The Accessible Quantum Past: Record Filtrations, Expected Lifts, and Visibility Bounds

This manuscript develops an operator-algebraic framework for describing an observer’s accessible quantum past. Past alternatives are represented by compatible families of record states on an increasing sequence of von Neumann algebras. As the accessible record algebra grows, distinguishability and optimal readability of earlier alternatives cannot decrease, without requiring collapse or modification of the universal quantum state. State-preserving conditional expectations are treated as an optional structural layer supplying reference-dependent lifts, symmetries, and martingale theory—not as physical outcome-selection mechanisms. For two-path systems, the paper distinguishes actual observed fringe visibility from the root-fidelity envelope determined by the conditional record states. It derives quantitative bounds for fragmented and correlated records, including access-erasure bounds, exponential fidelity suppression, a heterogeneous-fragment Chernoff gap, and a Bures-angle correlation budget. It also proves that certain triples of faithful mixed states cannot simultaneously attain all three pairwise fidelity envelopes within a single positive multi-path completion. A separately labeled constructive extension investigates whether a candidate settled-record filtration can be derived from operations that remain physically admissible in the future. It proves consequences for persistent classical records and their relationship to recoherent control, while clearly identifying observer-relative actuality, a quantitative holonomy bound, and a possible selector-echo law as physical postulates, conjectures, or optional new physics rather than established consequences of quantum mechanics. This July 2026 manuscript substantially revises and supersedes the November 22, 2025 version of Past-Selection Filtrations. It preserves the central record-filtration intuition while correcting and narrowing earlier claims, strengthening the operational framework, and explicitly separating established mathematics, proved consequences, conjectures, and physical postulates.