Addendum — Derivation of the Milgrom Constant from the Entangled Relativity Action

This addendum presents a zero-parameter structural derivation of the Milgrom acceleration constant a₀ within the Geometric Relay Programme (GRP), built on Olivier Minazzoli’s Entangled Relativity action L²ₘ/R. The derivation identifies the bare relay mass from the cosmological curvature scale of the ER trace equation, m₀² = R₀/3 = (8πG/3) ρₘ, then uses the unique intrinsic acceleration scale of the relay, m₀c. The key junction is that the MOND/GRT amplification factor ν is defined as a ratio of radial accelerations, ν = gₒbs/gbar, so the source term in the dual-relay equation must carry the radial projection of the scalar relay acceleration. By isotropic projection in three spatial dimensions, this gives a₀ = m₀c/3 = c√ (8πGρₘ) / (3√3). Using Planck 2018 cosmological parameters, the formula gives a₀ = 1. 225 × 10⁻¹⁰ m·s⁻², in agreement with the observed MOND value a₀ = (1. 20 ± 0. 24) × 10⁻¹⁰ m·s⁻², with a deviation of +2. 1% and no fitted parameter. This version strengthens the previous derivation by explicitly showing why the factor 1/3 is not added a posteriori: it is structurally built into the radial definition of ν and into the dual-relay equation. The accompanying Python script reproduces the numerical value, verifies convention independence, checks the projection theorem, explores the sensitivity to H₀ and Ωₘ, and generates the summary figure. Within the internal GRP hierarchy, the derivation is assigned status A. For external readers, it should be read as a falsifiable zero-parameter structural derivation of the Milgrom scale from a matter–geometry relay framework.