Published November 2, 2026
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The Fitted Cut: Paper #224's Completeness Magnitude, Fitted on the Clean Record — and Why It Lands on the Floor
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Description
Runs the fitted-Mc computation that paper #224 fenced off (Wave 9 sweep annex debt D-220-237-21), on the clean record established by Wave 9 packet #297 -- the deposited file was the correct USGS snapshot written twice; rebuilt from its ten yearly chunks, the clean catalog (10,330 M_L events, California 2014-2023) hashes to #224's printed SHA-256 exactly. Controls reproduce #224's prints at the fixed Mc = 3.0 (1.2445 +/- 0.0207, 1.1696 +/- 0.0181, 0.9914 +/- 0.0639; spread 0.2531) and #297's bin-width-corrected 1.4288. The primary KS-minimum fit returns Mc = 2.55 (bootstrap 2.56 +/- 0.09; 0.5% of resamples at or above 3.0). Cross-checks converge on the record's edge: MAXC returns 2.5, the download-floor bin itself; the Wiemer-Wyss goodness-of-fit test passes its bars only at the small-N end (R >= 95% first at 4.0, N = 139); EMR is unidentifiable across optimizer starts (Mc estimates 0.80 to 4.96) because the record's floor is a download cut, not a detection edge. At the fitted cut the estimators answer 0.9402 +/- 0.0099, 1.2029 +/- 0.0127, 1.0457 +/- 0.0467: the headline maximum-likelihood value moves by -0.3043 (14.7 times #224's printed error) while its own error halves, the spread persists at 0.2628 (5.63x), and the straddle of b = 1 survives with flipped anatomy -- the MLE is lowest at the fitted cut, extending #224's 2.5-floor incompleteness fingerprint to the fit. Verdict: on this record Mc can be fixed honestly (3.0, fenced) or fitted honestly (2.55, floor-bound), but not fitted into the working range. With #297's fine binning at the fitted cut the answer is 1.0417. Graded DERIVED-INDEPENDENT, mirroring #297: a fenced-off computation whose result moves the owing paper's headline by ~15 printed errors and reverses an ordering is a correction in kind.