Operational Provenance Deficiency in Black\-Hole Reconstruction: Present\-Capability Geometry, Distinguishability Certificates, and Exact Holographic\-QEC Calibrations

Abstract

We formulate a contract-relative operational test for whether future-predictive quantum information lies in the post-processing capability of any admissible present description. For a declared present-access family and typed recovery policy, the present-completion deficiency is the diamond-norm distance between the predictive target and a contract-defined present-capability set. The underlying quantum channel deficiency and sufficiency mathematics is established prior art; the contribution is its use inside a path-sensitive black-hole reconstruction framework that separates coarse endpoint from rich present state, claim descent from witness descent, information insufficiency from failure of joint realizability, and local recovery from path monodromy. We prove access- and target-monotonicity under explicit typed closure conditions, give a pairwise distinguishability-gap lower bound, state a finite-dimensional attainment criterion for finitely many compact channel-type components, and derive the single/joint/virtual access hierarchy. The exact [[5,1,3]] perfect-code benchmark covers all ten three-retained and all ten two-retained access channels: every three-retained channel is exactly reversible, every two-retained channel is completely depolarizing with optimal diamond-norm deficiency 3/2 to the logical identity, and a Bell-projector discrimination certificate attains that lower bound. Two distinct three-retained erasure histories have the same coarse endpoint but different rich-present channels while both remain exactly recoverable, providing a direct null calibration of the endpoint split. The Bousso-Kaya-Lin-Shahbazi-Moghaddam finite-region family is retained as a coarse-data insufficiency benchmark, not yet as a no-present-completion theorem. The next black-hole-specific target is a certified positive fiberwise completion lower bound surviving operational quotienting, joint-realizability controls, and declared contract variations.