Paper III: A Dynamical Speed of Light as a Consequence of Expansion-Rate Causality, with Electroweak Freezing Below TEW Paper III (v3 revised April 2026 with electroweak freezing

The speed of light c is dynamically coupled to the Hubble expansion rate H(t) through the Expansion-Rate Causality (ERC) constraint: c(t) = c0H(t)/H0 in the pre-electroweak epoch. This arises because the maximum signal speed on the brane is set by the brane's acoustic speed, which is proportional to the brane tension, which is itself set by the expansion rate. Combined with Paper IV's ℏ(t) ∝H(t)3, the ratio α = e2/ℏc is conserved exactly because both the electromagnetic winding energy and the rest mass energy are brane wave energies scaling as c2 their ratio is protected by covariance even when c varies. The critical new result of this revision is the Electroweak Freezing Theorem: at the electroweak transition TEW ∼160 GeV (redshift zEW ∼7×1014), the Higgs viscosity gradient (Paper LII) freezes into the brane fabric. The Higgs vev v = ⟨∇η⟩decouples c and ℏfrom the Hubble ow below TEW. All astronomical observations (Type Ia supernovae, quasar absorption spectra, BBN at z ∼1010, CMB at z ∼1100) occur in the frozen epoch and see exactly constant c, ℏ, G, and α. The varying-constants physics operates only at z > 7 × 1014, before the electroweak transition. The enhanced MOND scale a0(z) = c0H(z)/2π operates with frozen c0 but varying H(z) throughout all astronomical epochs and explains JWST's discovery of massive early galaxies without invoking varying constants in the observable universe.

Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.