Papers · William Alexander Aldred

The Same Refusal on Someone Else's Sky: The Closure Identity's Frozen Numbers Meet the ALFALFA Sample

by William Alexander Aldred — Independent Researcher

Publicly deposited November 1, 2026 · Zenodo · 11 pp · DOI: 10.5281/zenodo.23864317

Abstract

The Closure Identity (papers #82 and #83) froze its numbers on SPARC: an intercept of 1.81598 set by the radial acceleration relation's own scale, g_† = 1.150831×10⁻¹⁰ m/s², and two regime bands for the corrected baryonic Tully–Fisher slope — 3.50–3.63 in the low-V_f half, 3.21–3.27 in the high-V_f half. Every one of those numbers was measured on one database, reduced by one pipeline. This paper takes the frozen numbers, unchanged, to a sample this program did not build: the 930 isolated galaxies of Bradford, Geha & van den Bosch (2016), an ALFALFA-based baryonic Tully–Fisher sample with a different selection, a different telescope, and a different velocity observable. The test was registered and hashed before the data was retrieved; the kill and stand conditions are quoted in §3 and graded one by one in §6. The registered verdict is PARTIAL, and I print its composition at the same size as the verdict. The slope-4 closure is refused on this sky as firmly as on SPARC: the single corrected slope is 3.1591 ± 0.0645, 13.0 bootstrap standard errors from 4, and no kill condition fires — both regime slopes miss their bands away from 4, not toward it, and the offset anatomy identity of paper #82 reproduces to 0.009 dex, closing at −0.0087 dex against a registered tolerance of 0.02. What does not replicate is the levels. The regime split survives and grows — 0.635 here against SPARC's 0.320, low half above high half as before — but the low half lands at 3.1082 ± 0.1116 against its band [3.50, 3.63], and the high half at 2.4736 ± 0.1170 against [3.21, 3.27]. The frozen line's mean residual is −0.1188 dex over the sample, outside the registered ±0.10 band, and the miss lives in one regime: the low-V_f half sits on the frozen line at +0.0178 dex while the high-V_f half sits −0.2554 dex under it. One caveat stands at full size, here and not in a footnote: this sample's velocity is a W20 line width, not SPARC's resolved V_f, and the sample's own authors warn that the two observables are not commensurable — line-width relations in the literature run shallower than resolved ones, in the direction these levels moved. The level shifts may be the observable's definition, not the phenomenon's failure. What measurement would decide that is stated in §7. Grades print on the face, as they do in this program: the identity is derived; the frozen numbers are fitted to SPARC's reductions — the bands are fit products; the intercept is no fit at all, fixed by the radial acceleration relation's own scale — and spent, frozen, here; every verdict quantity is measured; the verdict is PARTIAL — the phenomenon travels, the SPARC numbers at their registered sizes do not. ---

The result, in plain language

The Closure Identity (papers #82 and #83) froze its numbers on SPARC: an intercept of 1.81598 set by the radial acceleration relation's own scale, g_† = 1.150831×10⁻¹⁰ m/s², and two regime bands for the corrected baryonic Tully–Fisher slope — 3.50–3.63 in the low-V_f half, 3.21–3.27 in the high-V_f half. Every one of those numbers was measured on one database, reduced by one pipeline. This paper takes the frozen numbers, unchanged, to a sample this program did not build: the 930 isolated galaxies of Bradford, Geha & van den Bosch (2016), an ALFALFA-based baryonic Tully–Fisher sample with a different selection, a different telescope, and a different velocity observable. The test was registered and hashed before the data was retrieved; the kill and stand conditions are quoted in §3 and graded one by one in §6. The registered verdict is PARTIAL, and I print its composition at the same size as the verdict. The slope-4 closure is refused on this sky as firmly as on SPARC: the single corrected slope is 3.1591 ± 0.0645, 13.0 bootstrap standard errors from 4, and no kill condition fires — both regime slopes miss their bands away from 4, not toward it, and the offset anatomy identity of paper #82 reproduces to 0.009 dex, closing at −0.0087 dex against a registered tolerance of 0.02. What does not replicate is the levels. The regime split survives and grows — 0.635 here against SPARC's 0.320, low half above high half as before — but the low half lands at 3.1082 ± 0.1116 against its band [3.50, 3.63], and the high half at 2.4736 ± 0.1170 against [3.21, 3.27].

The frozen line's mean residual is −0.1188 dex over the sample, outside the registered ±0.10 band, and the miss lives in one regime: the low-V_f half sits on the frozen line at +0.0178 dex while the high-V_f half sits −0.2554 dex under it. One caveat stands at full size, here and not in a footnote: this sample's velocity is a W20 line width, not SPARC's resolved V_f, and the sample's own authors warn that the two observables are not commensurable — line-width relations in the literature run shallower than resolved ones, in the direction these levels moved. The level shifts may be the observable's definition, not the phenomenon's failure. What measurement would decide that is stated in §7. Grades print on the face, as they do in this program: the identity is derived; the frozen numbers are fitted to SPARC's reductions — the bands are fit products; the intercept is no fit at all, fixed by the radial acceleration relation's own scale — and spent, frozen, here; every verdict quantity is measured; the verdict is PARTIAL — the phenomenon travels, the SPARC numbers at their registered sizes do not. ---

Program note

The replication arm of the Closure Identity program: papers 82 and 83 froze their numbers on SPARC, and this paper spends them unchanged on the Bradford, Geha & van den Bosch (2016) ALFALFA sample. Its verdict is printed on its face: PARTIAL — the phenomenon travels, the SPARC numbers at their registered sizes do not — with the velocity-observable caveat (W20 line widths against SPARC’s resolved Vf) stated at full size in the paper itself.

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