioning on J~Poisson(m) gives the sum of convolution powers with weights exp(-m)*m^j/j!. Each clone uses 1/[k(k+1)].
- CONFIRMED | "P(culture is empty) = p₀ = e^(−m)" | https://arxiv.org/pdf/1203.3422 | Codex N2 source re-read: [074 empty-estimator-formula] Hamon and Ycart p. 4 gives the no-mutant probability exp(-alpha), its small-alpha limitation and conversion of expected event count to mutation probability by dividing by final cell count. Algebra gives -ln(p0).
- CONFIRMED | "m̂ = −ln( fraction of empty cultures )" | https://arxiv.org/pdf/1203.3422 | Codex N2 source re-read: [075 invert-estimator] Hamon and Ycart p. 4 gives the no-mutant probability exp(-alpha), its small-alpha limitation and conversion of expected event count to mutation probability by dividing by final cell count. Algebra gives -ln(p0).
- CONFIRMED | "this estimator ignores the jackpots entirely" | https://arxiv.org/pdf/1203.3422 | Codex N2 source re-read: [076 jackpots-ignored] The formula uses only the indicator of a zero culture; changing a positive count to any other positive count leaves the estimator unchanged.
- CONFIRMED | "The coastline has no well-defined length because the answer scales with the ruler" | https://gis.humboldt.edu/olm/courses/gsp_510/Articles/Mandelbrot1967.pdf | Codex N2 source re-read: [123 related-coast-length] Read Mandelbrot p. 636: the abstract says geographical-curve lengths are "often infinite or, rather, undefinable". The body explains ruler-dependent measurements and statistical self-similarity.
- CONFIRMED | "the Luria–Delbrück mean has no well-defined value because it scales with how big you grew the culture (∼ m·ln N)." | https://rcpcm.ru/science/wp-content/uploads/2017/11/MSS-1992.pdf | Codex N2 source re-read: [124 related-culture-scaling] A finite culture has a finite, well-defined mean at fixed N. The wording is read with the explicit finite-culture qualification on the page, as absence of an N-independent limiting value.
- CONFIRMED | "Two faces of a quantity that refuses to converge" [...] "and in both cases the honest move is to report the scaling law, not a single number." | https://gis.humboldt.edu/olm/courses/gsp_510/Articles/Mandelbrot1967.pdf; https://gis.humboldt.edu/olm/courses/gsp_510/Articles/Mandelbrot1967.pdf; https://arxiv.org/pdf/1203.3422 | Codex N2 source re-read: [125 related-nonconvergence] The quoted recommendation to report scaling is an interpretation. Its checkable premises, coastline ruler dependence and logarithmic mean divergence in the ideal model, are supported by the two primary mathematical sources.
- CONFIRMED | "The Cold Hand overturns a result because the natural estimator is biased" | https://arxiv.org/abs/1902.01265 | Codex N2 source re-read: [126 related-hot-hand-bias] Opened the primary authors' arXiv abstract: "Upon correcting for the bias we find that the long-standing conclusions of the canonical study are reversed."
- CONFIRMED | "shows that its **mean is infinite** because the clone-size tail falls only as 1/s² (the truncated mean grows like m·ln N and never settles)," | https://rcpcm.ru/science/wp-content/uploads/2017/11/MSS-1992.pdf | Codex N2 source re-read: [133 markdown-infinite-tail] The ideal equal-fitness clone law gives harmonic divergence; the truncated mutant-count sum has leading term m*ln(N). The finite population simulation must not be confused with the limiting law.
- CONFIRMED | "The Lamarckian story: the environment writes the trait." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Codex N2 source re-read: [136 induced-label] This is a label for the explicitly hypothetical acquired-immunity mechanism, not an assertion that it occurred in the 1943 test.
- CONFIRMED | "The Darwinian story: variation comes first, selection only sorts." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Codex N2 source re-read: [137 spontaneous-label] This is a label for the spontaneous-variation-before-selection hypothesis tested by the experiment; the page separately states its scope limits.
- CONFIRMED | "Ma–Sandri–Sarkar (1992) recursion, m = expected mutations per culture" | https://rcpcm.ru/science/wp-content/uploads/2017/11/MSS-1992.pdf | Codex N2 source re-read: [138 recursion-year] MSS title page is dated 1992; equation (21) matches the recurrence, with m explicitly the expected number of mutations.
- CONFIRMED | "fraction of cultures that never mutate" | https://arxiv.org/pdf/1203.3422 | Codex N2 source re-read: [139 zero-fraction] For the model's resistance mutation events, no surviving mutants and no event are equivalent because there is no death or failed plating. The phrase does not refer to every possible genomic mutation.

- UNVERIFIABLE | [N2-050] "everyone before Luria had been throwing away as noise." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Re-read p. 494: it describes the authors' own experimental difficulties and recognition of the fluctuations' significance, not what every predecessor did. Removed this unsupported universal clause from public/strata/luria-delbruck/index.html. No claim that it was disproved.
- UNVERIFIABLE | [N2-120] "everyone before Luria had thrown away as noise." | https://www.bx.psu.edu/~anton/bioinf1-2014/delbruck-luria-1943.pdf | Re-read p. 494: it does not establish the universal about predecessors. Removed the clause from the closer-than-chance relates note in src/content/strata/luria-delbruck.md. No claim that it was disproved.

## Findings

- [fixed] X1 (MINOR): The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained. No page correction line, under the MINOR rule.
- [fixed] X2 (MINOR): The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained. No page correction line, under the MINOR rule.
- [fixed] X3 (MINOR): The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained. Changed kind from quote to paraphrase and removed the false verbatim-quote field. No page correction line, under the MINOR rule.
- [fixed] X4 (MINOR): The original title page, p. 491, confirms authors, Genetics 28 and November 1943. Replaced control counts with a title-page evidence summary; retained the paraphrase attribution. No page correction line, under the MINOR rule.
- [fixed] X5 (WRONG): The autobiographical passage reproduced by Robeva and Jungck, section 2.1, p. 4, dates the dance to February 1943. January changed to February. Dated correction mirrored in the page and markdown body.
- [fixed] X6 (MINOR): MIT News confirms flight from Italy and Nazi Europe; the Koch Institute dates US immigration to 1940. Added both located sources; retained the approximate three-calendar-year wording. No page correction line, under the MINOR rule.
- [fixed] X7 (MINOR): The autobiographical passage places Luria near the machine during a pause in the music, before the jackpot. Replaced the unsupported stops-dancing sequence with pause, observation and thought. No page correction line, under the MINOR rule.
- [fixed] X8 (MINOR): The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained. No page correction line, under the MINOR rule.
- [fixed] X9 (MINOR): The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained. No page correction line, under the MINOR rule.
- [fixed] X10 (WRONG): The actual code has induced mean m and spontaneous mean m*G*2^(G-1)/(2^G-1). With G=22 and m=2 these are 2 and 22.0000052452. Replayed sample means are 2.266667 and 14.416667. Corrected prose and generated caption; distinguished the finite simulation mean from the ideal infinite mean. Dated correction mirrored in the page and markdown body.
- [fixed] X11 (WRONG): The registered estimator click handler calls estRun(40), each iteration generating 100 cultures. Callback replay increased the experiment count from 40 to 80. Corrected the prose to 40 experiments per click. Dated correction mirrored in the page and markdown body.
- [fixed] X12 (MINOR): The 1943 Discussion, p. 509, and Summary, p. 510, support resistance mutations independent of virus action in the stated experimental case. Replaced the Burnet excerpt with a located summary of that conclusion. No page correction line, under the MINOR rule.
- [fixed] X13 (MINOR): The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained. No page correction line, under the MINOR rule.
- [fixed] X14 (WRONG): Coulson's publisher note says the manuscript and calculations had been completed just before Lea's June 1947 death; the issue date is December 1949. Changed writing date to completion in 1947 and publication in 1949, specifying a probability generating function. Dated correction mirrored in the page and markdown body.
- [fixed] X15 (WRONG): Hamon and Ycart, p. 3, point 2, places most divisions late in exponential growth. Replaced uniform clock time with constant probability per division and more late opportunities; kept the equal-fitness clone law. Dated correction mirrored in the page and markdown body.
- [fixed] X16 (MINOR): The 1943 Mutation Rate subsection, p. 507, uses 29 empty cultures out of 87 to estimate m about 1.10, then normalizes with cell count. Replaced the unrelated count-of-one excerpt with this located evidence summary. No page correction line, under the MINOR rule.
- [fixed] X17 (MINOR): Foster's analysis section says MSS uses all results; the 1943 paper, p. 507, calls zero-only estimation inefficient. Narrowed the summary to the p0 estimator ignoring jackpot sizes and being useful at small m. The repair pass also removed the remaining unqualified dismissal of jackpots from the end of the paragraph. No page correction line, under the MINOR rule.
- [fixed] X18 (MINOR): The 1943 introduction, pp. 491-492, distinguishes prior proposals from rigorous demonstration; the Summary, p. 510, gives the result. Replaced the Burnet excerpt with those locators, retaining the claim in its experimental scope. No page correction line, under the MINOR rule.
- [fixed] X19 (MINOR): PAI p. 16 completes the Andrew Murray passage with the 1969 prize shared with Hershey. Replaced the cut-off excerpt with a located summary of the complete assessment. No page correction line, under the MINOR rule.
- [fixed] X20 (MINOR): The 1943 Discussion, p. 509, explicitly restricts the proof to the experimental case and leaves generality open. Replaced the culture-volume excerpt with this scope locator and evidence summary. No page correction line, under the MINOR rule.
- [fixed] X21 (MINOR): Read the original 1988 abstract and PAI p. 15. The former concerns proposed mutation choice; the latter supplies the CRISPR-Cas comparison. Added the CRISPR source and locator, retaining the qualified page comparison. No page correction line, under the MINOR rule.
- [fixed] X22 (WRONG): The 1943 paper, pp. 496-498 and 507-508, models a finite mean and describes both zero-culture and average-based rate estimators. Removed the exclusive refusal story from prose, metadata, JSON-LD, dek and relates note. The ideal limiting law remains infinite-mean. Dated correction mirrored in the page and markdown body.
- [fixed] X23 (MINOR): Read Bak, Tang and Wiesenfeld's abstract, Mandelbrot p. 636 and Hamon and Ycart p. 7. Added separate coastline and clone-law sources and locators to the sandpile-only evidence. The analogy concerns scaling, not identical exponents. No page correction line, under the MINOR rule.
- [fixed] X24 (MINOR): The original Material and Methods, p. 501, identifies Escherichia coli B and virus alpha. Replaced the unrelated powers-of-two excerpt with the correct materials locator and summary. No page correction line, under the MINOR rule.
- [fixed] X25 (MINOR): The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained. No page correction line, under the MINOR rule.
- [fixed] X26 (WRONG): The offline run uses seed 424242 and 4000 spontaneous cultures before induced draws; the page uses seed 13579 and 60 interleaved cultures. Their spontaneous variance/mean values are 608.5712 and 102.9371. Corrected the reproduction promise, including the live-check heading and README. Dated correction mirrored in the page and markdown body.
- [fixed] X27 (WRONG): Foster, Confidence Limits for p0, identifies the zero fraction as a binomial parameter. Across C independent cultures the empty count is Binomial(C,exp(-m)); mutation events within a culture are Poisson(m). Corrected the displayed comment. Dated correction mirrored in the page and markdown body.
- [fixed] X28 (MINOR): The 1943 Discussion, p. 509, and Summary, p. 510, support resistance mutations independent of virus action in the stated experimental case. Replaced the Burnet excerpt with a located summary of that conclusion. No page correction line, under the MINOR rule.
- [fixed] X29 (MINOR): The exact convolution uses c_k=1/[k(k+1)]; the growth simulator uses powers-of-two clones. At m=2 the two laws give P(2)=0.1127794 and 0.1353353. Changed the checking claim to two exact calculations plus a separate growth simulation, including README and verifier comments. No page correction line, under the MINOR rule.
- [fixed] X30 (WRONG): Viewed public/og/default.png and verified that this is the image selected in metadata. It is a site title card with text and a stack of bars. Replaced the nonexistent-cultures description without changing the image. Dated correction mirrored in the page and markdown body.
- [fixed] X31 (MINOR): The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained. No page correction line, under the MINOR rule.
- [fixed] X32 (MINOR): The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained. No page correction line, under the MINOR rule.
- [fixed] X33 (WRONG): The 1943 paper, pp. 496-498 and 507-508, models a finite mean and describes both zero-culture and average-based rate estimators. Removed the exclusive refusal story from prose, metadata, JSON-LD, dek and relates note. The ideal limiting law remains infinite-mean. Hamon and Ycart p. 7 gives the single-clone law 1/[k(k+1)], independent of m. Changed the dek's m/n² attribution to total mutant counts. Dated correction mirrored in the page and markdown body.
- [fixed] X34 (MINOR): The exact convolution uses c_k=1/[k(k+1)]; the growth simulator uses powers-of-two clones. At m=2 the two laws give P(2)=0.1127794 and 0.1353353. Changed the checking claim to two exact calculations plus a separate growth simulation, including README and verifier comments. No page correction line, under the MINOR rule.
- [fixed] X35 (WRONG): The 1943 paper, pp. 496-498 and 507-508, models a finite mean and describes both zero-culture and average-based rate estimators. Removed the exclusive refusal story from prose, metadata, JSON-LD, dek and relates note. The ideal limiting law remains infinite-mean. Dated correction mirrored in the page and markdown body.
- [fixed] X36 (MINOR): The exact convolution uses c_k=1/[k(k+1)]; the growth simulator uses powers-of-two clones. At m=2 the two laws give P(2)=0.1127794 and 0.1353353. Changed the checking claim to two exact calculations plus a separate growth simulation, including README and verifier comments. This duplicates X29's social-description claim. No page correction line, under the MINOR rule.
- [fixed] X37 (WRONG): The actual code has induced mean m and spontaneous mean m*G*2^(G-1)/(2^G-1). With G=22 and m=2 these are 2 and 22.0000052452. Replayed sample means are 2.266667 and 14.416667. Corrected prose and generated caption; distinguished the finite simulation mean from the ideal infinite mean. Dated correction mirrored in the page and markdown body.
- [fixed] X38 (WRONG): For the model, P(empty)=exp(-m); at m=2 this is 0.135335. Replaying the actual default code gives only 6 empty spontaneous cultures out of 60. Changed the generated label to mostly small counts. Dated correction mirrored in the page and markdown body.
- [fixed] X39 (WRONG): The actual accumulated-sample ratio falls from 113.600595 at 180 cultures to 97.965989 at 240. Replaced monotone-growth wording in the generated caption and the prose with fluctuations and occasional jackpot jumps. Dated correction mirrored in the page and markdown body.
- [fixed] X40 (MINOR): Read Mendel: From genes to genome, Mendel's ratios section. It attributes the suspicion to Fisher and describes disagreement among later researchers. Attributed the concern to Fisher and called it disputed, in this layer's relates note and cousin card. No page correction line, under the MINOR rule.
- [fixed] X41 (MINOR): The same Mendel review documents dispute over the too-close fit. Replaced spread-is-the-lie wording with an attributed, disputed suspicion; preserved the limited comparison with the ideal infinite-mean law. No page correction line, under the MINOR rule.
- [fixed] X42 (MINOR): Hamon and Ycart p. 7 gives the equal-fitness clone law 1/[k(k+1)], whose mean diverges harmonically. Added the clone-law source and locator to the sandpile-only evidence; retained the ideal-law infinite mean. No page correction line, under the MINOR rule.
- [fixed] X43 (WRONG): The 1943 paper, pp. 496-498 and 507-508, models a finite mean and describes both zero-culture and average-based rate estimators. Removed the exclusive refusal story from prose, metadata, JSON-LD, dek and relates note. The ideal limiting law remains infinite-mean. Dated correction mirrored in the page and markdown body.
- [fixed] X44 (MINOR): The 1943 introduction, pp. 491-492, distinguishes prior proposals from rigorous demonstration; the Summary, p. 510, gives the result. Replaced the Burnet excerpt with those locators, retaining the claim in its experimental scope. No page correction line, under the MINOR rule.
- [fixed] X45 (MINOR): The 1943 paper, pp. 503-504, contrasts the Table 1 same-culture control with the far larger independent-culture fluctuations in Tables 2-3. Replaced the misplaced excerpt with a located evidence summary in N1; supported page wording retained. No page correction line, under the MINOR rule.
- [fixed] X46 (MINOR): Hamon and Ycart, p. 4, distinguishes expected event count from per-cell mutation probability. Changed the markdown to expected mutation count and stated normalization by final cell count in the large-population approximation. No page correction line, under the MINOR rule.
- [fixed] N2-050 (UNVERIFIABLE): Removed the unsupported universal about all predecessors discarding the variance as noise from the page's Ground Truth cousin paragraph. The source supports the authors' own experience, not that universal history.
- [fixed] N2-120 (UNVERIFIABLE): Removed the same unsupported universal from this layer's markdown relates note. Both authored copies now retain the supported variance comparison without asserting what every predecessor did.