The QICT Program: From Gauge-Coded Microscopic Unitary Dynamics to an Audited Micro–Macro Closure

We present a self-contained, audit-grade formulation of the Quantum Information Copy-Time (QICT) program as a micro–macro closure framework. The microscopic layer is strictly unitary and localitypreserving (a quantum cellular automaton, QCA), including a gauge-coded code-subspace construction and a continuum Dirac limit as a controlled long-wavelength approximation. The central micro–macro bottleneck is the emergence of diffusion from deterministic unitary dynamics. Rather than overclaiming a resolved theorem where the general problem remains open, we (i) replace informal “fast mixing” language by a structured, measurable spectral criterion in the hydrodynamic sector (SDC), and (ii) provide a quantitative bridge showing how certified second-moment (design-channel) diffusion controls infinite-temperature density correlators whenever a local approximate-design property holds (with explicit error bounds). We supply complementary numerical evidence: exact-unitary diagnostics by ED at L = 12 with an L = 14 cross-check, a max-L certification up to L = 512 at the momentchannel level, including a vanishing ballistic/Drude proxy, and a scalable unitary MPS–TEBD typicality diagnostic with explicit Drude bounds and bond-dimension convergence tests. We then propagate audited parameter intervals through a phenomenological closure map, with an explicit reproducibility contract (JSON, hashes, and PASS/FAIL verifier). All claims are labeled as PROVEN, CERTIFIEDNUMERICAL, EXTERNAL-DATUM, HYPOTHESIS, or CONJECTURE.