Geometric Markov Bounds and Rate Inheritance Modulo Fixed Points: A Scalar Entropic Interface from Static Locality to Davies Dynamics

We propose an entropic interface between locality, recoverability, and dynamical decay rates across a geometric collar. The central scalar invariant is the conditional mutual information (CMI) I_rho(A:C|B), where B is a buffer separating A and C. In finite dimension (Type I algebras), the Fawzi-Renner theorem implies that small CMI yields a quantitative recovery channel acting on B. We formulate a volume-uniform geometric Markov bound with a boundary prefactor, I_rhoLambda(A:C|B) <= sigma(dB) g(w), and summarize recent literature inputs establishing exponential CMI decay in shielded/high-temperature regimes. On the dynamical side, we formulate a Rate Inheritance Principle (RIP) for Davies/KMS-symmetric generators: static Markovness across the collar constrains decay rates on the fast sector F-perp modulo the fixed-point algebra F = ker L (the omega = 0 floor), with a dynamical input stated as a Poincare inequality for a local collar Dirichlet form. The only remaining nontrivial link is isolated as an explicit Dirichlet comparison assumption. We verify a diagonal (classical) heat-bath comparison and derive a diagonal subsector corollary with an explicit transfer coefficient. Finally, we define a split reduction datum and a split-regularized CMI target quantity for an AQFT lift and include finite-size illustrations/diagnostics. v2 corrects two points and adds verification: (i) the Fawzi-Renner factor under the squared-fidelity convention is -log F, not -2 log F (as in the companion 2512.0101 v2), so the geometric recovery bound reads 1 - F <= sigma(dB) g(w); (ii) the v1 bulk-collar comparison for diagonal heat-bath observables is false as stated -- exact-enumeration counterexamples are exhibited -- and is replaced by a proved version with the collar extension taken on the enlarged neighborhood B^(+2r) (commuting-projection argument). A full verification suite (exact enumeration, N = 9 Ising-Z) ships with the paper, checking the corrected comparison (0 violations), the transfer constants, the exact vanishing of CMI for the 1D Markov field, and the corrected FR factor on random tripartite states. Throughout, the target RIP theorem remains conditional on the bulk-collar comparison assumption; the diagonal heat-bath result verifies only a corrected commuting-subsector comparison, and also exhibits a 1D degeneracy of the transfer constant.