Matter from Finite Access: Reachable Sectors, Poles and Readable Particles in the Quantum Gauge Theory of Time

This paper develops the matter sector of the Quantum Gauge Theory of Time (QGT) by distinguishing the successive conditions required for a mode of the retained dynamics to become physically readable matter. Starting from a finite non-invertible access, exact elimination of the retained sector produces the self-energy and its time-domain memory kernel. The dynamically active sector is identified as the cyclic subspace generated by the physical port, while its complement remains conserved but silent for that port. The paper establishes the chain from structural address to dynamical reachability, dressed pole, residue, observable transition and physical identity; derives the corresponding reachability and residue results; and separates these operatorial statements from the additional representation, statistics, dispersion and dimensional-scale identifications required to name a physical particle. The generational and Koide readouts are retained at their explicitly stated conditional level.