Thermodynamic Hilbert Sectors with Replicated Entropy Bookkeeping

A theoretical and computational framework separating accepted protocol support, record-quality diagnostics, replicated entropy moments and implementation-level bookkeeping. A bounded positive effect induces a completed quotient Hilbert space; integer density-matrix moments are calculated through permutations on identical product copies; signed entropy increments telescope along a fixed reduction. Version 3.2 clarifies support versus distinguishability, finite-dimensional assumptions, higher-order observables, finite-copy uncertainty, numerical rank, logarithm units, additive ledgers and the limits of return diagnostics. A failed chosen inverse does not alone establish irreversible dynamics, and zero entropy residual does not establish state or apparatus return. The companion provides new reproducible central-spin and 500-state SWAP checks, an explicitly defined dephasing control, the recovered historical ledger script and its rerun, editable equations and manuscript sources. Missing historical central-spin and entropy-fit generators are disclosed. The associated Finite Record Protocol Calculator v0.3.0 supplies instrument/record diagnostics, Python and JavaScript parity checks, strict validation and a reduced-state entropy-path interface. This is the first deposit of this manuscript series, superseding working drafts v1.0 through v3.1. All examples are analytic or simulated; no laboratory measurements, empirical anchor, independent Born-rule derivation, emergent geometry or thermodynamic cost inferred from the accepted effect alone are claimed. The manuscript uses CC BY 4.0. Executable software and source code in the companion retain separate rights; see LICENSE_SCOPE.txt and software_dependency/RIGHTS.txt.