Galactic Dynamics in a Two-Phase Medium: A Quasi-Static Baryon-Locked Response with Yield-Gated Screening

Galaxies rotate faster than the gravity of their visible matter alone predicts. The two standard explanations are nonbaryonic dark matter or a change to gravity at low acceleration. This paper develops a third: space as one physical substrate with two effective mechanical roles—a stretched lattice and a permeating fluid—in which matter reorganizes the medium into a wake that contributes to gravity. On the established branch, the wake strength is locked to the baryonic source by one fixed formula shared across galaxies, with no object-by-object response parameters. Applied pointwise to SPARC, a public catalogue of 175 nearby disk galaxies, the formula gives an unweighted root-mean-square log residual of 0.1989 dex across 3,389 usable points. Under the same fixed disk-and-bulge mass-to-light assumptions, this differs from the RAR-exponential comparator by 0.000016 dex; the comparison establishes numerical similarity under the declared metric, not statistical equivalence or a test against fitted halo models. A complementary gas-dominated check, evaluated at the declared fixed stellar mass-to-light ratios, returns a median preferred scale from 61 galaxies of 1.07 (+0.11/−0.09) × 10⁻¹⁰ m s⁻² (bootstrap 16–84%), containing the fixed a_W. The closure also enforces the slope-four BTFR scaling, but its fixed-slope normalization remains high by 0.1734 dex at the reference stellar mass scale, meaning that the law requires 1.491 times the inventoried baryonic mass at a given rotation speed; a linked global mass-to-light calibration reduces the offset to 0.1354 dex without closing it. A separate disk-geometry calculation removes a residual trend with the shape of the visible-matter field on a common 3,382-point sample. An isolated equal-mass binary calculation gives a circular orbital speed about 22.5% above Newtonian at 1.4 times its response-transition radius. The medium also has an acquisition gate and memory: a subsystem is eligible to establish a wake when its own Newtonian field exceeds the ambient field, and an established wake persists until reorganization. Two presently similar systems can therefore behave differently because of their histories. That history dependence is the framework’s sharpest prediction and its largest present weakness, because no independent observational branch selector yet exists. The wide-binary test is therefore reported as unscored. Transport, a global action joining systems with different histories, a positive microscopic realization in arbitrary geometry, and a relativistic account of gravitational lensing remain open.