Papers · William Alexander Aldred

One Scale, Two Tables: The Gas-Fraction Anatomy — Split by Composition, Read by Velocity, on SPARC

by William Alexander Aldred — Independent Researcher

Published November 1, 2026 · Zenodo · 10 pp · DOI: 10.5281/zenodo.23858302

Abstract

The Square left one phenomenon standing. One scale pays both tables' normalization, and the corrected slope refuses 4 by regime: about 3.5 to 3.6 at low V_f, about 3.2 to 3.3 at high V_f, for every form tested. Every split in that work was a split by velocity, because the registration split by velocity. This paper runs the split nobody registered: by what the galaxy is made of. The baryonic gas fraction f_gas = M_gas/M_b is computed for the matched 116 galaxies from SPARC's own main table (M_gas = 1.33 M_HI, M_star = 0.5 L[3.6]), the sample is cut at the frozen terciles of that variable (edges 0.185772 and 0.532701; bins of 39, 38, and 39), and the closure anatomy is read inside the bins. The verdict, under bands frozen before the run, is MIXED, and both halves of it print at full size. The level does not track composition. The frozen-line residual correlates with log f_gas at r = +0.200 for the McGaugh form and +0.288 for the standard form ν_1, and the correlation grows with a form's sharpness across the nine-form space, up to +0.380. Hold V_f fixed and it dies: the partial correlations are -0.016 and +0.051 for the two primary forms, and no form in the space exceeds |r_partial| = 0.146. Gas fraction and velocity are tied in this sample at corr(log f_gas, log V_f) = -0.787, and the level signal rides that tie. But the anatomy is not blind to composition either, so the null headline is barred by its own registered gates. Inside the gas-fraction terciles the corrected slope is not flat. The middle tercile sits at slope 3.969 to 4.011 for all nine forms, each within 0.14 widened standard errors of the identity's 4. The gas-poor tercile sits at 3.056 to 3.222, the gas-rich tercile at 3.453 to 3.556. That pattern carries its confound on its face: the gas-poor bin is 38 of 39 high-V_f galaxies and the gas-rich bin is 39 of 39 low-V_f galaxies, so the end bins read their regimes; the middle bin is the only mixed bin, and a joint fit over a mixed bin can tilt on geometry. The separation between the middle and gas-poor slopes is about two widened standard errors on the primary forms. No tracking, no blindness, no mechanism. The defect's level follows velocity through composition, and its slope, read by composition bins, is the regime structure seen from the side, plus one mixed-bin number this program does not yet own.

The result, in plain language

The Square left one phenomenon standing: one scale pays both tables’ normalization, and the corrected slope refuses 4 by regime — about 3.5 to 3.6 at low velocity, about 3.2 to 3.3 at high. Every split in that work was by velocity, because the registration split by velocity. This paper runs the split nobody registered: by composition, the baryonic gas fraction, computed for SPARC’s matched 116 galaxies and cut at terciles frozen before the run.

The verdict is MIXED, and both halves print in full. The level does not track composition: the frozen-line residual correlates with gas fraction at r = +0.200 (McGaugh form) and +0.288 (standard form), and hold velocity fixed and it dies — partial correlations −0.016 and +0.051, no form in the nine-form space above |r| = 0.146. Gas fraction and velocity are tied in this sample at −0.787, and the level signal rides that tie. But the anatomy is not blind to composition either: inside the terciles the corrected slope is not flat — the middle tercile sits at 3.969 to 4.011 for all nine forms, each within 0.14 widened standard errors of the identity’s 4, against 3.056 to 3.222 (gas-poor) and 3.453 to 3.556 (gas-rich). The confound prints on its face: the end bins read their velocity regimes — 38 of 39 gas-poor are high-velocity, 39 of 39 gas-rich are low — and the middle bin is the only mixed bin. No tracking, no blindness, no mechanism.

Program note

Cube Campaign Batch 1, target C-07 — the Closure Identity program’s first split by composition, after paper 82 and paper 83 split the defect by velocity. The tercile edges (0.185772 and 0.532701), the bands, and the verdict gates were frozen before the run; the paper’s numeral audit passes with zero unexplained. Its grades are printed on its face: the level signal is a costume (it dies when velocity is held), the slope anatomy is non-flat and non-monotonic, and the middle tercile’s sit at slope 4 is printed beside its own confound — a joint fit over the one mixed bin can tilt on geometry, and the program does not yet own that number. The vacuum catastrophe is not spent anywhere in this paper and stands NOT SOLVED in the main program.

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