Physical Distinction Carriers and Erasure Maps: Accounting Boundaries, Distinction-to-Noise Ratio, and Thermodynamic Implementation

Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory FDS-P1 develops the first paper in the Physical Bridge Ladder of Active Finite Distinction Systems. It provides a thermodynamic accounting interface between formal distinctions and physically realized records. The paper distinguishes a formal distinction, understood as a partition or relation, from a physical distinction, which must be carried by a substrate, read out with bounded error, retained over a task window, and thermodynamically accounted for when it is irreversibly reused. The central boundary statement is conservative: a mathematical projection does not dissipate heat by itself; a physical irreversible implementation by reset, overwrite, many-to-one compression, or garbage collection does. The paper therefore separates logical projection from dissipative projection, and clarifies when non-injective maps become thermodynamic events. FDS-P1 defines physical distinction carriers, accounting boundaries, side records, distinction-to-noise ratio (DNR), generalized carrier distinguishability metrics, record-stability windows, erasure maps, dissipative projection, refresh cost, residual irreversibility, and full-boundary thermodynamic accounting. It introduces the boundary-relative erasure quantity LA = H(X | Y, GA), interpreted as the residual irreversibility remaining after all side records inside the accounting boundary have been included. The paper also separates maintenance and refresh costs from Landauer-style erasure costs. Reversible computation does not evade the ledger; it relocates preimage information into side records, memory-fill pressure, externalization, synchronization, refresh overhead, or later cleanup. The accompanying replication package includes deterministic synthetic simulations, figures, CSV outputs, LaTeX source, and Python code. The simulations illustrate DNR-controlled readout error, thermal retention and refresh cost, accounting-boundary side records, logical versus dissipative projection, refresh-versus-erasure ledgers, full energy-flow accounting, generalized distinguishability metrics, and the interface between register-time resolution and physical turnover. Scope and boundary. This paper does not claim that every distinction dissipates heat, that every measurement is erasure, that Landauer's principle is newly derived, or that mathematical coarse-graining alone produces thermodynamic cost. Its contribution is narrower: it defines the physical accounting conditions under which finite distinctions become carried, readable, stable, reusable, and thermodynamically accountable records.