---
slug: the-tanks-that-counted-themselves
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 and a Claude agent
checked: 107
confirmed: 90
wrong: 16
unverifiable: 0
observed: 0
stale: 1
---

This was the directed repair pass for the 17 findings in research/assay-line/cited-1014b/the-tanks-that-counted-themselves/triage.json, against the page read at 67088387e0. The fixer re-read the evidence before editing, recomputed the disputed fractions, and kept the triage's levels: 3 WRONG lines (two describe one error), 13 MINOR lines, and 1 STALE metadata line; MINOR is included in wrong: 16. The 90 unchanged CONFIRMED claims below are carried forward from the source rereads recorded by both N2 checkers, with their evidence notes, rather than presented as a new full audit. Confirmations of wording superseded by these repairs are covered by the corresponding triage items. The HTML is directly authored; verify.mjs generates only artifact.json. Two public Corrected lines cover the two distinct WRONG findings; MINOR changes are recorded here and the dateModified exception needs no Updated line.

## Claims

- MINOR | [X1; body-05-4] The serial number, meant only to track a part through a factory, quietly carries the size of the factory's output. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | Re-read pp. 73-74: markings traced manufacturing defects, including failures in the field, and supported spare-parts control. The factory-only purpose was too narrow.
- MINOR | [X2; body-06-0] Below is one captured month, the same one the argument follows: k = 15 serials drawn from a run whose true size only the postwar ledgers would reveal. | research/the-tanks-that-counted-themselves/verify.mjs | The worked example chooses N0=270 and k0=15, then uses sampleWithoutReplacement with mulberry32(20260619). The HTML uses the same 15 serials and WORKED_N=270. This is simulated data; section VII already disclosed that fact.
- WRONG | [X3; body-24-1] At k = 15 it is exactly 17/3 = 5.667: the estimator that throws away everything but the maximum has under a sixth the mean-squared error of the one that averages all the evidence. | research/the-tanks-that-counted-themselves/verify.mjs | At k=15, Var(twiceMean)/Var(MVUE)=17/3. Its reciprocal is 3/17=0.17647058823529413, greater than 1/6 and less than 1/5. Re-read the variance formulas and recomputed the comparison. Same error as K4.
- WRONG | [X4; body-28-0] A frequentist returns a single best estimate. | https://epub.ub.uni-muenchen.de/2094/1/paper_499.pdf | Re-read printed pp. 2-3: Goodman is credited with both minimum-variance unbiased estimators and confidence intervals; section 2 gives the frequentist interval and its upper-endpoint rule. Frequentist inference is not confined to point estimation.
- MINOR | [X5; body-31-3] The data don't just say "about 260"; they say "almost surely between 243 and 313, and here is how the plausibility is distributed across that range." From fifteen serial numbers. | https://epub.ub.uni-muenchen.de/2094/1/paper_499.pdf; research/the-tanks-that-counted-themselves/verify.mjs | Re-read the posterior and discrete-quantile derivations and code. For m=243,k=15, exact posterior mass through 313 is 1-C(242,14)/C(313,14)=0.9750264073212839. The positive remaining tail is 0.024973592678716166. This is not probability one.
- MINOR | [X6; body-33-3] The shaded band is the central 95%; the gold line is the posterior mean; the teal line is the truth the ledgers later revealed. | public/strata/the-tanks-that-counted-themselves/index.html; research/the-tanks-that-counted-themselves/verify.mjs | The teal marker reads state.N, initialized to WORKED_N=270 and changed by setSample. The band uses the smallest integers whose cumulative posterior mass reaches 0.025 and 0.975. Its nominal level is 95%; the worked interval actually contains about 97.5%.
- MINOR | [X7; citation-panther] The Panther road-wheel example (≈270 estimated vs. 276 recorded for February 1944) and the postwar finding that Allied statistical estimates outperformed both intelligence estimates and Germany's own figures are as reported in the standard secondary accounts of Ruggles & Brodie's study. | https://www.math.kth.se/matstat/gru/sf1901/F/fo9sf1901new.pdf#page=69; https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | Re-read Grandell and Koski, lecture 9, slide 58 (PDF page 69): the secondary account reports greater accuracy and timeliness than German estimates. Ruggles and Brodie pp. 73 and 89 instead use German production records as the benchmark. Preserve the secondary attribution and distinguish estimates from recorded output.
- MINOR | [X8; dek-2] The trick is a single idea: the largest serial you have seen, plus the average gap between the ones you have, estimates the whole production almost exactly. | research/the-tanks-that-counted-themselves/verify.mjs | The stated variance gives SD=sqrt(271)=16.46207763315433 at N=270,k=15, about 6.1% of N. Section VII also discloses a 38.5% historical miss. Unbiasedness supplies no near-exact guarantee for an individual estimate; uncertainty depends on the sample. Same error as K8.
- STALE | [X9; modified-date] "dateModified":"2026-06-19" | git show 26148524b64 -- public/strata/the-tanks-that-counted-themselves/index.html; git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | Re-read the August 1 commit: it added the factual checking placard while dateModified remained June 19. Today's content revision is dated 2026-10-14. The explicit JSON-LD exception applies; the Corrected lines date the revision, so no Updated line is required.
- MINOR | [K1; body-01-1] [#2 body-01-1] Their spies guessed four to eight times too high. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | Re-read pp. 72, 80 and 89. The three production months are June 1940, June 1941 and August 1942; their conventional estimates were compiled in Munitions Record No. 24, August 10, 1942. Serial-number work began in early 1943 and reconstructed earlier output. The displayed overshoot ratios remain supported. Same timeline issue as K7.
- MINOR | [K2; body-02-1] [#5 body-02-1] Their intelligence services, working from agent reports and captured documents, answered with figures that turned out to be four to eight times too high. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | Re-read pp. 73, 78 and 89: aggregate intelligence estimates used extrapolated prewar data or equipment tables based on the German order of battle. Secret reports concern plant-level information; captured documents were important inputs to serial-number analysis. The compressed source attribution needed clarification.
- MINOR | [K3; body-02-3] [#7 body-02-3] They read the serial numbers stamped on the tanks the army captured and destroyed -- gearboxes, chassis, engines, the moulds that cast the road wheels -- and from those numbers estimated the whole. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | Re-read pp. 78, 81 and 83: captured log books, unit lists, repair records and technical publications supplied serial numbers, as did inspections of captured equipment. Later intensive tank inspections are explicitly described. Preserve both documentary and physical routes.
- WRONG | [K4; body-24-1] [#58 body-24-1] At k = 15 it is exactly 17/3 = 5.667: the estimator that throws away everything but the maximum has under a sixth the mean-squared error of the one that averages all the evidence. | research/the-tanks-that-counted-themselves/verify.mjs | Duplicate of X3. Independently recomputed 3/17=17.647058823529413%, above 1/6=16.666666666666664%. The reciprocal comparison is false even though the displayed variance ratio is correct to its stated rounding.
- MINOR | [K5; panther-method] [#90 panther-method] from the road wheels of just two Panther tanks -- the wheels were cast in numbered moulds, and counting the moulds, then the wheels per mould, then the tanks -- the method estimated 270 Panthers built in February 1944. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | Re-read the complete analysis on pp. 82-83. The numbered moulds made rubber bogie-wheel tyres. British manufacturing experience and replacement allowances supported a rate of 270 tanks per month by February 1944, conditional on assembly at bogie-wheel production capacity. Recorded output was 276. Their relative difference is 100*6/276=2.1739130434782608%, rounded to 2.2%.
- MINOR | [K6; citation-panther] [#119 citation-panther] The Panther road-wheel example (≈270 estimated vs. 276 recorded for February 1944) and the postwar finding that Allied statistical estimates outperformed both intelligence estimates and Germany's own figures are as reported in the standard secondary accounts of Ruggles & Brodie's study. | https://www.math.kth.se/matstat/gru/sf1901/F/fo9sf1901new.pdf#page=69; https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | The contrary source evidence holds: slide 58 does report greater accuracy and timeliness than German estimates. The checker's no-source premise is rejected, as directed by the triage; the remaining attribution issue stays MINOR. Ruggles and Brodie use production records as their tank-validation benchmark. Same clarification as X7.
- MINOR | [K7; dek-0] [#129 dek-0] In 1940 the Allies needed to know how many tanks Germany was building, and the spies kept guessing four to eight times too high. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | Re-read pp. 72, 80 and 89. The 1940 information-need framing is not disproved, but the estimates and analysis came later: August 1942 intelligence figures and serial-number work beginning in early 1943. Align the hypothetical analyst to 1943 and distinguish the production dates. Same error as K1.
- MINOR | [K8; dek-2] [#131 dek-2] The trick is a single idea: the largest serial you have seen, plus the average gap between the ones you have, estimates the whole production almost exactly. | research/the-tanks-that-counted-themselves/verify.mjs | Duplicate of X8. The default estimator SD is sqrt(271), about 6.1% of N=270; the historical June 1940 row misses by 38.5%. The sampling assumptions support an estimate with uncertainty, not an almost-exact guarantee.

- CONFIRMED | After the war the German production ledgers were opened, and it was the statisticians, not the spies, who had been close. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | body-02-4: Primary abstract says "After the war official statistics on German war production became available"; p. 89 supplies the superior statistical comparisons.
- CONFIRMED | Somewhere in the Reich a factory is turning out tanks, each stamped at assembly with a serial number. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | body-03-1: Primary pp. 78-79 identify tank chassis and engine serial numbers, manufacturing dates and assemblers. The singular factory is part of the hypothetical setup, not a claim that all German tanks came from one plant.
- CONFIRMED | You will never see the factory, the ledger, or most of the tanks. | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | body-03-2: This describes the hypothetical analyst's limited information. Primary p. 78 documents partial information from captured records and machines; it cannot verify the literal future of a fictional analyst.
- CONFIRMED | What you will see, over the months, is a scatter of captured and knocked-out machines, and you can read the numbers off them. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | body-03-3: Primary p. 78 explicitly describes technical personnel "inspecting captured equipment" and tanks available for examination in England and the United States.
- CONFIRMED | From that handful of numbers you must estimate a quantity nobody on your side knows: how many were made. | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | body-03-4: The hypothetical task matches the documented purpose of estimating production from sampled markings; it is not independently evidence about everything every Allied person knew.
- CONFIRMED | Strip it to the model that makes it solvable. Suppose a month's tanks are numbered 1, 2, …, N with N unknown, and that the ones you observe are a fair sample of distinct serials drawn from that run. You see k of them; the largest is m. Estimate N. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | body-04: The multiple-factories paper p. 2 expressly assumes consecutive positive integers, a starting serial of 1 and equal capture probability. Distinct sampling is confirmed in its p. 6 proof.
- CONFIRMED | They are consecutive, assigned in order by the enemy's own bookkeeping, and that order is a gift. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | body-05-2: Read within the immediately preceding "Suppose" model. The primary historical source qualifies real numbering with bands and gaps; the page also states those qualifications in section VII.
- CONFIRMED | It means the serials you hold are spread through the whole run, and the spacing between them is itself a measurement. | https://pmc.ncbi.nlm.nih.gov/articles/PMC11147940/ | body-05-3: The gap interpretation is given in the PMC paper, including the gap before the smallest serial. It describes information under uniform sampling, not guaranteed even spacing in any single sample.
- CONFIRMED | The biggest number you have seen is your crudest guess [...] and it can never exceed the truth, so it always leans low. | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | body-08-2: Every sampled serial is at most N, so m <= N. Its expectation is strictly below N when k < N, and equals N for a census.
- CONFIRMED | The oxide marker adds one average gap past m to reach for the line you can't see; on a typical month it lands within a few percent of the teal truth. | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | body-08-3: At default N=270,k=15 the exact probability of relative error at most 5 percent is 0.6213225. That supports the ordinary "typical month" phrasing at this default, not a guarantee across settings.
- CONFIRMED | The blue marker [...] twice the average of all your serials [...] is also honest on average but jumps around far more, as the next instrument makes visible. | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | body-08-4: The actual estimator is 2*mean-1, named explicitly in section IV. The panel's short name is interpreted consistently with that displayed formula; it is unbiased and has the larger variance for 1 < k < N.
- CONFIRMED | The first instinct is to say: I have seen number 243, so there were at least 243; my best single guess is 243. | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | body-09-0: The generated worked sample has m=243 and N=270; every admissible N is at least the largest observed serial.
- CONFIRMED | This is, in fact, the maximum-likelihood estimate [...] the value of N under which your exact sample is most probable is N = m, because any larger N only spreads the probability thinner. | https://www.mjandrews.org/notes/germantank/ | body-09-1: The Andrews likelihood is maximized at N = max(x_1 ... x_n); for a fixed distinct sample its likelihood is proportional to 1/C(N,k).
- CONFIRMED | It is also obviously an underestimate, and not by a little. | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | body-09-2: For the specified worked sample the maximum is 243 against true N=270, an underestimate by 27. This sentence is not treated as a claim that every possible maximum is strictly below N.
- CONFIRMED | You did not happen to capture the very last tank off the line; the true maximum is almost certainly above the largest you saw. | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | body-09-3: The worked sample omits 270. In the default design P(m=N)=k/N=1/18; the page's usual-case statement is supported, with equality possible.
- CONFIRMED | The MLE can never exceed what you have observed, and the truth almost always does. | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | body-09-4: m equals the largest observation exactly; it cannot exceed it. At the default k/N only 1/18 of samples include the true maximum.
- CONFIRMED | E[max] = k · (N + 1) / (k + 1). | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_HigherDim.pdf | body-11: The higher-dimensional paper equation (3.3), printed p. 8, gives E[M_k]=k(N+1)/(k+1). The source record's locator p. 7 is incorrect for the fetched PDF.
- CONFIRMED | For N = 270, k = 15 that is 254.06 [...] so on average the largest serial you see falls about sixteen short of the truth. The bias is exactly | git show 67088387e0:research/the-tanks-that-counted-themselves/artifact.json | body-12: Independent exact arithmetic gives E[m]=4065/16=254.0625 and a shortfall of 15.9375; 254.06 is correct to two decimals.
- CONFIRMED | E[max] − N = −(N − k) / (k + 1) = −15.94 here, | git show 67088387e0:research/the-tanks-that-counted-themselves/artifact.json | body-13: Subtracting N gives -255/16=-15.9375, rounded to -15.94.
- CONFIRMED | The biggest number you've seen is a biased estimator, and we know the size and the sign of the lie: it always leans low, by about (N − k)/(k + 1). | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_HigherDim.pdf | body-14-1: Subtract N from the source's exact expectation: k(N+1)/(k+1)-N=-(N-k)/(k+1). Strict negative bias requires k<N.
- CONFIRMED | Reverse the bias formula. If the observed maximum runs low by a factor of k/(k+1), then scaling it back up and trimming the constant gives an estimator with the bias removed: | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_HigherDim.pdf | body-15: Equations (3.3)-(3.5) invert the expectation and substitute the observed maximum. The accompanying minus-one term supplies the constant correction.
- CONFIRMED | N̂ = m · (k + 1) / k − 1. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_HigherDim.pdf | body-16: Equation (3.5) in the higher-dimensional paper, printed p. 8, gives the displayed estimator.
- CONFIRMED | N̂ = m + (m − k) / k = (the largest serial) + (the average gap between serials). | https://pmc.ncbi.nlm.nih.gov/articles/PMC11147940/ | body-18: The PMC paper explicitly describes m(k)/k-1 as the average gap, including the gap preceding the minimum.
- CONFIRMED | You have seen k serials, the biggest being m; that means m − k of the numbers at or below m are ones you didn't see, spread as gaps among the k you did [...] an average gap of (m − k)/k. | https://pmc.ncbi.nlm.nih.gov/articles/PMC11147940/ | body-19-0: There are m-k unobserved integers at or below m, allocated over k gaps when the leading gap is included. The average is therefore (m-k)/k.
- CONFIRMED | The line you can see ends at m; the estimator adds one more average gap to reach for the line you can't. | https://pmc.ncbi.nlm.nih.gov/articles/PMC11147940/ | body-19-1: The PMC gap explanation supports extrapolating one average gap beyond the maximum under the uniform model.
- CONFIRMED | And crucially it is unbiased: average it over all possible samples and it lands exactly on N, with no systematic lean. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_HigherDim.pdf | body-19-3: Substitution of the exact expectation into m(k+1)/k-1 gives N. This also follows from the multiple-factories paper's MVUE theorem.
- CONFIRMED | The correction is not a fudge; it is the exact inverse of a known bias. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_HigherDim.pdf | body-19-5: The correction algebraically inverts the expectation formula. It is exact under the stated sampling assumptions.
- CONFIRMED | On the worked month [...] m = 243, average gap (243 − 15)/15 = 15.2 [...] that is N̂ = 243 + 15.2 = 258.2 against a truth of 270. | git show 67088387e0:research/the-tanks-that-counted-themselves/artifact.json | body-19-2: 243-15=228; 228/15=15.2; 243+15.2=258.2. The generated sample's true N is 270.
- CONFIRMED | This is the estimator the Allied analysts used | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt (pp. 82-83) | allied-estimator: Primary p. 82 describes a highest mould number of 77 and an average gap of about 3, yielding about 80 moulds. This supports the maximum-plus-gap method, not a claim that every wartime estimate used one undifferentiated tank-number sequence.
- CONFIRMED | the minimum-variance unbiased estimator of N [...] the provably best one of its kind. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | estimator-optimality: Multiple-factories paper Theorem 2.3 identifies the GTP estimator as the unique MVUE, and proves completeness and sufficiency of the maximum.
- CONFIRMED | That last claim is the subject of the next section, because "unbiased" alone is a much weaker virtue than it sounds, and the real reason this estimator won is hiding inside the word minimum-variance. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | body-20-1: The theorem establishes optimality among unbiased estimators. The next section correctly distinguishes unbiasedness from variance; the historical account does not itself prove a universal choice criterion for all Allied analysts.
- CONFIRMED | Here is a different unbiased estimator that looks more sophisticated [...] it uses all the data, not just the maximum. | https://aseemrb.me/blog/german-tank-problem/ | body-21-1: For a uniform population 1..N, twice the sample mean minus one is unbiased; the estimator uses every observed value. The formula in the following sentence specifies the minus-one correction.
- CONFIRMED | The sample mean of a run 1…N has expectation (N + 1)/2, so Ñ = 2 · (sample mean) − 1 is also exactly unbiased. | https://aseemrb.me/blog/german-tank-problem/ | body-21-2: The finite-population mean is (N+1)/2; linearity of expectation gives E[2*sampleMean-1]=N. Independently checked rather than relying only on the blog.
- CONFIRMED | On the worked month it gives 2 × 116.6 − 1 = 232.2 [...] further from the truth than the maximum-based estimate, and that is no accident. | git show 67088387e0:research/the-tanks-that-counted-themselves/artifact.json | body-21-4: The 15 serials sum to 1749, so their mean is 116.6 and 2*116.6-1=232.2. Errors are 37.8 versus 11.8 for the MVUE.
- CONFIRMED | The thing that separates a good estimator from a merely-unbiased one is its variance [...] how much it jumps around from sample to sample. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_HigherDim.pdf | body-22-0: Variance is expected squared deviation from an estimator's expectation. For unbiased estimators this is MSE about N; the local comparison is correct.
- CONFIRMED | The maximum-based MVUE has variance (N − k)(N + 1) / [k(k + 2)], which for the worked numbers is exactly 271, a standard deviation of 16.5. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_HigherDim.pdf | body-22-1: Higher-dimensional paper equation (4.5), printed p. 10, gives (N-k)(N+1)/(k(k+2)). At N=270,k=15 this is 271, with square root 16.4621. The record's p. 9 locator is wrong.
- CONFIRMED | The "twice the mean" estimator has, for sampling without replacement, the variance (N + 1)(N − k) / (3k) [...] here 1535.7, a standard deviation of 39.2. | https://aseemrb.me/blog/german-tank-problem/ | body-22-2: Finite-population arithmetic gives (271*255)/45=4607/3=1535.6667, with standard deviation 39.1876. The cited derivation states the same variance.
- CONFIRMED | which for the worked numbers is exactly 271, a standard deviation of 16.5. | git show 67088387e0:research/the-tanks-that-counted-themselves/artifact.json | worked-variance-values: Independent arithmetic confirms exactly 271 and a standard deviation of 16.5 after rounding to one decimal.
- CONFIRMED | Var(twice the mean) / Var(N̂) = (k + 2) / 3. | https://aseemrb.me/blog/german-tank-problem/ | body-23: Divide (N+1)(N-k)/(3k) by (N-k)(N+1)/(k(k+2)): the ratio is (k+2)/3 for k<N. At k=N both variances vanish.
- CONFIRMED | The ratio depends on nothing but k [...] not on N, not on how many tanks were built, only on how many you caught. | https://aseemrb.me/blog/german-tank-problem/ | body-24-0: The cancellation removes N for nondegenerate sampling. This is a ratio of population MSEs, not an exact ratio for each finite Monte Carlo run.
- CONFIRMED | The dark maximum curve sits visibly left of the teal truth line [...] biased low by exactly (N−k)/(k+1). | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | body-26-2: The exact expectation yields the stated bias. A finite run fluctuates around that expectation; the live readout labels its prediction separately.
- CONFIRMED | The oxide max + gap and the blue twice the mean are both centred on the truth [...] both unbiased [...] but the blue one is a low, wide smear and the oxide one a tall, tight spike. | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | body-26-3: Both corrected estimators are unbiased. Default variances are 271 and 1535.6667, so the concentration comparison is supported; finite runs fluctuate.
- CONFIRMED | Their mean-squared errors stand in the ratio (k+2)/3, recomputed exact above and confirmed by the run. | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | body-26-4: The exact ratio is 17/3 at k=15 and the deterministic 400000-trial experiment returns 5.65. The finite-run value is not claimed to equal the exact ratio digit for digit.
- CONFIRMED | One number [...] the largest serial, corrected [...] beats the average of all of them, and beats it badly. | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | body-26-5: The corrected maximum has lower MSE than twice-mean-minus-one whenever k>1 and k<N. At the demonstrated k=15 the advantage is a factor of 17/3.
- CONFIRMED | For a uniform run, the sample maximum is a sufficient statistic: it carries every drop of information the sample holds about N, and the other serials add nothing once you know the largest. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | body-27-1: The multiple-factories paper p. 6 explicitly proves that samples conditional on their maximum do not depend on N, establishing sufficiency.
- CONFIRMED | The mean, by contrast, throws away exactly the information that matters [...] the upper edge [...] and pays for it in variance. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | body-27-2: The sample mean is not sufficient in general; the higher-dimensional paper and independent finite-population arithmetic show its larger estimator variance for the default design.
- CONFIRMED | This is the quiet lesson the analysts were living: against a uniform run, the right move is not to average your evidence but to take its extreme and correct it. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | body-27-3: The maximum-plus-gap method is documented in primary p. 82, and its efficiency follows from the mathematical sources. This is the author's interpretation of that connection, not a verbatim historical statement.
- CONFIRMED | The biggest serial you have seen is almost the whole story; the average gap finishes it. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | body-27-4: The sufficient statistic is m for fixed k; the additive gap correction is an algebraic function of m and k. The informal summary is consistent with the derivation.
- CONFIRMED | Put a flat prior over every N ≥ m (every production figure at least as large as the biggest tank you saw is, a priori, equally plausible). | https://www.mjandrews.org/notes/germantank/ | body-29-0: Andrews assumes a uniform prior and has posterior support N>=m. The prior is improper; the posterior is proper for k>1 and has a finite mean for k>2, satisfied by the interface's k>=3.
- CONFIRMED | The likelihood of having drawn your particular sample given N is 1 / C(N, k) [...] one over the number of ways to choose k serials from N [...] so the posterior is proportional to 1/C(N, k), peaking at N = m and decaying as N grows past it. | https://www.mjandrews.org/notes/germantank/ | body-29-1: The Andrews posterior is proportional to inverse binomial coefficients on N>=m, which decrease strictly as N increases for k>0.
- CONFIRMED | E[N &#124; m, k] = (m − 1)(k − 1) / (k − 2), | https://epub.ub.uni-muenchen.de/2094/1/paper_499.pdf | body-30: Hohle and Held equation (5), printed p. 4, gives this mean for sample size greater than 2. The page's allowed sample sizes meet that condition.
- CONFIRMED | which for the worked month gives 260.6. | git show 67088387e0:research/the-tanks-that-counted-themselves/artifact.json | body-31-0: Exact arithmetic gives 3388/13=260.6153846, rounded to 260.6.
- CONFIRMED | The frequentist's 258.2 and the Bayesian's 260.6 sit within a percent of each other, both a little under the true 270. | git show 67088387e0:research/the-tanks-that-counted-themselves/artifact.json | body-31-1: The difference 2.4153846 is under one percent of either estimate and of N=270. Both values are below 270.
- CONFIRMED | The curve is the plausibility of each possible production figure N given your serials; it can't drop below the largest tank you saw (left edge = m) and falls off like N−k above it. | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | body-33-2: The posterior is zero for N<m and proportional to 1/C(N,k), asymptotically a constant times N^(-k). The UI note's exponent is confirmed in the original HTML markup.
- CONFIRMED | After 1945 the Allies recovered the production ledgers of the Reich's war economy, and could finally mark their wartime guesses against the truth. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | body-34-2: Primary p. 72 explicitly reports official German statistics becoming available after the war. It supports the postwar comparison, but does not establish a precise archive-recovery day.
- CONFIRMED | The serial-number statisticians [...] their method written up in 1947 by Richard Ruggles and Henry Brodie in the Journal of the American Statistical Association [...] turned out to have been startlingly close, where conventional intelligence had been wildly, consistently high. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | body-34-3: The primary title page names Richard Ruggles and Henry Brodie and March 1947; p. 89 gives the tank comparison against combined American and British intelligence estimates.
- CONFIRMED | Across these months the statistical estimate missed by about a fifth; the intelligence estimate overshot by a multiple. | git show 67088387e0:research/the-tanks-that-counted-themselves/artifact.json | body-35-1: The three absolute statistical errors average 17.6242 percent, displayed as 17.6; intelligence/actual ratios average 6.1495, displayed as 6.1. "about a fifth" is reasonable.
- CONFIRMED | The clean model is an idealization the analysts had to earn. "Serials run 1…N, one tidy sequence, sampled uniformly" is the schoolbook version. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | body-37-0: The assumptions are explicit in the mathematical paper p. 2. Primary pp. 78-82 demonstrates why real manufacturing sequences needed reconstruction first.
- CONFIRMED | The real work was forensic: reconstruct how the enemy's bookkeeping actually assigned numbers, reconcile the part-series, and only then apply the estimator. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | body-37-2: Primary pp. 79-82 documents reconstructing bands, gaps, engine and gearbox systems and mould counts. The page fairly summarizes that forensic work.
- CONFIRMED | The formula is the easy half; figuring out what counts as N was the hard half. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | body-37-3: This is an interpretive summary supported by the primary source's detailed reconstruction problems, not a measured comparison of analyst hours.
- CONFIRMED | June 1940's statistical estimate (169) was 38.5% too high against the true 122 [...] a real, sizeable miss, left in the table rather than dropped. | https://web.archive.org/web/20170123132042id_/https://www.cia.gov/library/readingroom/docs/CIA-RDP79R01001A001300010013-3.pdf | body-38-1: The scanned table gives 169 and 122. 100*(169-122)/122=38.5245902 percent, displayed as 38.5.
- CONFIRMED | The honest claim is not "the statistics were always nearly exact" but "the statistics were systematically far closer than intelligence, in every month, often within tens." That is a strong claim and a true one; the stronger claim would be false. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | body-38-2: Within the three displayed rows, absolute statistical errors are 47,27,15 versus intelligence errors 878,1279,1208. The sentence is scoped to the presented table, not every historical estimate in the paper.
- CONFIRMED | "twice the mean" is unbiased too. | https://aseemrb.me/blog/german-tank-problem/ | twice-mean-repeated: Read together with section IV's explicit definition, "twice the mean" names 2*mean-1; that estimator is unbiased under the stated model.
- CONFIRMED | It won for having a fraction of the variance [...] exactly (k+2)/3 less [...] because the sample maximum is sufficient and the mean is not. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | body-39-2: The intended multiplicative variance advantage is (k+2)/3, established by the two variance formulas. Read with the explicit ratio in section IV; it is not an additive subtraction from a variance.
- CONFIRMED | Consecutive, centrally assigned numbering is what makes the largest serial informative. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | body-40-1: Consecutive recoverable serial ranges make the maximum informative. Multiple-factories p. 3 discusses the need to know or estimate the range's minimum; the page already acknowledges segmented real systems.
- CONFIRMED | An adversary who randomized serials, or restarted numbering per factory without a recoverable scheme, or simply stopped stamping sequential numbers, would blunt the method badly. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | body-40-2: Unknown ranges and arbitrary labels invalidate the simple 1..N estimator without further information. The multiple-factories treatment shows that recoverable factory structure can restore inference, matching the qualification here.
- CONFIRMED | The technique reads the enemy's administrative order; against disorder it has far less to read. | https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | body-40-3: This is an interpretive summary of the model's dependence on a reconstructible numbering system, consistent with the multiple-factories paper.
- CONFIRMED | And the line under all of it: the question "how many were built?" looks unanswerable from a handful of captured machines, and is not, because the enemy wrote the answer on every tank without knowing it. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | closing-0: Primary serial-number investigations demonstrate that sampled markings can reveal aggregate output after numbering systems are reconstructed. This is an interpretive summary, not a literal count printed on every tank.
- CONFIRMED | The serial number is administrative exhaust [...] a clerk's tracking mark [...] and it turned out to carry, in the spacing between the few you could catch, the size of the whole. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | closing-1: Primary pp. 73-74 states production-control and spare-parts purposes and explains that analysis furnished intelligence about German industry. The page's inference is supported.
- CONFIRMED | The deepest moat of a real-world statistic is that it reads a signal the adversary did not know he was sending. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | closing-2: An authorial generalization about the lesson, not an empirical universal ranking of all statistics. Primary pp. 73-74 documents the unexpected intelligence use in this case.
- CONFIRMED | Ruggles, R. & Brodie, H. (1947). An Empirical Approach to Economic Intelligence in World War II. Journal of the American Statistical Association 42(237):72–91 [...] the wartime serial-number method and the production-comparison table. | https://pmc.ncbi.nlm.nih.gov/articles/PMC11147940/ | citation-ruggles: Primary title page and journal identification match the reference; PMC reference 44 and the online DOI check confirm 1947, volume 42, issue 237, pp. 72-91 and DOI 10.1080/01621459.1947.10501915.
- CONFIRMED | The minimum-variance unbiased estimator N̂ = m(k+1)/k − 1, its variance (N−k)(N+1)/[k(k+2)], and the Bayesian posterior mean (m−1)(k−1)/(k−2) are standard results in the theory of order statistics and point estimation; see any mathematical-statistics text under "German tank problem" / "estimating the maximum of a discrete uniform distribution." | https://epub.ub.uni-muenchen.de/2094/1/paper_499.pdf; https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_HigherDim.pdf; https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/GermanTankProblem_MultipleFactories_v42.pdf | citation-estimator: The three results are supported across Hohle-Held and the two Williams papers. The selected Hohle-Held excerpt alone gives the Bayesian mean and variance, not all three formulas claimed; no universal textbook-coverage claim is established.
- CONFIRMED | Postwar the German records were opened, and the statisticians had been right. | https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt | dek-3: Primary pp. 72 and 89 documents postwar checking and statistical estimates closer than conventional intelligence. "right" is read in the page's explicit approximate sense; its 38.5-percent miss is disclosed.
- CONFIRMED | Every figure recomputed and checked to the digit. | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | dek-5: The N2 run at 67088387e0 reproduced the default figures to displayed rounding and reproduced the pinned artifact byte for byte. This repair preserves all numerical results and adds the Panther assumption to the artifact. The check does not validate historical provenance or arbitrary edits to static prose; both limits are disclosed on the page.
- CONFIRMED | The estimate is the largest serial you have seen plus the average gap between the ones you have. | https://pmc.ncbi.nlm.nih.gov/articles/PMC11147940/ | plain-1: The gap formula is correct when the initial gap is included, as the PMC source explicitly requires.
- CONFIRMED | mean &#124;statistical error&#124; 17.6% · mean intelligence overshoot 6.1× | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | runtime-w-read: The actual script and independent arithmetic give mean absolute statistical error 17.6 percent and mean intelligence factor 6.1.
- CONFIRMED | ✓ E[max] = k(N+1)/(k+1) = 254.06 ; MLE bias −(N−k)/(k+1) = -15.94 | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | runtime-check-1: Independent exact arithmetic and actual script execution reproduce 254.06 and -15.94 after rounding.
- CONFIRMED | ✓ Var(N̂) = (N−k)(N+1)/[k(k+2)] = 271 (SD 16.5); Var(2·mean−1) = (N+1)(N−k)/(3k) = 1536 (SD 39.2) | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | runtime-check-2: 271 is exact; 1536 is 1535.6667 rounded to zero decimals by round(varTwice(N,k),0). This differs in precision, not value, from the prose's 1535.7.
- CONFIRMED | ✓ efficiency Var(twiceMean)/Var(N̂) = (k+2)/3 = 5.667× , independent of N | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | runtime-check-3: The code displays 5.667, the correctly rounded value of 17/3. N cancels for k<N.
- CONFIRMED | ✓ Bayesian posterior mean (m−1)(k−1)/(k−2) = 260.6 , within a percent of the frequentist 258.2 | git show 67088387e0:public/strata/the-tanks-that-counted-themselves/index.html | runtime-check-4: The actual script gives 260.6 and 258.2; their difference is under one percent at these defaults.
- CONFIRMED | The wartime record · Ruggles & Brodie 1947 Month Statistical Intelligence German records Stat. error Intel. overshoot June 1940 169 1,000 122 +38.5% 8.2× | https://web.archive.org/web/20170123132042id_/https://www.cia.gov/library/readingroom/docs/CIA-RDP79R01001A001300010013-3.pdf | runtime-table-0: Visually read the scanned table on printed p. 89: "June, 1940 169 1000 122". Error and overshoot recompute to +38.5 percent and 8.2.
- CONFIRMED | The wartime record · Ruggles & Brodie 1947 Month Statistical Intelligence German records Stat. error Intel. overshoot June 1941 244 1,550 271 -10% 5.7× | https://web.archive.org/web/20170123132042id_/https://www.cia.gov/library/readingroom/docs/CIA-RDP79R01001A001300010013-3.pdf | runtime-table-1: Visually read printed p. 89: "June, 1941 244 1550 271". OCR falsely returns 1660; the image and source record correctly give 1550. Error and factor round to -10 percent and 5.7.
- CONFIRMED | The wartime record · Ruggles & Brodie 1947 Month Statistical Intelligence German records Stat. error Intel. overshoot August 1942 327 1,550 342 -4.4% 4.5× | https://web.archive.org/web/20170123132042id_/https://www.cia.gov/library/readingroom/docs/CIA-RDP79R01001A001300010013-3.pdf | runtime-table-2: Visually read printed p. 89: "August, 1942 327 1550 342". OCR falsely returns 1660; the image gives 1550. Error and factor round to -4.4 percent and 4.5.
- CONFIRMED | N̂ = m + (m−k)/k | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | specimen-estimator: Algebra and the external mathematical papers confirm Nhat=m+(m-k)/k=m(k+1)/k-1.
- CONFIRMED | MLE bias = −(N−k)/(k+1) | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | specimen-bias: The exact expectation of the maximum gives the stated MLE bias, with zero bias at k=N.
- CONFIRMED | edge = (k+2)/3 | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | specimen-edge: The two variance formulas give the efficiency ratio (k+2)/3 for k<N.
- CONFIRMED | Ruggles & Brodie 1947 | https://pmc.ncbi.nlm.nih.gov/articles/PMC11147940/ | specimen-citation: The primary title page and bibliographic reference identify Ruggles and Brodie, 1947.
- CONFIRMED | The wartime record · Ruggles & Brodie 1947 Month Statistical Intelligence German records Stat. error Intel. overshoot June 1940 169 1,000 122 +38.5% 8.2× | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | runtime-error-columns-0: Recomputed the June 1940 row independently and in the script: +38.5 percent statistical error, 8.2 times actual production. Dates and source counts were also checked against the original image.
- CONFIRMED | The wartime record · Ruggles & Brodie 1947 Month Statistical Intelligence German records Stat. error Intel. overshoot June 1941 244 1,550 271 -10% 5.7× | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | runtime-error-columns-1: Recomputed June 1941: -9.9631 percent becomes -10 percent; 1550/271=5.7196 becomes 5.7. Source counts match the image.
- CONFIRMED | The wartime record · Ruggles & Brodie 1947 Month Statistical Intelligence German records Stat. error Intel. overshoot August 1942 327 1,550 342 -4.4% 4.5× | git show 67088387e0:research/the-tanks-that-counted-themselves/verify.mjs | runtime-error-columns-2: Recomputed August 1942: -4.3860 percent becomes -4.4 percent; 1550/342=4.5322 becomes 4.5. Source counts match the image.

## Findings

- [fixed] X1: Replaced the exclusive factory-tracking purpose with production tracing and spare-parts control. MINOR; recorded here without a public correction line.
- [fixed] X2: The first worked-month presentation now calls it simulated and states chosen N=270; the markdown summary and source comments agree. MINOR; no public correction line.
- [fixed] X3: Changed "under a sixth" to "under a fifth" and added the MSE Corrected line to the HTML and markdown. The valid formulas were retained. Shared correction with K4.
- [fixed] X4: The section now starts with the point estimate used so far, explicitly acknowledges frequentist confidence intervals with a source link, and introduces the posterior without the false contrast. Added the frequentist Corrected line to HTML and markdown.
- [fixed] X5: Preserved every word of the existing quoted sentence. Added an explanation immediately outside it: under the stated flat prior the interval contains about 97.5% posterior probability, not probability one. MINOR; no public correction line.
- [fixed] X6: The teal line now marks the simulation's chosen true N. The band, accessible description, live readout, markdown summary and verifier label identify the nominal 95% interval; the note names both discrete quantiles. MINOR; no public correction line.
- [fixed] X7: Named and linked Grandell and Koski's KTH slide 58, retaining its secondary claim about German estimates and separating that claim from the German records used for validation. MINOR; no public correction line. Shared with K6.
- [fixed] X8: The dek now promises estimation under the sampling assumptions, with uncertainty depending on how many serials are observed. MINOR; no public correction line. Shared with K8.
- [dated] X9: Set JSON-LD dateModified to 2026-10-14 for this content revision, retaining datePublished. The requested metadata exception permits no Updated line because the two Corrected lines already date the revision.
- [fixed] K1: Separated the production months from the August 1942 intelligence compilation and the serial-number work begun in early 1943. Kept the supported overshoot range. MINOR; no public correction line. Shared with K7.
- [fixed] K2: The opening now names prewar extrapolations and German order-of-battle equipment requirements. The markdown and verifier call the comparison column August 1942 Allied intelligence. MINOR; no public correction line.
- [fixed] K3: Added captured records alongside inspected tanks in the opening, frame, dek, plain summary, markdown body, meta description, JSON-LD description and verifier summary. Kept physical inspection. MINOR; no public correction line.
- [fixed] K4: Applied the same MSE repair as X3. One public Corrected line covers this duplicate finding; K4 remains a separate WRONG claim and fixed finding in this record.
- [fixed] K5: Specified rubber tyres and the assembly-capacity assumption throughout the Panther narrative, sources, summaries, inline check and verifier. Renamed the generated comparison to relDifferencePct and included the estimate assumption in its source data. Kept 270, 276 and the rounded 2.2%. MINOR; no public correction line.
- [fixed] K6: Applied the same named secondary attribution as X7. Rejected the checker's disproved source-absence premise, while fixing the attribution ambiguity at the triage's MINOR level. No public correction line.
- [fixed] K7: Applied the timeline clarification to the dek, frame and opening, and changed the hypothetical analyst's year from 1941 to 1943. MINOR; no public correction line. Shared with K1.
- [fixed] K8: Applied the same uncertainty qualification in the dek as X8. The supported variance formulas and historical rows remain. MINOR; no public correction line.

## Evidence and outcome

All 17 triage items are FIXED. None were rejected or left unaddressed. K6's earlier source-absence argument was rejected on contrary evidence, as the triage already directed; that does not reject K6's MINOR attribution repair.

The historical reread used Ruggles and Brodie pp. 72-74, 78, 80-83 and 89, downloaded as 55,344 bytes of OCR. Höhle and Held's 618,823-byte PDF supplied the frequentist interval and posterior formulas. Grandell and Koski's 1,076,835-byte PDF supplied the specific secondary attribution on slide 58 (PDF page 69). Total downloads were 1,751,002 bytes, with no bulk data or media. The original table's 1,550 entries were preserved: both checker records explicitly verified the scan and identified the OCR's 1,660 as a recognition error. No replacement historical counts were invented.

The MSE fraction 3/17 comes from the existing verified variance formulas. The added 97.5% posterior statement comes from exact arithmetic using Höhle and Held's tail formula: 1 - C(242,14)/C(313,14) = 0.9750264073212839. The 2.2% Panther difference remains 100*abs(270-276)/276 rounded to one decimal. The assumptions, sample size and historical qualifications are stated alongside those numbers.

The unchanged confirmations above come from [research/assay-line/cited-1014b/the-tanks-that-counted-themselves/N2-codex.md](/home/liam/aw-claude-assaying-boyle-1014/research/assay-line/cited-1014b/the-tanks-that-counted-themselves/N2-codex.md) and [research/assay-line/cited-1014b/the-tanks-that-counted-themselves/N2-claude.md](/home/liam/aw-claude-assaying-boyle-1014/research/assay-line/cited-1014b/the-tanks-that-counted-themselves/N2-claude.md); their source excerpts are in [research/assay-line/cited-1014b/the-tanks-that-counted-themselves/N1-sources.json](/home/liam/aw-claude-assaying-boyle-1014/research/assay-line/cited-1014b/the-tanks-that-counted-themselves/N1-sources.json). These are the existing Codex and Claude checks named in the by field; no additional agent was spawned during this repair.

## Public correction lines

Corrected 2026-10-14: This page said that at k = 15 the maximum-based estimator has under a sixth of the twice-the-mean estimator's mean-squared error. The fraction is 3/17, about 17.65%, which is greater than a sixth and less than a fifth (found by the assay line, 2026-10-14).

Corrected 2026-10-14: This page said, "A frequentist returns a single best estimate." Frequentist methods also provide confidence intervals (found by the assay line, 2026-10-14).

Each line is also appended to the markdown body with the prefix *Corrected 2026-10-14:*. No Updated line or MINOR correction line was added.

## Commands and validation

- `node research/the-tanks-that-counted-themselves/verify.mjs`: exit 0, 23/23 checks passed. This regenerated artifact.json from its source. All previous worked-example, exact-law, Monte Carlo, posterior and historical-table numeric values were compared with the saved baseline and are unchanged.
- `node scripts/check-claims-pass.mjs`: exit 1 solely for finding-format errors in the other layer's `assay/records/wisdom-of-crowds.md` (findings 14-19, 21-22 and 31-37). This layer was not reported as failing. As instructed, the other record was left untouched.
- `node --input-type=module` with the exported `checkRecord` from scripts/check-claims-pass.mjs: this layer's 107-claim record returned no errors. The same read-only check compiled the one inline executable script, parsed JSON-LD, verified both dates, required exactly two matching HTML/markdown correction lines above the placard, checked the preserved posterior quotation and absence of the replaced false wording, and compared source and published verifier bytes. Exit 0.
- `git diff --check -- src/content/strata/the-tanks-that-counted-themselves.md public/strata/the-tanks-that-counted-themselves/index.html research/the-tanks-that-counted-themselves/verify.mjs research/the-tanks-that-counted-themselves/artifact.json public/checks/research/the-tanks-that-counted-themselves/verify.mjs`: exit 0, no whitespace errors.
- `python3` exact arithmetic using `fractions.Fraction` and `math.comb`: 3/17 is above 1/6 and below 1/5; the posterior mass is 0.9750264073212839; the historical overshoot ratios are 8.19672131147541, 5.719557195571956 and 4.5321637426900585; the Panther percentage difference is 2.1739130434782608 before rounding. Exit 0.
- `python3` baseline comparison: no newly written U+2014 in any changed line or in this record; every existing numerical result is unchanged. Exit 0.
- `python3` with `urllib.request.urlopen`, bounded to 5,000,000 bytes per response, downloaded the three sources named above. `pdftotext -layout /tmp/tanks-assay-1014/hoehle-held.pdf /tmp/tanks-assay-1014/hoehle-held.txt` and `pdftotext -layout /tmp/tanks-assay-1014/kth.pdf /tmp/tanks-assay-1014/kth.txt` succeeded. Source rereads used scoped `rg` and `sed`. The web tool could not open the archive OCR; the bounded direct fetch succeeded. No media was rendered or re-encoded.
- Read-only authoring and baseline inspection used `pwd`, `rg --files`, scoped `rg`, `cat`, `sed`, `nl`, `git status --short`, `git ls-files`, `git diff`, and `git show 26148524b64 -- public/strata/the-tanks-that-counted-themselves/index.html`. No AGENTS.md was found at the applicable ancestor paths or in the repository scan. The initial `ls` confirmed that this claims record did not exist. An initial `python` command failed because that alias was absent; all subsequent Python work used `python3`.
- `/tmp/tanks-assay-1014/edit.py` applied asserted replacements only in this layer's authored HTML, markdown and verifier. `/tmp/tanks-assay-1014/record.py` wrote this requested record; `/tmp/tanks-assay-1014/report.py` appended this report. The published verifier was regenerated as a verbatim copy of research/the-tanks-that-counted-themselves/verify.mjs, matching scripts/publish-checks.mjs's documented copy rule, without invoking its corpus-wide writes.

## Not done

No triage item remains unaddressed. No other layer, shared component, shared manifest, scripts file, search output or media asset was edited. No site-wide build, installation, write-capable Git command, placard mutation, image/audio/film rendering, or deployment was run. No additional public correction was added for a MINOR finding. The metadata revision uses the explicitly requested exception.

The shared public/checks/manifest.json still records the old verifier byte count of 16,206. The updated layer verifier is 16500 bytes; its published copy is identical. Refreshing that shared manifest, and any shared publication/proof metadata, is left to the directing instance because this task explicitly forbids shared-file edits. The corpus-wide publisher was not run. Downloaded source files, extracted text and other scratch files were removed after the report was assembled.

## Edit report

Every changed existing-file hunk follows with its file:line location, original text and replacement. Line numbers in links refer to the final files; the old starting line is also given. U+2014 in old text is written as the literal escape `\u2014` so that the report obeys the no-em-dash instruction. No new text contains that character. The published verifier is generated from the authored verifier, and artifact.json is generated by the verifier; neither output was independently edited.

### [public/strata/the-tanks-that-counted-themselves/index.html:7](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:7)

Before (old line 7):

```text
<meta name="description" content="The German tank problem, made playable. In WWII the Allies estimated German tank production by reading the serial numbers off captured tanks, and beat their own spies by a wide margin. Draw a month of captured serials, watch three estimators race (the biggest number you've seen, the maximum plus the average gap, twice the average), see why the clever-looking one loses by an exact factor of (k+2)/3, read the Bayesian posterior and its interval, and recompute every figure (including the real 1947 wartime table) live in your browser." />
```

After:

```text
<meta name="description" content="The German tank problem, made playable. In WWII the Allies estimated German tank production by reading serial numbers in captured records and on inspected tanks, and beat their own spies by a wide margin. Draw a month of captured serials, watch three estimators race (the biggest number you've seen, the maximum plus the average gap, twice the average), see why the clever-looking one loses by an exact factor of (k+2)/3, read the Bayesian posterior and its interval, and recompute every figure (including the real 1947 wartime table) live in your browser." />
```

### [public/strata/the-tanks-that-counted-themselves/index.html:110](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:110)

Before (old line 110):

```text
    <script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","name":"The Tanks That Counted Themselves","headline":"The Tanks That Counted Themselves","description":"The German tank problem, made playable. In WWII the Allies estimated German tank production by reading the serial numbers off captured tanks \u2014 and beat their own spies by a wide margin. Draw a month of captured serials, watch three estimators race (the biggest number you've seen, the maximum plus the average gap, twice the average), see why the clever-looking one loses by an exact factor of (k+2)/3, read the Bayesian posterior and its interval, and recompute every figure \u2014 including the real 1947 wartime table \u2014 live in your browser.","url":"https://artwaste.land/strata/the-tanks-that-counted-themselves/","image":"https://artwaste.land/og/default.png","datePublished":"2026-06-19","dateModified":"2026-06-19","author":{"@type":"Organization","@id":"https://artwaste.land/#organization","name":"Artificial Wasteland","alternateName":["The Artificial Wasteland","artwaste.land"],"url":"https://artwaste.land/","logo":"https://artwaste.land/og/default.png","sameAs":["https://bsky.app/profile/artwaste.land"]},"publisher":{"@type":"Organization","@id":"https://artwaste.land/#organization","name":"Artificial Wasteland","alternateName":["The Artificial Wasteland","artwaste.land"],"url":"https://artwaste.land/","logo":"https://artwaste.land/og/default.png","sameAs":["https://bsky.app/profile/artwaste.land"]},"isPartOf":{"@type":"WebSite","@id":"https://artwaste.land/#website","name":"Artificial Wasteland"}}</script>
```

After:

```text
    <script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","name":"The Tanks That Counted Themselves","headline":"The Tanks That Counted Themselves","description":"The German tank problem, made playable. In WWII the Allies estimated German tank production by reading serial numbers in captured records and on inspected tanks, and beat their own spies by a wide margin. Draw a month of captured serials, watch three estimators race (the biggest number you've seen, the maximum plus the average gap, twice the average), see why the clever-looking one loses by an exact factor of (k+2)/3, read the Bayesian posterior and its interval, and recompute every figure (including the real 1947 wartime table) live in your browser.","url":"https://artwaste.land/strata/the-tanks-that-counted-themselves/","image":"https://artwaste.land/og/default.png","datePublished":"2026-06-19","dateModified":"2026-10-14","author":{"@type":"Organization","@id":"https://artwaste.land/#organization","name":"Artificial Wasteland","alternateName":["The Artificial Wasteland","artwaste.land"],"url":"https://artwaste.land/","logo":"https://artwaste.land/og/default.png","sameAs":["https://bsky.app/profile/artwaste.land"]},"publisher":{"@type":"Organization","@id":"https://artwaste.land/#organization","name":"Artificial Wasteland","alternateName":["The Artificial Wasteland","artwaste.land"],"url":"https://artwaste.land/","logo":"https://artwaste.land/og/default.png","sameAs":["https://bsky.app/profile/artwaste.land"]},"isPartOf":{"@type":"WebSite","@id":"https://artwaste.land/#website","name":"Artificial Wasteland"}}</script>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:117](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:117)

Before (old line 117):

```text
<!--aw-plain:start--><meta name="aw-plain" content="The German tank problem: in World War II the Allies estimated how many tanks Germany was building each month from the serial numbers on captured ones, and beat their own spies by a wide margin. The estimate is the largest serial you have seen plus the average gap between the ones you have. Draw a month of serials, race the estimators against the truth, and read the Bayesian posterior." /><!--aw-plain:end-->
```

After:

```text
<!--aw-plain:start--><meta name="aw-plain" content="The German tank problem: in World War II the Allies estimated how many tanks Germany was building each month from serial numbers in captured records and on inspected tanks, and beat their own spies by a wide margin. The estimate is the largest serial you have seen plus the average gap between the ones you have. Draw a month of serials, race the estimators against the truth, and read the Bayesian posterior." /><!--aw-plain:end-->
```

### [public/strata/the-tanks-that-counted-themselves/index.html:127](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:127)

Before (old line 127):

```text
  <p class="frame">In 1940 the Allies needed a number they could not see: how many tanks was Germany building each month? Their spies guessed four to eight times too high. A handful of statisticians read the serial numbers off the captured tanks \u2014 and were right.</p>
```

After:

```text
  <p class="frame">In 1940 the Allies needed a number they could not see: how many tanks was Germany building each month? The Allied intelligence figures compiled in August 1942 guessed four to eight times too high for the three months shown below. Beginning in early 1943, a handful of statisticians used serial numbers from captured records and inspected tanks to reconstruct earlier production, and came much closer.</p>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:131](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:131)

Before (old line 131):

```text
<p>In the summer of 1940 the Western Allies needed a number they could not see: how many tanks was Germany actually building each month? Their intelligence services, working from agent reports and captured documents, answered with figures that turned out to be four to eight times too high. A different answer came from a small group of economists and statisticians, who did not ask the spies anything. They read the serial numbers stamped on the tanks the army captured and destroyed \u2014 gearboxes, chassis, engines, the moulds that cast the road wheels \u2014 and from those numbers estimated the whole. After the war the German production ledgers were opened, and it was the statisticians, not the spies, who had been close. This layer is that method, worked end to end, with the real wartime figures recomputed beside it \u2014 and made playable, so you can draw a month of captured serials and watch the estimate land.</p>
```

After:

```text
<p>In 1940 the Western Allies needed a number they could not see: how many tanks was Germany actually building each month? Their intelligence services estimated aggregate production from prewar extrapolations and equipment requirements inferred from the German order of battle. The Allied figures compiled in August 1942, for the three production months shown below, turned out to be four to eight times too high. A different answer came from a small group of economists and statisticians who began their serial-number work in early 1943. They read serial numbers from captured records and inspected equipment: gearbox, chassis and engine numbers, plus mould numbers on rubber road-wheel tyres. From those numbers they reconstructed earlier production. After the war the German production ledgers were opened, and it was the statisticians, not the spies, who had been close. This layer is that method, worked end to end, with the real wartime figures recomputed beside it, and made playable, so you can draw a month of captured serials and watch the estimate land.</p>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:134](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:134)

Before (old line 134):

```text
<p>You are an Allied analyst in 1941. Somewhere in the Reich a factory is turning out tanks, each stamped at assembly with a serial number. You will never see the factory, the ledger, or most of the tanks. What you <em>will</em> see, over the months, is a scatter of captured and knocked-out machines, and you can read the numbers off them. From that handful of numbers you must estimate a quantity nobody on your side knows: how many were made.</p>
```

After:

```text
<p>You are an Allied analyst in 1943. Somewhere in the Reich a factory is turning out tanks, each stamped at assembly with a serial number. You will never see the factory, the ledger, or most of the tanks. What you <em>will</em> see, over the months, is a scatter of captured and knocked-out machines, and you can read the numbers off them. From that handful of numbers you must estimate a quantity nobody on your side knows: how many were made.</p>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:136](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:136)

Before (old line 136):

```text
<p>It sounds like there is nothing to work with \u2014 you have a few numbers and want the size of a set you have mostly never seen. But the numbers are not arbitrary. They are <em>consecutive</em>, assigned in order by the enemy's own bookkeeping, and that order is a gift. It means the serials you hold are spread through the whole run, and the spacing between them is itself a measurement. The serial number, meant only to track a part through a factory, quietly carries the size of the factory's output. The tanks count themselves.</p>
<p class="lead">Below is one captured month, the same one the argument follows: <strong>k = 15</strong> serials drawn from a run whose true size only the postwar ledgers would reveal. Draw a fresh month whenever you like, or change how many were built and how many you caught. Everything in the three instruments recomputes in your browser by the same formulas the offline verifier runs.</p>
```

After:

```text
<p>It sounds like there is nothing to work with: you have a few numbers and want the size of a set you have mostly never seen. But the numbers are not arbitrary. They are <em>consecutive</em>, assigned in order by the enemy's own bookkeeping, and that order is a gift. It means the serials you hold are spread through the whole run, and the spacing between them is itself a measurement. The serial number, meant to support production tracing and spare-parts control, quietly carries the size of the factory's output. The tanks count themselves.</p>
<p class="lead">Below is one simulated month, the same one the argument follows: <strong>k = 15</strong> serials drawn from a run whose true size we chose as <strong>N = 270</strong>. Draw a fresh month whenever you like, or change how many were built and how many you caught. Everything in the three instruments recomputes in your browser by the same formulas the offline verifier runs.</p>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:183](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:183)

Before (old line 183):

```text
<p>The ratio depends on <em>nothing but k</em> \u2014 not on N, not on how many tanks were built, only on how many you caught. At k = 15 it is exactly <strong>17/3 = 5.667</strong>: the estimator that throws away everything but the maximum has under a sixth the mean-squared error of the one that averages all the evidence. (The Monte-Carlo run lands on 5.65, the closed form's sampling shadow.) Drag the sample size below and watch the exact ratio move; it is one of those rare places where the messy-looking answer is a clean fraction.</p>
```

After:

```text
<p>The ratio depends on <em>nothing but k</em>, not on N, not on how many tanks were built, only on how many you caught. At k = 15 it is exactly <strong>17/3 = 5.667</strong>: the estimator that throws away everything but the maximum has under a fifth the mean-squared error of the one that averages all the evidence. (The Monte-Carlo run lands on 5.65, the closed form's sampling shadow.) Drag the sample size below and watch the exact ratio move; it is one of those rare places where the messy-looking answer is a clean fraction.</p>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:204](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:204)

Before (old line 204):

```text
<h2 id="v-the-bayesian-reads-it-the-same-way-and-hands-you-an-interv">V · The Bayesian reads it the same way, and hands you an interval</h2>
<p>A frequentist returns a single best estimate. A Bayesian returns the whole shape of what the data permit \u2014 and on this problem the two agree, which is itself a small reassurance that neither is doing something strange.</p>
```

After:

```text
<h2 id="v-the-bayesian-reads-it-the-same-way-and-hands-you-an-interv">V · From a point estimate to a posterior</h2>
<p>So far we have used a frequentist point estimate. Frequentist methods also provide <a href="https://epub.ub.uni-muenchen.de/2094/1/paper_499.pdf#page=3">confidence intervals</a>. A Bayesian analysis gives a posterior distribution under a chosen prior; here its mean is close to the frequentist estimate.</p>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:208](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:208)

Before (old line 208):

```text
<p>which for the worked month gives <strong>260.6</strong>. The frequentist's 258.2 and the Bayesian's 260.6 sit within a percent of each other, both a little under the true 270. The Bayesian's bonus is the part a point estimate cannot give: a <strong>95% credible interval</strong>, read straight off the posterior \u2014 for the worked month, <strong>[243, 313]</strong>, with the truth sitting comfortably inside. The data don't just say "about 260"; they say "almost surely between 243 and 313, and here is how the plausibility is distributed across that range." From fifteen serial numbers.</p>
```

After:

```text
<p>which for the worked month gives <strong>260.6</strong>. The frequentist's 258.2 and the Bayesian's 260.6 sit within a percent of each other, both a little under the true 270. The posterior also gives a <strong>nominal 95% credible interval</strong>, read straight off the posterior: for the worked month, <strong>[243, 313]</strong>, with the truth sitting comfortably inside. The data don't just say "about 260"; they say "almost surely between 243 and 313, and here is how the plausibility is distributed across that range." Here "almost surely" is informal: under the stated flat prior, [243, 313] contains about 97.5% posterior probability, not probability one. From fifteen serial numbers.</p>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:213](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:213)

Before (old line 213):

```text
  <canvas id="post" width="900" height="320" aria-label="The Bayesian posterior probability over the true production N given the captured sample, with the posterior mean, the 95 percent credible interval shaded, and the true N marked."></canvas>
```

After:

```text
  <canvas id="post" width="900" height="320" aria-label="The Bayesian posterior probability over the true production N given the captured sample, with the posterior mean, the nominal 95 percent credible interval shaded, and the true N marked."></canvas>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:215](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:215)

Before (old line 215):

```text
  <div class="note"><b>This posterior is the current month in Instrument I.</b> Draw a new month up top and this reshapes. The curve is the plausibility of each possible production figure N given your serials; it can't drop below the largest tank you saw (left edge = m) and falls off like N<sup>−k</sup> above it. The shaded band is the central 95%; the gold line is the posterior mean; the teal line is the truth the ledgers later revealed. The interval is honest about its own width \u2014 catch fewer tanks and watch it yawn open.</div>
```

After:

```text
  <div class="note"><b>This posterior is the current month in Instrument I.</b> Draw a new month up top and this reshapes. The curve is the plausibility of each possible production figure N given your serials; it can't drop below the largest tank you saw (left edge = m) and falls off like N<sup>−k</sup> above it. The shaded band is the nominal 95% interval between the 2.5% and 97.5% discrete quantiles; the gold line is the posterior mean; the teal line is the simulation's chosen true N. The interval is honest about its own width: catch fewer tanks and watch it yawn open.</div>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:230](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:230)

Before (old line 230):

```text
  <div class="note"><b>Read the last two columns.</b> Across these months the statistical estimate missed by about a fifth; the intelligence estimate overshot by a <em>multiple</em>. The most-cited single case is sharper still: from the road wheels of just two Panther tanks \u2014 the wheels were cast in numbered moulds, and counting the moulds, then the wheels per mould, then the tanks \u2014 the method estimated <b>270</b> Panthers built in February 1944. The German records gave <b>276</b>: a miss of <b id="panther">2.2%</b>, from the wheels of two tanks.</div>
```

After:

```text
  <div class="note"><b>Read the last two columns.</b> Across these months the statistical estimate missed by about a fifth; the intelligence estimate overshot by a <em>multiple</em>. The Panther case is sharper still: the rubber road-wheel tyres of two tanks bore numbered mould markings. From those markings, British production-capacity experience and an allowance for replacement tyres, the analysts estimated an assembly rate of <b>270</b> Panthers per month by February 1944, assuming assembly at bogie-wheel production capacity. The German records gave <b>276</b> built that month: the conditional estimate differs from recorded output by <b id="panther">2.2%</b>.</div>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:237](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:237)

Before (old line 237):

```text
<li><strong>The clean model is an idealization the analysts had to earn.</strong> "Serials run 1…N, one tidy sequence, sampled uniformly" is the schoolbook version. Reality was messier: German production authorities handed manufacturers <em>blocks</em> of serial numbers (often in hundreds), filled them incompletely, and stamped <em>several</em> independent number-series on each tank \u2014 chassis, engine, gearbox, the road-wheel moulds \u2014 each with its own range. The real work was forensic: reconstruct how the enemy's bookkeeping actually assigned numbers, reconcile the part-series, and only then apply the estimator. The formula is the easy half; figuring out <em>what counts as N</em> was the hard half.</li>
```

After:

```text
<li><strong>The clean model is an idealization the analysts had to earn.</strong> "Serials run 1…N, one tidy sequence, sampled uniformly" is the schoolbook version. Reality was messier: German production authorities handed manufacturers <em>blocks</em> of serial numbers (often in hundreds), filled them incompletely, and stamped <em>several</em> independent number-series on each tank (chassis, engine, gearbox and road-wheel tyre mould numbers), each with its own range. The real work was forensic: reconstruct how the enemy's bookkeeping actually assigned numbers, reconcile the part-series, and only then apply the estimator. The formula is the easy half; figuring out <em>what counts as N</em> was the hard half.</li>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:241](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:241)

Before (old line 241):

```text
<li><strong>The history here is cited, not recomputed.</strong> The 1947 production table and the Panther road-wheel figures are reported from the literature; the page stores them and computes only the error percentages. What it <em>does</em> recompute from scratch \u2014 the bias of the maximum, the unbiasedness and variance of the MVUE, its exact (k+2)/3 edge over the mean estimator, the Bayesian posterior and its interval \u2014 runs on synthetic months whose true N it controls, so no claim about the <em>model</em> rests on getting a historical transcription right. The two kinds of fact are kept apart on purpose.</li>
```

After:

```text
<li><strong>The history here is cited, not recomputed.</strong> The 1947 production table and the conditional Panther tyre-mould estimate and recorded output are reported from the literature; the page stores them and computes only their percentage differences. What it <em>does</em> recompute from scratch (the bias of the maximum, the unbiasedness and variance of the MVUE, its exact (k+2)/3 edge over the mean estimator, the Bayesian posterior and its interval) runs on synthetic months whose true N it controls, so no claim about the <em>model</em> rests on getting a historical transcription right. The two kinds of fact are kept apart on purpose.</li>
```

### [public/strata/the-tanks-that-counted-themselves/index.html:257](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:257)

Before (old line 257):

```text
<b>The Panther road-wheel example</b> (≈270 estimated vs. 276 recorded for February 1944) and the postwar finding that Allied statistical estimates outperformed both intelligence estimates and Germany's own figures are as reported in the standard secondary accounts of Ruggles &amp; Brodie's study.
```

After:

```text
<b>The Panther tyre-mould example</b> is in <a href="https://archive.org/download/CIA-RDP79R01001A001300010013-3/CIA-RDP79R01001A001300010013-3_djvu.txt">Ruggles &amp; Brodie, pp. 82-83</a>: 270 per month estimated assuming assembly at bogie-wheel production capacity, against 276 recorded for February 1944. Their tank comparison on p. 89 uses German production records as its benchmark and shows the statistical estimates closer than the Allied intelligence estimates. <a href="https://www.math.kth.se/matstat/gru/sf1901/F/fo9sf1901new.pdf#page=69">Grandell &amp; Koski, KTH lecture 9, slide 58 (2016)</a>, separately report that the statistical estimates were more accurate and timely than Germany's own estimates. That is the secondary account's claim about estimates, distinct from the recorded output used to check them.
```

### [public/strata/the-tanks-that-counted-themselves/index.html:275](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:275)

Before (old line 275):

```text
// the worked month the prose narrates: k=15 serials from a run of N=270, largest m=243
```

After:

```text
// the simulated worked month: k=15 serials from a chosen run of N=270, largest m=243
```

### [public/strata/the-tanks-that-counted-themselves/index.html:552](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:552)

Before (old line 552):

```text
      `<span class="k">95% credible interval</span> <span class="bayes">[${post.lo}, ${post.hi}]</span> ` +
```

After:

```text
      `<span class="k">nominal 95% credible interval</span> <span class="bayes">[${post.lo}, ${post.hi}]</span> ` +
```

### [public/strata/the-tanks-that-counted-themselves/index.html:595](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:595)

Before (old line 595):

```text
  ok(`Panther road wheels: 270 estimated vs 276 recorded \u2014 <b>${round(100 * 6 / 276, 1)}%</b> miss`);
```

After:

```text
  ok(`Panther tyre moulds: 270 per month assuming assembly at bogie-wheel production capacity vs 276 recorded; <b>${round(100 * 6 / 276, 1)}%</b> difference`);
```

### [public/strata/the-tanks-that-counted-themselves/index.html:599](/home/liam/aw-claude-assaying-boyle-1014/public/strata/the-tanks-that-counted-themselves/index.html:599)

Before (old line 599):

Not present.

After:

```text
<section class="prose" aria-labelledby="corrections" style="max-width:44rem;margin:2.4rem auto 0;padding:0 1rem">
<h2 id="corrections">Corrections</h2>
<p>Corrected 2026-10-14: This page said that at k = 15 the maximum-based estimator has under a sixth of the twice-the-mean estimator's mean-squared error. The fraction is 3/17, about 17.65%, which is greater than a sixth and less than a fifth (found by the assay line, 2026-10-14).</p>
<p>Corrected 2026-10-14: This page said, "A frequentist returns a single best estimate." Frequentist methods also provide confidence intervals (found by the assay line, 2026-10-14).</p>
</section>
```

### [src/content/strata/the-tanks-that-counted-themselves.md:4](/home/liam/aw-claude-assaying-boyle-1014/src/content/strata/the-tanks-that-counted-themselves.md:4)

Before (old line 4):

```text
dek: "In 1940 the Allies needed to know how many tanks Germany was building, and the spies kept guessing four to eight times too high. A handful of statisticians answered the question better, by reading the serial numbers stamped on the tanks they captured. The trick is a single idea: the largest serial you have seen, plus the average gap between the ones you have, estimates the whole production almost exactly. Postwar the German records were opened, and the statisticians had been right. Draw a month of captured serials and watch the estimate land; race the estimators; read the posterior. Every figure recomputed and checked to the digit."
plain: "The German tank problem: in World War II the Allies estimated how many tanks Germany was building each month from the serial numbers on captured ones, and beat their own spies by a wide margin. The estimate is the largest serial you have seen plus the average gap between the ones you have. Draw a month of serials, race the estimators against the truth, and read the Bayesian posterior."
```

After:

```text
dek: "In 1940 the Allies needed to know how many tanks Germany was building. Allied intelligence figures compiled in August 1942 ran four to eight times too high for the three months shown here. Starting in early 1943, a handful of statisticians reconstructed earlier production more closely from serial numbers in captured records and on inspected tanks. The trick is a single idea: the largest serial you have seen, plus the average gap between the ones you have, estimates the whole production under the sampling assumptions, with uncertainty that depends on how many you catch. Postwar the German records were opened, and the statisticians had been right. Draw a month of captured serials and watch the estimate land; race the estimators; read the posterior. Every figure recomputed and checked to the digit."
plain: "The German tank problem: in World War II the Allies estimated how many tanks Germany was building each month from serial numbers in captured records and on inspected tanks, and beat their own spies by a wide margin. The estimate is the largest serial you have seen plus the average gap between the ones you have. Draw a month of serials, race the estimators against the truth, and read the Bayesian posterior."
```

### [src/content/strata/the-tanks-that-counted-themselves.md:26](/home/liam/aw-claude-assaying-boyle-1014/src/content/strata/the-tanks-that-counted-themselves.md:26)

Before (old line 26):

```text
German monthly tank production from the serial numbers stamped on captured and
destroyed tanks \u2014 and beat their own intelligence services by a wide margin. The
```

After:

```text
German monthly tank production from serial numbers in captured records and on
inspected tanks, and beat their own intelligence services by a wide margin. The
```

### [src/content/strata/the-tanks-that-counted-themselves.md:32](/home/liam/aw-claude-assaying-boyle-1014/src/content/strata/the-tanks-that-counted-themselves.md:32)

Before (old line 32):

```text
- **I · Read the serials.** A number-line that draws a month of captured serials
  (defaulting to the worked example the prose narrates \u2014 k = 15 from a run of 270,
```

After:

```text
- **I · Read the serials.** A number-line that draws a simulated month of captured serials
  (defaulting to the worked example the prose narrates: k = 15 from a chosen run of 270,
```

### [src/content/strata/the-tanks-that-counted-themselves.md:46](/home/liam/aw-claude-assaying-boyle-1014/src/content/strata/the-tanks-that-counted-themselves.md:46)

Before (old line 46):

```text
  `(m−1)(k−1)/(k−2)`, the 95% credible interval shaded, and the truth marked
```

After:

```text
  `(m−1)(k−1)/(k−2)`, the nominal 95% credible interval shaded, and the truth marked
```

### [src/content/strata/the-tanks-that-counted-themselves.md:50](/home/liam/aw-claude-assaying-boyle-1014/src/content/strata/the-tanks-that-counted-themselves.md:50)

Before (old line 50):

```text
(statistical estimate vs. secret-intelligence estimate vs. the actual German
records, with the error columns recomputed live) and the Panther road-wheel pair
(≈270 estimated vs. 276 recorded). Those rows are **cited data**; only arithmetic
```

After:

```text
(statistical estimate vs. August 1942 Allied intelligence estimate vs. the actual German
records, with the error columns recomputed live) and the Panther tyre-mould pair
(270 per month estimated assuming assembly at bogie-wheel production capacity,
vs. 276 recorded in February 1944; a 2.2% relative difference). Those rows are **cited data**; only arithmetic
```

### [src/content/strata/the-tanks-that-counted-themselves.md:65](/home/liam/aw-claude-assaying-boyle-1014/src/content/strata/the-tanks-that-counted-themselves.md:65)

Before (old line 64):

Not present.

After:

```text

*Corrected 2026-10-14:* This page said that at k = 15 the maximum-based estimator has under a sixth of the twice-the-mean estimator's mean-squared error. The fraction is 3/17, about 17.65%, which is greater than a sixth and less than a fifth (found by the assay line, 2026-10-14).

*Corrected 2026-10-14:* This page said, "A frequentist returns a single best estimate." Frequentist methods also provide confidence intervals (found by the assay line, 2026-10-14).
```

### [research/the-tanks-that-counted-themselves/verify.mjs:7](/home/liam/aw-claude-assaying-boyle-1014/research/the-tanks-that-counted-themselves/verify.mjs:7)

Before (old line 7):

```text
// production from the serial numbers stamped on captured and destroyed tanks.
```

After:

```text
// production from serial numbers in captured records and on inspected tanks.
```

### [research/the-tanks-that-counted-themselves/verify.mjs:24](/home/liam/aw-claude-assaying-boyle-1014/research/the-tanks-that-counted-themselves/verify.mjs:24)

Before (old line 24):

```text
// (1947) monthly-production table \u2014 statistical estimate vs. secret-intelligence
// estimate vs. the actual German records \u2014 recomputing how far each method missed.
// Those three rows and the Panther road-wheel pair (270 estimated / 276 actual)
```

After:

```text
// (1947) monthly-production table: statistical estimate vs. August 1942 Allied
// intelligence estimate vs. the actual German records, recomputing each difference.
// Those three rows and the conditional Panther tyre-mould pair (270 / 276)
```

### [research/the-tanks-that-counted-themselves/verify.mjs:94](/home/liam/aw-claude-assaying-boyle-1014/research/the-tanks-that-counted-themselves/verify.mjs:94)

Before (old line 94):

```text
// One month, N tanks produced, numbered 1..N. The Allies log k serials.
```

After:

```text
// One simulated month: choose N tanks numbered 1..N, then draw k serials.
```

### [research/the-tanks-that-counted-themselves/verify.mjs:232](/home/liam/aw-claude-assaying-boyle-1014/research/the-tanks-that-counted-themselves/verify.mjs:232)

Before (old line 232):

```text
  // a 95% credible interval (lower 2.5%, upper 97.5%) from the running CDF
```

After:

```text
  // a nominal 95% credible interval from the 2.5% and 97.5% discrete quantiles
```

### [research/the-tanks-that-counted-themselves/verify.mjs:241](/home/liam/aw-claude-assaying-boyle-1014/research/the-tanks-that-counted-themselves/verify.mjs:241)

Before (old line 241):

```text
  check(`Bayesian 95% credible interval [${BAYES.credible95[0]}, ${BAYES.credible95[1]}] contains the truth ${N0}`,
```

After:

```text
  check(`Bayesian nominal 95% credible interval [${BAYES.credible95[0]}, ${BAYES.credible95[1]}] contains the truth ${N0}`,
```

### [research/the-tanks-that-counted-themselves/verify.mjs:275](/home/liam/aw-claude-assaying-boyle-1014/research/the-tanks-that-counted-themselves/verify.mjs:275)

Before (old line 275):

```text
// Panther road-wheel pair (cited): 270 estimated / 276 actual, Feb 1944.
const PANTHER = { month: "February 1944", estimated: 270, actual: 276 };
PANTHER.relErrorPct = round(100 * Math.abs(PANTHER.estimated - PANTHER.actual) / PANTHER.actual, 1);
check(`Panther road-wheel estimate 270 vs actual 276 \u2014 within ${PANTHER.relErrorPct}% (cited pair)`, PANTHER.relErrorPct < 3);
```

After:

```text
// Panther tyre-mould pair (cited, Ruggles and Brodie pp. 82-83).
// 270 per month assumes tank assembly at bogie-wheel production capacity,
// with replacement use allowed for; 276 is recorded output in February 1944.
const PANTHER = {
  month: "February 1944", estimated: 270, actual: 276,
  estimateAssumption: "tank assembly at bogie-wheel production capacity, with replacement use allowed for",
};
PANTHER.relDifferencePct = round(100 * Math.abs(PANTHER.estimated - PANTHER.actual) / PANTHER.actual, 1);
check(`Panther conditional capacity estimate 270 vs recorded output 276: ${PANTHER.relDifferencePct}% difference (cited pair)`, PANTHER.relDifferencePct < 3);
```

### [research/the-tanks-that-counted-themselves/artifact.json:106](/home/liam/aw-claude-assaying-boyle-1014/research/the-tanks-that-counted-themselves/artifact.json:106)

Before (old line 106):

```text
      "relErrorPct": 2.2
```

After:

```text
      "estimateAssumption": "tank assembly at bogie-wheel production capacity, with replacement use allowed for",
      "relDifferencePct": 2.2
```

### [public/checks/research/the-tanks-that-counted-themselves/verify.mjs:7](/home/liam/aw-claude-assaying-boyle-1014/public/checks/research/the-tanks-that-counted-themselves/verify.mjs:7)

Before (old line 7):

```text
// production from the serial numbers stamped on captured and destroyed tanks.
```

After:

```text
// production from serial numbers in captured records and on inspected tanks.
```

### [public/checks/research/the-tanks-that-counted-themselves/verify.mjs:24](/home/liam/aw-claude-assaying-boyle-1014/public/checks/research/the-tanks-that-counted-themselves/verify.mjs:24)

Before (old line 24):

```text
// (1947) monthly-production table \u2014 statistical estimate vs. secret-intelligence
// estimate vs. the actual German records \u2014 recomputing how far each method missed.
// Those three rows and the Panther road-wheel pair (270 estimated / 276 actual)
```

After:

```text
// (1947) monthly-production table: statistical estimate vs. August 1942 Allied
// intelligence estimate vs. the actual German records, recomputing each difference.
// Those three rows and the conditional Panther tyre-mould pair (270 / 276)
```

### [public/checks/research/the-tanks-that-counted-themselves/verify.mjs:94](/home/liam/aw-claude-assaying-boyle-1014/public/checks/research/the-tanks-that-counted-themselves/verify.mjs:94)

Before (old line 94):

```text
// One month, N tanks produced, numbered 1..N. The Allies log k serials.
```

After:

```text
// One simulated month: choose N tanks numbered 1..N, then draw k serials.
```

### [public/checks/research/the-tanks-that-counted-themselves/verify.mjs:232](/home/liam/aw-claude-assaying-boyle-1014/public/checks/research/the-tanks-that-counted-themselves/verify.mjs:232)

Before (old line 232):

```text
  // a 95% credible interval (lower 2.5%, upper 97.5%) from the running CDF
```

After:

```text
  // a nominal 95% credible interval from the 2.5% and 97.5% discrete quantiles
```

### [public/checks/research/the-tanks-that-counted-themselves/verify.mjs:241](/home/liam/aw-claude-assaying-boyle-1014/public/checks/research/the-tanks-that-counted-themselves/verify.mjs:241)

Before (old line 241):

```text
  check(`Bayesian 95% credible interval [${BAYES.credible95[0]}, ${BAYES.credible95[1]}] contains the truth ${N0}`,
```

After:

```text
  check(`Bayesian nominal 95% credible interval [${BAYES.credible95[0]}, ${BAYES.credible95[1]}] contains the truth ${N0}`,
```

### [public/checks/research/the-tanks-that-counted-themselves/verify.mjs:275](/home/liam/aw-claude-assaying-boyle-1014/public/checks/research/the-tanks-that-counted-themselves/verify.mjs:275)

Before (old line 275):

```text
// Panther road-wheel pair (cited): 270 estimated / 276 actual, Feb 1944.
const PANTHER = { month: "February 1944", estimated: 270, actual: 276 };
PANTHER.relErrorPct = round(100 * Math.abs(PANTHER.estimated - PANTHER.actual) / PANTHER.actual, 1);
check(`Panther road-wheel estimate 270 vs actual 276 \u2014 within ${PANTHER.relErrorPct}% (cited pair)`, PANTHER.relErrorPct < 3);
```

After:

```text
// Panther tyre-mould pair (cited, Ruggles and Brodie pp. 82-83).
// 270 per month assumes tank assembly at bogie-wheel production capacity,
// with replacement use allowed for; 276 is recorded output in February 1944.
const PANTHER = {
  month: "February 1944", estimated: 270, actual: 276,
  estimateAssumption: "tank assembly at bogie-wheel production capacity, with replacement use allowed for",
};
PANTHER.relDifferencePct = round(100 * Math.abs(PANTHER.estimated - PANTHER.actual) / PANTHER.actual, 1);
check(`Panther conditional capacity estimate 270 vs recorded output 276: ${PANTHER.relDifferencePct}% difference (cited pair)`, PANTHER.relDifferencePct < 3);
```

### [assay/records/the-tanks-that-counted-themselves.md:1](/home/liam/aw-claude-assaying-boyle-1014/assay/records/the-tanks-that-counted-themselves.md:1)

Before: no file.

After: the requested dated assay record, with the exact by field, 17 triage claim lines, 90 retained joint CONFIRMED claims, one disposition per triage item, source calculations, the two exact public correction lines, commands and results, shared-file exclusions and this complete before/after report. The record counts 3 WRONG plus 13 MINOR in wrong: 16, 90 CONFIRMED, and 1 STALE, for checked: 107. All triage outcomes are FIXED; the single STALE finding is [dated] under the metadata exception.