The Cosmological Evolution of the MOND Acceleration Scale in Substrate Theory

Substrate theory distinguishes an infinite, non-gravitating equilibrium substrate (F1) from the finite, observed, perturbed region (F2) bounded by the distance time quanta have propagated since the Big Bang, RH = c/H₀. We show that this single structural feature yields two independent results from the same horizon: the MOND acceleration scale a₀ = cH₀/2π ≈ (1.04–1.13)×10⁻¹⁰ m s⁻², arising when the inertial response length c²/a exceeds the horizon mode; and the dark-energy density ρDE ~ MP²H₀², arising because only the finite F2 gravitates and its energy is holographically bounded — closing the 122-order-of-magnitude cosmological-constant gap. Because both scales are set by the horizon, a₀ must evolve: a₀(z) = cH(z)/2π. We derive this prediction, the implied radial-acceleration-relation (RAR) lift and baryonic Tully–Fisher (bTFR) zero-point shift, and confront them with SPARC, MIGHTEE-HI, and MUSE-DARK III. The data confirm that a₀ rises with redshift (~30σ) — a signature unique to the substrate among live options. A direct shape test of all public a₀(z) measurements finds the substrate’s H(z) scaling consistent with the data (free-exponent fit a₀ ∝ H^{0.78±0.15}, with H¹ acceptable at p-value 0.30); the residual tension is in amplitude rather than shape, and is comparable to the systematic offset between the z≈ 0 and intermediate-z surveys. We further show that wide-binary tests, contrary to common framing, neither support nor exclude the framework: the substrate's modified-inertia external-field-effect boost is degenerate with modified gravity at leading order, and the reported 36-binary anomaly is modeling-dependent (γ = 1.12–1.60). The framework's discriminating power is cosmological, and the parameter-free, normalization-independent bTFR zero-point shift is its cleanest near-term test.