Source-Instantiated Finite-Service Recurrence in Autonomous Source Refresh

A sequence of completed services does not by itself establish a service recurrence. We prove a source-instantiated one-step implication for a specified finite-packet Hamiltonian family, starting from an actual labelled terminal state and a fresh packet installed at the original preparation. A common mechanical box, active-norm bound, resident bound, and completed router and clock guards return at the same prescribed elapsed time. The proof retains all archives, imperfect residuals, mechanical histories, physical phases, and signed source-value traces. It combines explicit source analysis, exact pulse and clock inequalities, validated coupled occupancy and recovery, and a correlated fixed-time return argument. An isometric record embedding gives the all-internal-record estimate EN < √((0.000409)2 + (N − 2)(0.000372)2) for every prescribed finite N ≥ 2, seeded by the separately established second service. The source has 24N − 4 physical coordinates throughout a prescribed N-service construction and requires one additional payload, three blank registers, one history, one router, and one paid clock per supplied transition. After freezing the recurrence, a separately propagated fourth-service family reaches the original terminal box at the unchanged exact readout, with local all-64-internal-coordinate error below 0.000371052741 and accumulated internal error below 0.000665841675. This is a finite supplied construction with explicit resource growth; payload choice after earlier output requires a separate physical contract. A specified supporting subset of record algebra, conditional error transport, and rational witnesses has been executed in Lean and its returned evidence assessed; the physical source and validated-numerics arguments remain outside that subset.