The Seam Holds: The Two Reductions of the Same Sky Agree Galaxy by Galaxy, and a Prediction Dies

This program's two earlier SPARC papers (#82 and #83) forced two reductions of the same sky to pay each other globally. One scale, fitted on the radial acceleration relation, had to reproduce the baryonic Tully–Fisher relation along a line of slope exactly 4. It did not, and the failure had a clean anatomy. But every test in that work speaks about the sample as a whole: a mean, a slope, a scatter. This paper asks the question nobody in the program had asked. Do the two reductions agree galaxy by galaxy? For each of 76 galaxies, the scale its own rotation curve asks for (a fit of the McGaugh form to that galaxy's resolved mass-model points) is set against the scale its integrated quantities imply under the Closure Identity at the global scale fitted in the earlier papers' first test. The difference, d, is computed with an error budget whose every piece is computed — bootstrap of the resolved fit, a joint distance Monte Carlo that carries the covariance between the two sides, and the tables' own error columns. A prediction was fixed before the computation, derived from the established slope anatomy: the seam should fail, with χ²/dof above 3, a drift of the implied scale against velocity inside [+0.30, +1.00], and scatter surviving the drift. None of it landed. χ²/dof around zero is 0.938. The drift is +0.176 ± 0.110, the predicted sign at half the smallest size the prediction would accept, and 1.6σ from no drift at all. The χ²/dof around the drift line is 0.852. Under the bands fixed before the data were examined, the verdict is: the seam holds — the prediction fails. The two reductions of the same sky agree galaxy by galaxy at the priced size. The one-scale failure does not live in a per-galaxy seam. It lives where the earlier papers found it: in the slope of the mean relation. One anomaly stands, small and printed: the weighted mean of d is +0.061 ± 0.021 dex, a 15% offset of the integrated scale above the resolved scales, inside the ±0.10 dex band this program uses throughout and 2.9σ from zero.