Two Reductions of the Same Sky: The Reconciliation of the SPARC g† Estimates

The radial acceleration relation (RAR) carries one fitted scale, the characteristic acceleration g†, and the SPARC galaxy database supports two reductions of it. Fitting the relation's standard form to the published RAR table gives g† = 1.162058×10⁻¹⁰ m/s². Recomputing the baryonic accelerations from the SPARC mass models and fitting the same form to the full mass-model set gives g† = 9.513507×10⁻¹¹ m/s² — a factor 1.221482 lower, a disagreement of roughly 2.7 bootstrap standard errors on the mass-model side alone. Two reductions of the same sky should not disagree about the sky's one constant, and a disagreement of this size invites two readings: one of the reductions is flawed, or the two reductions are not fitting the same sample. This note settles which. The mass-model recompute was repeated under the field's standard quality cut — galaxies flagged Q = 1 in the SPARC properties table, with inclination at least 30° — and the cut fit returns g† = 1.150831×10⁻¹⁰ m/s²: the two reductions then agree within 0.98% (split ratio 1.009756). The composition accounting that explains the full-set discrepancy is printed in full. The 82 galaxies the cut removes, fitted as a block on their own 1,329 points, return g† = 7.130004×10⁻¹¹ m/s²; the 76 quality-flagged galaxies among them return 6.413264×10⁻¹¹ on their own, while the 6 galaxies removed on inclination alone pull the other way and are too few to matter. A leave-one-galaxy-out pass over all 175 galaxies shows no single galaxy moves the full-set fit by more than 0.009944 dex — an eighth of the 0.082671 dex the block removal shifts it — so the drag is a population property of the excluded set, not the leverage of a few bad actors. The verdict is composition, not flaw: the unweighted full-set fit is dragged by exactly the galaxies the standard convention exists to exclude, and the reconciliation convention is stated in one sentence any reader can re-apply. Every g† in this note is fitted, none is derived; nothing here spends the reconciled value, and the note's downstream consumer — a fixed target band of 1.15–1.16×10⁻¹⁰ m/s² — inherits the value as a fitted constant with its provenance attached. The methods lesson is the note's second product, and it generalizes past this dataset: an unweighted fit over a record of mixed quality manufactures discrepancies that are properties of the sample, not of the sky — and, in a companion result from the same tables, manufactures correlations as well.