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      lex: "The download and derivation are shared with claim ch03-18 (../thompson1917-ch03-18/fetch.py; fetch.py here delegates to it): per species a preliminary OLS of log10 W on log10 L drops 258 fish with |residual| > 0.5 (pre-registered), then fish are binned per species x quarter x 1-cm length class with n, sum and sum of squares of log10 W (derived/ns_ibts_lw_bins.csv). analysis.py keeps taxa with >= 500 fish and a 97.5th/2.5th percentile length ratio >= 3 (20 taxa: 12 teleosts, 5 elasmobranchs, 3 scyphozoan jellyfish), fits log10 W = a + b1 x + b2 x^2 (x = log10 L) by weighted least squares on class means (exact individual-level OLS since all fish in a class share L), tests it against the cube law (b1 = 3, b2 = 0) by F-test, and computes the ratio of fitted k = W/L^3 between its maximum and minimum over the 2.5-97.5 percentile length range; \'variable k\' = P < 0.001 and ratio >= 1.10. Within-quarter fits and a fish-only count are reported as sensitivity checks; the plaice k profile by 1-cm class is the pre-registered secondary."
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      lex: "Measured: 0.7 fraction of eligible taxa (14 of 20) in which k = W/L^3 varies by >= 10% across the growing range and the cube law is rejected at P < 0.001 (n = 20, exactly at the pre-registered 70% threshold; fish only (17 taxa, jellyfish excluded): 11/17 = 0.647; within-quarter fits: 21 of 30 variable). Interpretation: The first half of the claim (W = k L^3 for an animal of fixed form and density) is geometry and is not tested. The empirical content is Thompson\'s expectation that k \'is by no means constant\' while growth continues, because form keeps changing; the 10% threshold is the amount of k variation that would be clearly visible on his Fig. 21 (plaice k rises about 15% from small fish to the 30-cm maximum). Changes of k can also come from density, gut fullness or gonad state rather than shape (assessors\' caveat); the test cannot separate these, so a supporting result shows that k varies, not that form is the reason. Pooling years and quarters mixes seasonal condition cycles into the k-vs-length relation; the analysis therefore also reports results within each quarter as a robustness check (pre-registered, not part of the verdict). Length conversion: LngtCode \'1\' means LngtClass in cm; \'.\' or \'0\' means mm. A single probe request (NS-IBTS 2019 Q1 CA, HTTP status and first record only) was made before this pre-registration to confirm that the web service is reachable."
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      lex: "Pre-registered (claim refuted). At most 30% of eligible species have variable k (k is effectively constant across the growing range in most fishes, contrary to Thompson\'s expectation). Between 30% and 70% is \'mixed\'. If fewer than 10 species are eligible the verdict is \'inconclusive\' (data-unavailable)."
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      lex: "A varying k is consistent with, but does not demonstrate, a change of form: condition, gut fullness, gonad state and ontogenetic changes in density or fat content also change W at fixed L (assessors\' caveat). The test therefore addresses Thompson\'s empirical expectation that k will be found to vary, not his inference about form."
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      lex: "Eutrigla appears twice (species-level and genus-level records); neither set has variable k (the genus-level set is the only taxon in which the cube law is not even rejected), so merging them would give 14/19 = 0.74."
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      lex: "Lengths are 1-cm (or coarser) classes, weights are from survey scales at sea (whole-gram or coarser), sexes and years are pooled, and fish are treated as independent; the F-test P-values are therefore nominal. The 10% k-range threshold, not the P-value, is what separates taxa here."
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      lex: "The result sits exactly on the pre-registered threshold (14/20 = 70.0%), so the verdict is fragile: excluding the three jellyfish taxa (bell diameter is not a fish length, though they are \'other growing animals\' within the claim\'s scope) gives 11/17 = 65% and the verdict would be \'mixed\'. The robust findings are weaker than the verdict label: the cube law is rejected statistically in 19 of 20 taxa (huge samples make any departure significant), the median exponent b is 3.07 (range 2.35-3.38), but only 9 of 20 taxa have |b - 3| > 0.1, and k varies by >= 10% across the central 95% of lengths in 14. So k is \'by no means constant\' in a majority, but in a sizeable minority of fishes (plaice, dab, grey gurnard, starry ray, starry smooth-hound) it is constant to within 5-10% across a 3-fold length range."
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