Recovery–Curvature Thresholds and Asymptotic Stabilization in Sequential Quantum Evolution

This paper develops a geometric stabilization framework for long-depth sequential quantum evolution through the introduction of the Recovery--Curvature Accumulation (RCA), a transport quantity measuring recovery-weighted projected commutator growth under ordered realization dynamics. Extending the classical threshold-theorem viewpoint beyond reduced logical-channel correctness, the theory analyzes how coherent noncommutative transport structure accumulates across sequential depth through projected Magnus geometry and asymptotic operator-flow behavior. A sharp curvature--recovery threshold is established, separating asymptotically stable transport from critical logarithmic scaling and persistent coherent amplification. Numerical simulations on toric-code realization architectures verify the predicted transport phases, higher-order Magnus suppression, and projected operator-flow convergence. The resulting framework connects threshold stabilization, Stinespring realization transport, Floquet dynamics, monitored systems, and noncommutative geometric transport through a unified asymptotic summability criterion for coherent sequential quantum evolution.