Self-Initiated Phase Re-Coherence (SIPR) 3.2: Autonomous Quantum Kinetic Proofreading for Phase-Selective Recoherence

Abstract

Self-Initiated Phase Re-Coherence (SIPR) asks whether an open quantum system can autonomously recover a phase-compatible state after perturbation through fixed system-environment dynamics, without measurement-conditioned feedback. The original SIPR v2.1.1 proposal used a two-bath pure-dephasing model and claimed a nearly universal recoherence threshold and a metastable plateau. Here the published coherence law is audited exactly. For dimensionless time u = Γt, frequency ratio r = ω_R/Γ, and structured-bath strength R = λ_R²/[γ_N Γ(1+r²)], transient growth of the coherence magnitude occurs if and only if r exp[-3π/(2r)] > 1 and R > [r exp(-3π/(2r)) - 1]⁻¹. The unique frequency threshold is r★ = 3.6441736716456…, while the asymptotic logarithmic decay rate remains -γ_N(1+R); therefore the original universal threshold and nonzero long-time plateau do not follow from the published equation. Two structural no-go results then delimit the microscopic programme. First, a Gaussian pure-dephasing channel can exhibit information backflow and partial revival but cannot selectively contract an arbitrary relative-phase error toward a prescribed phase. Second, a passive excitation-conserving single-pseudomode architecture that makes a Bell singlet dark also leaves the ground state stationary, preventing a unique global Bell attractor. These results redirect SIPR from passive revival toward a nonequilibrium, autonomous repair cycle inspired by biological kinetic proofreading. In the proposed network, phase mismatch populates a bright Bell sector, stationary hot resources lift bright and ground sectors into an auxiliary manifold, and a cold phase-selective decay deposits population into a target dark Bell state. The target terminates the cycle because all ideal repair operators annihilate it. The paper specifies the effective Lindblad network, local-detailed-balance constraints, uniqueness conditions, phase-activated repair current, thermodynamic ledger, pseudomode memory intervention, temporal-window analysis, comparator battery, and optional geometric and dynamical-criticality qualification layers. Loschmidt-amplitude or DQPT-like events are treated only as preregistered diagnostics, never as proof of SIPR by themselves. No simulation result is claimed. The contribution is an exact correction, two explicit no-go statements, and a falsifiable programme for deciding whether environment-powered quantum phase proofreading is merely known reservoir engineering or a distinct SIPR regime.