Inverse Threshold-State Bridge from a Reduced L-H Closure to Threshold-Point Benchmarks

This record provides Phase-Model Paper 01B: Inverse Threshold-State Bridge from Paper 01 to Threshold-Point Benchmarks. The paper addresses a specific methodological gap in the L-H transition program. A dynamical closure such as Paper 01 is defined in latent variables and, in principle, should be tested with time-resolved diagnostics and shared-parameter trajectory fits. Public threshold-point benchmark datasets, however, usually contain only extracted rows of observables rather than the initial conditions and discharge histories required for full dynamical validation. Paper 01B formalizes the narrowest nontrivial claim that can still be tested: whether each observed threshold point can be mapped to a physically admissible latent threshold state under a fixed observation map and fixed closure parameters. The paper introduces an inverse threshold-state formulation, defines bridge-level residuals and admissibility classes, and states explicit rejection logic. It also includes a public benchmark-facing snapshot derived from the bundled observation-space predictions. In the current public snapshot, even the weakest power-side bridge criterion is rejected for all rows. This negative result is treated as scientifically informative rather than hidden as a failed validation, because it shows that observation-space agreement should not be interpreted as evidence for a validated latent threshold manifold unless the bridge-level conditions are satisfied. This record is intended as a falsifiable methodological companion to the broader phase-model series. Its purpose is to separate what can be claimed from threshold-point benchmark data from what cannot, and to provide a reproducible framework for latent-state inference, benchmark interpretation, and model rejection in reduced L-H transition closures. Update (April 8, 2026): Corrected minor figure-layout issues and restored the missing reference to the primary provenance source.