Copy-Time Certificates and a Conditional Higgs-Portal Mass Benchmark: Operational Definition, Rigorous Domains, and Reproducible Constraints

We formulate copy time τcopy as a fully specified hypothesis-testing task for quantum dynamics with a conserved global U(1) charge, calibrated by a disturbance budget using the Bures metric. The central point of the paper is methodological: the notion of an information-transfer timescale is defined operationally (state family, measurement class, and error criterion) and then linked to explicit sufficient conditions under which a diffusive heat-kernel envelope controls the receiver’s distinguishability advantage. The frequently invoked Lambert-W−1 structure is shown to be a certificate inversion associated with this envelope and is deliberately demoted to a conditional analytic tool, with an alternative non-diffusive/non-perturbative branch discussed. As a separate, explicitly conditional application, we present a reproducible pipeline that maps τcopy to an infrared coarse-graining scale ΛIR via an explicit window-function construction and then to a minimal Higgs-portal singlet-scalar UV completion. Under stated assumptions (thermal “copy-limited” saturation near the electroweak crossover and a minimal Functional Renormalization Group (FRG) truncation executed in the Supplement), the pipeline yields a benchmark dark mass scale mχ = 58.4(60) GeV. The manuscript is written to separate assumptions from consequences and to supply the scripts required to reproduce every figure, ensuring full academic transparency and reproducibility.