Receiver-Side Linear Closure of QICT: Spectral Inversion, Rest-Gap Reconstruction, and Falsifiable Threshold Diagnostics

We study a receiver-side closure built on the operational copy-time core of QICT and analyze its linear receiver-accessible sector to quadratic order in momentum. The logical scope is kept explicit throughout: the operational copy time is the only ingredient imported from QICT itself, whereas validator selection, shell geometry, local link structure, receiver maps, and benchmark dynamics are introduced as closure-level assumptions. Within this framework, we show that a calculable and falsifiable receiver-side inverse problem requires five structural ingredients: a validator sector, a certified transport support, a local covariance law, a closed benchmark normal form, and a declared receiver map. We then establish equivariant validator selection on homogeneous substrates, identify a six-cell contour as the minimal nearest-neighbor audited cycle on a codimension-one receiver shell with opposite pairing, and derive compact ring and spoke gauge sectors within the declared closure. For a real two-channel six-cell benchmark, we obtain the exact propagator, receiver-visible and receiver-dark transfer laws relative to a chirality-selective receiver, and the associated hydrodynamic limit. We further derive an algebraic reconstruction of the benchmark parameters from five spectral observables, analyze small-signal stability against weak nonlinear corrections, and formulate a set of platform-independent consistency tests based on dispersion asymmetry, short-time visible curvature, gap identities, and reduced rest-gap-time extraction. The paper also identifies a receiver-side non-identifiability boundary: the linear observable sector alone does not fix family structure, mixing data, anomaly coefficients, or absolute masses without additional microscopic input. No cosmological dark-matter interpretation is assumed; the receiver-dark sector is defined only relative to the declared receiver map. The result is a mathematically explicit and experimentally testable closure framework, rather than a derivation of the Standard Model from QICT alone.