The KMS Foundation of Relational Information Dynamics: Why the Bunch-Davies Vacuum Implies g† = 2cH0,dS/π2

Papers 1 and 2 of this series derived the galactic acceleration floor g† = 2cH₀,dS/π² and provided physical mechanisms for the coefficient. Both papers relied on the proportionality aₙ ∝ τₙ ∝ 1/n (coupling amplitude proportional to Margolus-Levitin evolution time), labelled explicitly as heuristic. This paper identifies the single physical principle from which that proportionality follows rigorously, and from which the entire RID derivation chain can be reconstructed without heuristic steps.

The principle is: the Bunch-Davies vacuum is a KMS state with respect to modular flow at inverse temperature β = 2π/H₀,dS.

For a KMS state, the fluctuation-dissipation theorem gives a two-point function C̃(ω) ∝ 1/ω at the natural mode frequencies ωₙ = nH₀,dS (where βωₙ = 2πn and the Bose factor is exponentially suppressed). This directly gives aₙ ∝ 1/n, replacing the heuristic with a theorem.

The trilogy is then complete: Paper 1 states the result; Paper 2 provides the covariant mechanism; Paper 3 identifies the single axiom — the KMS condition of the Bunch-Davies vacuum — from which everything follows.