Autonomous Source Refresh: Exact Spatial Exchange and a Certified Recovery Domain

Motivated by Complementarity-First's distinction between a relational operation and its physical implementation, we study one-use source refresh in a supplied autonomous classical Hamiltonian model. A moving courier must reach a stationary source, exchange arbitrary internal contents with it, and expose the fresh input and retained old output at one fixed readout time. A positive completed-square kinetic coupling makes the completed exchange depend on spatial area rather than entering speed. A separate position-dependent recovery interaction transfers energy from a main mechanical carrier to a courier that may be nearly stopped.

For four real four-coordinate internal registers and two mechanical pairs, the combined construction admits the fixed product domain ||(x,y,b,c)|| ≤ 1, 18.6193 ≤ α ≤ 18.6248, with mechanical preparation independent of the unknown internal data. Exact-rational certificates for a reduced three-coordinate release law, together with recovery estimates, give source completion before time 47 and an interaction-free readout at 33π/2. Certification here concerns reduced-system arithmetic, not a formal-kernel proof or validated integration of all twenty coordinates.

Fresh loading is exact; the source/old-output pair has error at most ε_pre ||(x,y,b)||, with ε_pre < 0.007338, against its declared ideal comparison. This is not a whole-processor accuracy bound.

The full endpoint retains two additional main-port passages, the remaining internal registers, and both mechanical records. Its mechanical energy allocation excludes immediate reapplication of the same ready-state contract, while a source-only witness excludes an exact payload-only linear reduction. The result supplies a bounded one-use implementation conditional on the stated architecture. Physical rearming, all-input/all-word linear control, and primitive selection of the carrier and interactions remain outside the theorem.