Speed, Precision, and Dissipation Bounds for Boundary Maintenance in Finite Distinction Systems: Finite Update Windows, Bottleneck Throughput, and Resource-Ledger Exit Theorems

FDS-P6 develops the speed–precision–dissipation paper in the physical bridge sequence of Finite Distinction Systems (FDS). It studies boundary maintenance as a real-time physical process constrained by finite update windows, finite precision, bottleneck throughput, effective causal reach, and resource-ledger costs. The central claim is that a distinction is not operationally maintained merely because it is representable in memory. A boundary-relevant distinction must be updated, verified, corrected, or acted upon within its relevant update window. If the rate-distortion demand required for maintaining a boundary task at tolerance ε over update window τ exceeds the sustainable internal throughput, the system must enter at least one exit channel: higher resource or dissipation cost, increased error, latency growth, task relaxation, externalization, invariant compression, resource expansion, or boundary-maintenance failure. The paper introduces boundary-maintenance throughput, bottleneck internal rate, precision and confidence demand, correction burden, effective causal reach, externalization relief, invariant-compression relief, and a resource-first dissipation ledger. It distinguishes broad resource-ledger accounting from thermodynamic dissipation proper: entropy-production claims require additional thermal-reservoir calibration. FDS-P6 connects and extends the neighboring FDS physical bridge papers: P4 on coarse-grained anti-recurrence and capacity-recovery asymmetry, O3 on finite-memory entropy/resource ledgers, and P7 on invariant quotients and topological side-ledgers. It also relates the FDS account to rate-distortion theory, information thermodynamics, thermodynamic uncertainty relations, quantum speed limits, finite-time dissipation speed limits, and control under communication constraints. Deterministic numerical demonstrations are included. They illustrate speed–precision load surfaces, resource-ledger decomposition, finite-resource precision floors, effective causal reach, externalization break-even, invariant-compression relief, finite-boundary regime diagrams, and a Physical AI worked-example normal form. The numerical figures are normal-form demonstrations, not empirical phase diagrams or fitted thermodynamic data. This release includes the paper PDF, LaTeX source, reproducibility code, generated figures, and CSV outputs.