Quantum Information Copy Time (QICT): Spectral Foundations, Canonical Filtered-Certification Protocols, and Transport Benchmarks

We present a self-contained, publication-oriented formulation of Quantum Information CopyTime (QICT), a timescale governing the certifiable replication of a conserved information labelY in local quantum many-body systems. The framework is built from an inverse-Liouvillianquadratic form in the Kubo–Mori (Bogoliubov) operator Hilbert space. To make the constructionmathematically well-posed and operational, we (i) define QICT using the Moore–Penrose pseu-doinverse of the Liouvillian generator (no hydrodynamic closure assumed), (ii) derive an exactspectral representation with a sharp finiteness criterion, (iii) introduce a controlled infrared (IR)regularization tcopy(Y; ϵ), and (iv) specify an explicit local certification task: binary hypothesistesting between opposite small biases ±θ in a local Gibbs family using filtered local currents.We prove that the exponential filter Jϵ =∞0 e−ϵt˙Y(t) dt is canonical in two precise senses: it is(a) the unique readout of a minimal Markovian “detector with finite memory” and (b) the resol-vent/Laplace transform naturally produced by linear response. We then link the signal-to-noiseratio (SNR) of any such certification protocol to the regulated QICT functional and providea hypothesis-testing translation from SNR to target error probability δ via standard inequali-ties. Finally, we state a transport-regime agnostic “Master” Golden Relation (free dynamicalexponent z), provide benchmark estimates for the matching constant CΛ using independentlycomputed chaos/transport inputs in canonical strong- and weak-coupling limits, and propagatetemperature-dependent transport uncertainties into the resulting mass band.