The Heisenberg Cut as a Resource Boundary: An Operational Outlook from Coherence Maintenance Costs

We revisit the proposal that the Heisenberg cut is best understood operationally, as a resource boundary: a superposition counts as effectively classical for an agent once the power required to maintain its coherence against decoherence, P_extra >= k_B T Cdot_loss, exceeds that agent's budget. Version 1 supported the key dynamical ingredient — the rate-inheritance hypothesis, that decoherence rates transmitted through a gapped buffer of width eps are suppressed as poly(eps) e^(-m eps) — with a windowed numerical proxy on a transverse-field Ising chain. Two things change in this revision. First, rate inheritance is now derived in an exactly solvable quasi-free model and verified against exact Liouvillian rapidities: for a probe mode of renormalized sub-gap frequency omega_b coupled through a Kitaev buffer to a Markovian loss, the exact Liouvillian rapidity obeys kappa(eps) proportional to e^(-2 q(omega_b) eps) with cosh q(omega) = (mu^2 + 4 - omega^2)/(4 mu), verified to four decimal places over ten decades of kappa; the exponent is the squared (amplitude^2) one, resolving Remark 8.1 of v1, and it closes continuously at the band edge. Second, the central numerical evidence of v1 (its Fig. 1) is withdrawn: an exact critical-point control shows that the co-moving-window proxy decays faster when the gap is removed, so what it measured was arrival kinematics, not gap physics. We identify the mechanism with photonic-band-gap suppression of emission and evanescent atom-photon bound states, restate carefully what is imported versus what is new, derive a logarithmic law for the resource cost of coherence lifetime, note that the protected object is a sub-gap subalgebra rather than a spatial region, and state the interacting-buffer conjecture that would take rate inheritance beyond the quasi-free class. The non-claims of v1 stand unchanged: nothing here derives the Born rule or selects single outcomes.