CHICAGO — The MQ galactic manuscript develops a relation linking the gravitational acceleration calculated from stars and gas with the realized acceleration used to predict orbital motion. Its functional form matches the empirical radial acceleration relation, or RAR, published by McGaugh, Lelli and Schombert in 2016. MQ’s proposed contribution is a derivation and an upstream acceleration normalization, rather than discovery of that observational relation.

The construction has two principal steps. A positive quadratic norm in the realized description supplies a dimensionless realization depth. A subdivision-consistency requirement makes the unrealized fraction combine multiplicatively across depth increments. With the stated continuity, boundary and depth-normalization assumptions, the resulting realization fraction is exponential.

Figure 1 shows where those premises enter. The source’s identification of the normalized depth with the additive exponential parameter fixes the unit generator; continuity and multiplicative composition alone do not select that numerical rate.

The ordinary-matter source remains essential. Stars and gas supply a Newtonian gravitational calculation; MQ maps that baryonic field into a larger realized response when the baryonic acceleration is low. At high acceleration the realization fraction tends toward unity and the baryonic Newtonian limit is recovered.

The manuscript fixes the present-epoch acceleration scale before evaluating galaxy curves and applies the same scale across galaxies at that epoch. That design is more restrictive than choosing a separate MQ normalization for each object. It still depends on the cosmological inputs and physical realization used upstream, and on the quality of each reconstructed stellar and gas distribution.

The low-acceleration limit yields a slower decline of the realized field than the baryonic Newtonian field. For an isolated finite baryonic mass, the model has a radius-independent asymptotic circular speed and a fourth-power baryonic Tully–Fisher scaling. Those related limits are consequences of the same law, rather than separate independent confirmations.

The prior empirical RAR is important context, not an MQ-specific test. Independent assessment asks whether the stated premises select the law and its normalization, whether the parameters were fixed before residual inspection, and how well predictions from independently specified baryonic sources match external kinematics. Galaxy points share distance, inclination and stellar-source uncertainties, which must be retained in that assessment.

The companion Brief gives the equations, explains the depth and exponential assumptions, and provides a reproducible dimensionless example. It also separates galaxy-rotation predictions from the additional relativistic, lensing, cluster and cosmological calculations required for a broader account of dark matter.

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