Recoverability as an Ordered Operational Framework: State Ceilings, Environmental Records, Memory Activation, and Certified Comparison

Recoverability of quantum coherence is formulated as a family of success-constrained operational frontiers indexed by a state, channel, or multi-time process, a task, an interface, and an exact- or minimum-success convention. The framework separates state ceilings from experimentally reachable performance and distinguishes restrictions due to control, time, uncertainty, environmental records, memory, and inaccessible channel structure.

The manuscript develops a typed simulation preorder on complete response families, a compiler-relative closure order, and a directed response deficiency on success-tagged behaviors. It gives exact static trace-norm ceilings, success-frontier geometry, explicit memory and record benchmarks, primal-dual finite-experiment separation programs, and reference-assisted channel-lineage witnesses. “Shadow activation” denotes the interface-relative exposure of a pre-existing process distinction under an enriched tester interface; it is not proposed as a new microscopic law.

Version 1.0 follows a claim-by-claim bibliography and content audit. It is a separate work, conceptually derived in part from the earlier Italian criterion DOI 10.5281/zenodo.21333992, but it is neither a translation nor a new version of that record.

This is a theoretical preprint and has not been peer reviewed.