Directional Asymmetry in the Radial Acceleration Relation: A Thales Partition Diagnostic Linking Plasma Shocks, Galaxy Dynamics, and Dimensional Stratification

We apply the Thales partition framework to the radial acceleration relation (RAR) using 2,693 radial acceleration measurements from the SPARC galaxy sample (Lelli et al. 2017). Each data point is decomposed into a baryonic channel fraction a = g_bar/g_obs and a dark matter channel fraction b = 1 − a, with the Thales mediator h = √(ab), deficit δ = 1 − 2h, and signed asymmetry χ = b − a computed for 2,562 valid partition points. Five empirical results are reported. First, the deficit–residual correlation is positive and highly significant (ρ = +0.300, p = 6.6 × 10⁻³⁷) only when the dark matter channel dominates (χ > 0), reversing sign (ρ = −0.166) when baryons dominate — confirming directional asymmetry in the gravitational partition. Second, a clean monotonic quartile gradient from ρ = −0.114 (baryon-dominated) to ρ = +0.437 (p = 10⁻³⁰, deep dark matter regime) traces the full transition across the partition axis. Third, the e^(1/3) ≈ 1.396 threshold from the dimensional stratification framework separates the correlation-active regime (ρ = +0.241, p = 3.7 × 10⁻³¹) from the correlation-absent regime (ρ = −0.059, p = 0.30), independently confirming this geometric boundary. Fourth, residual scatter is minimized near equipartition (|χ| < 0.05), confirming the stationarity theorem at the partition fixed point. Fifth, early-type galaxies show the directional transition radially within individual systems (inner ⟨R⟩ = 1.58; outer ⟨R⟩ = 3.26). These results replicate the structural pattern found in interplanetary plasma shocks, where magnetic-channel dominance (β < 1) selects the active correlation direction. The dark matter channel is to galactic dynamics what the magnetic field is to solar wind reconnection: the channel whose partition asymmetry drives the observable response. We discuss connections to generalized mean hierarchies, conformal cyclic cosmology, and testable predictions for Type Ia supernova light curves. No modification of general relativity or dark matter theory is proposed; the framework provides a diagnostic coordinate system that reveals directional structure in the partition geometry of existing data.