The Result

Theorem (The Floor). The minimum acceleration of a closing tension field line in a manifold with Hubble parameter H₀ and constraint-set rate c is a₀ = αcH₀/(2π), where α = 2 ln(sec(½) + tan(½)) ≈ 1.0445, derived exactly from {S, B} + EH/AP20 (Propositions 2–3, 3.6). No free parameters. You hold every step of the derivation.

Classification: the functional form a₀ ∝ cH₀ is DERIVED. The exact coefficient α/(2π) ≈ 0.1662 is DERIVED. The result is parameter-free.

Proof. (1) The tension field lines must close (Axiom S, AP06 Theorem 3.1). (2) The maximum radius for closure is Rₕ = c/H₀ (Axioms R + C, via EH proved in AP20). (3) The apex acceleration of the widest closing line is c²/Rₕ = cH₀ (Axiom C). (4) The field line closes in a dipolar loop of circumference 2πRₕ (derived from {S, B, C} via Poincaré–Hopf, 3.3). (5) The coherent fraction of the loop is τ/T = 1/(2π), where τ = 1/H₀ is the coherence time and T = 2π/H₀ is the loop period (3.4). (6) The acceleration scales linearly with the coherent fraction (Lemma 1: measure homomorphism on (ℳ,·) via Axiom R + AP20; 3.5). (7) The S² dipole tension profile T(θ)/T_apex = 1/sinθ (Proposition 2) gives the exact correction factor α = 2 ln(sec(½) + tan(½)) ≈ 1.0445 (Proposition 3). Derived from {S, B} + EH/AP20. No free parameters. (8) The floor acceleration is a₀ = αcH₀/(2π) ≈ 1.0445 × cH₀/(2π).