Return Theory (RT): Asymptotic Records Sector Connection — Gravitational Memory, Endpoint Records and Path Records

A derivationally self-contained RT sector connection, relative only to RT Foundations 1.0.0, for gravitational memory at future null infinity. Displacement memory is typed as an endpoint record and spin and gyroscopic memory as path records. The release gives the exact Poisson sampling law of path records and their fibre without a band limit, the exact polynomial survival of a memory ramp under a timing fit on a finite span, the zero-frequency boundary of interferometric access, the cutoff independence and exact continuum local law under a red background, the exact sky-mode separation of a pulsar-timing array with an eigenvalue floor from the pulsar term, and the identification of memory as the record of a vacuum transition modulo translations. It contains twelve mathematical results, eleven host-law consequences, three RT assignments, fixed-seed computations, machine-readable B1–B10 declarations, a three-way result ledger, source and verification scripts. The discriminating-prediction class is explicitly empty in version 1.0.0; two prospective protocols validate host laws and implementations.