Papers · William Alexander Aldred

One Scale, Two Skies: The Closure Identity on Early-Type Galaxies — the Kill Widens, the Normalization Still Pays

by William Alexander Aldred — Independent Researcher

Published October 31, 2026 · Zenodo · 8 pp · DOI: 10.5281/zenodo.23851572

Abstract

The Square ran the Closure Identity on SPARC's late-type galaxies and killed the algebraic one-scale class there: nine forms, no closure, matched set of 116. The same SPARC release ships a second sample the Square never touched — 16 early-type galaxies with published acceleration pairs and two-radius rotation decompositions. This paper builds the two reductions for that sample and runs the same test on it. The early-type analogue of V_f is V_obs at the outermost measured radius (assumed — these curves decline; no flat asymptote is in the tables and none is invented); the baryonic mass is the shipped component ledger, bulge plus disk. The verdict is KILL, and it fails earlier and harder than the late-type kill did. Lock 0 fails for all nine forms: the sample's two RAR reductions do not agree on one scale (ratios 0.513–0.666 against the [0.98, 1.02] band). Lock 2 fails for all nine forms: corrected slopes run 1.81–2.24 against the identity's 4, at z = -2.82 to -4.01, with intercept offsets of +4.10 to +5.08 dex, and no form replicates on any withheld half. One thing survives, and it is the same thing that survived on the late types: measured along the frozen line, the normalization pays — frozen-line means sit at +0.079 to +0.097 dex, inside the ±0.10 dex band, for every form in the space. The failure is a slope failure, again, and worse: where the late-type corrected slope refused 4 by regime (≈3.5–3.6 low, ≈3.2–3.3 high), the early-type slope sits near 2. The claim is sized to what was run: 16 early-type galaxies, 32 published RAR pairs, the named nine-form space, the Square's machinery. A closure here would have fenced the late-type kill to one system class. There is no closure. The kill widens to a second, independent class of galaxies — at the power this small sample carries, stated in §5 at full size.

The result, in plain language

The Square killed the one-scale class on disk galaxies. Fair question: does it live where the bulges rule? The same identity, run on SPARC’s early-type sample — 16 galaxies the Square never touched — doesn’t live there either. The corrected slope sits near 2, not 4, for all nine forms, and the sample’s own two tables can’t even agree on the scale.

One thing still pays on both skies: the normalization — frozen-line means inside ±0.10 dex for every form, on the second system class too.

Program note

Cube Campaign Batch 1, target C-05b — the Closure Identity carried to a second system class: SPARC’s early-type galaxies, untouched by the Square (papers 82–83, which ran on the disk sample). Its grades are printed on its face: measured on an independent second sample; the V_f analogue is graded ASSUMED; three deviations are disclosed — D1 (house-VM execution, the campaign’s standing deviation), D2 (an error floor applied to one galaxy, NGC4278), D3 (the registration’s baseline misprint, 0.25 → measured 0.401 dex, corrected by an erratum appended to the registration with the registered text unedited). The power caveat is printed at full size: a pass would have read as consistency, not closure; the kill rests on measured failures.

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