CHICAGO — An MQ analysis applies one fixed galactic realization law to all 175 galaxies in the SPARC catalog. The manuscript reports 3,366 radial comparisons and a ratio of mean predicted to mean observed velocity of 1.0001888, about 0.019 percent above unity. That statistic compares two pooled averages; it does not mean that individual velocities are predicted to 0.019-percent precision.

The same source reports a pooled root-mean-square residual of 22.82 kilometres per second and a mean absolute residual of 16.20 kilometres per second. Positive and negative deviations nearly cancel in the pooled signed mean. Figure 1 places that cancellation beside the remaining absolute errors.

SPARC supplies published rotation velocities and reconstructions of the gravitational contributions from stars and gas. MQ uses the reconstructed ordinary-matter source to calculate a realized rotation speed. The analysis holds its acceleration scale fixed rather than assigning a separate MQ scale or dark-halo fit to each galaxy. Distances, inclinations and stellar mass-to-light assumptions still enter through the adopted source models.

Weighting each galaxy equally gives a different result from weighting each radius equally. The manuscript reports an equal-galaxy mean signed bias of +3.3195 kilometres per second, with 112 galaxies having positive mean residuals and 63 having negative mean residuals. These findings expose structure that a near-zero pooled mean alone cannot show.

The independently catalog-classified highest-quality subset contains 99 galaxies. Its galaxy-weighted geometric predicted-to-observed velocity ratio is 1.0042, with a reported 95-percent galaxy-bootstrap interval of 0.9763–1.0325. That subset and estimator differ from the full-catalog ratio of means, so the two central values are not interchangeable measures of accuracy.

The law has the same functional form as the empirical radial acceleration relation published in 2016. MQ’s proposed contribution concerns its derivation and upstream acceleration normalization. Applying it to SPARC tests that construction under the adopted inputs; it is not an independent discovery of the earlier empirical relation.

The companion Brief supplies the equations, frozen input scale, definitions of the averaging conventions, residual statistics and bootstrap intervals. It also identifies a public-input row-count discrepancy that must be reconciled before the reported 3,366-point calculation can be claimed as independently reproduced.

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