The Problem

AP17 told you the room holds the stars. It did not prove it. It claimed a floor acceleration a₀ ≈ cH₀ without deriving it from the axioms.

This paper derives it — every factor, every coefficient, from {S, B, R, C}. And the result matches observation to within measurement uncertainty.

AP17 (The Room) identifies the mechanism: the tension field of ε between 0 and 1, topologically closed, provides a floor acceleration that flattens galactic rotation curves and produces the Tully–Fisher relation v⁴ ∝ M. AP17 claims the floor is a₀ ≈ cH₀. It does not derive it from the axioms. This paper derives it. And you are about to see every step.

The derivation uses all four axioms {S, B, R, C} and one bridge hypothesis (EH, proved in AP20). Axioms S, B, and C provide the topology and geometry; Axiom R provides the linear scaling of acceleration with the coherent fraction.

The result is a₀ = αcH₀/(2π), with α = 2 ln(sec(½) + tan(½)) ≈ 1.0445 derived exactly in 3.6. This matches the empirical MOND acceleration scale to within measurement uncertainty (sub-percent) at H₀ = 74. The factor of 2π is geometry; α is S² flux conservation. Neither is a parameter. You derived both.