Stress Testing the Rate Inheritance Principle: Spectral Decoherence Rates and an Operational Resource Horizon

In gapped quantum many-body systems, static correlations decay exponentially with distance. A common heuristic expectation is that this geometric suppression carries over to dynamical decoherence rates induced by local environments; this expectation has been isolated as the Rate Inheritance Principle (RIP). We stress test RIP in a fully specified Davies-type Markovian setting: a gapped transverse-field Ising chain weakly coupled to a thermal bosonic bath through a strictly local operator. RIP is formulated operatorially through two spectral envelopes of the Dirichlet form on operators supported at distance eps from the coupling region: a ceiling kappa_sup(eps) (v1's envelope) and a floor kappa_perp(eps) (smallest nonzero rate, new in v2 — the quantity a maintenance no-go actually needs; v1's inference from ceiling saturation to a power floor was a non sequitur and is corrected here). Numerically, rate inheritance remains conditional: for energy-exchange-dominated coupling the ceiling decreases with separation, while for near-zero-Bohr-frequency coupling it saturates — and, more importantly for the no-go, the projected floor also persists in that regime. Version 2 adds the diagnostic that the series' methodology demands: the near-zero-frequency Bohr components of the local coupling are strongly delocalized at finite size (about 90 percent of their weight beyond the coupling site), so the saturation is established within the Davies model class, whose secular construction is nonlocal; the exactly solvable local-sink model of the companion paper shows genuine geometric suppression, and the two results bracket the physics. Combined with the corrected maintenance bounds of the companion work theorem, a persistent projected spectral floor yields a quadratic-proxy resource horizon; the corresponding relative-entropy no-go is stated with its required uniform-Cdot_loss / MLSI-type hypothesis explicit.