Abstract
A numerical construction can preserve its stored input and reproduce its output while failing to represent the exact preparation or mathematical law named in its interpretation. This paper studies that distinction in the autonomous source-refresh model. Three objects are kept separate: an intended Hamiltonian model, a real piecewise system defined by frozen source constants, and an executed floating-point program. An inherited boundary fixture passes its floating admission predicates but violates the exact norm and payload caps. A separately named positive-radical preparation preserves the reconstructed raw directions and satisfies both caps exactly; its coordinate enclosure and nearest floating serialization are not themselves admitted preparations. We formulate source-specific transverse continuation at two main interfaces under a continuous, absolutely continuous, almost-everywhere solution convention. The first exchange determines a work invariant, and the work rotation determines a different contrast for the next exchange. Complete state reconstruction retains the original phases and the courier’s correctly matched free branch. Because the frozen support length is not mathematical 2π, the source scalar has two strictly positive downward debits along this continuous trajectory. Their smallness does not make them zero, and their accounting does not supply a physical dissipation mechanism. A restricted obstruction rules out repairing the same canonical branch fields by additive constants on an open full phase-space neighborhood. Inherited directed records instantiate a finite preparation-derived prefix through 805/256, not a complete first endpoint, a preparation-to-reference theorem, or a global floating-program error bound. The contribution is the explicit separation and composition of exact preparation, source interpretation, local transition, and finite evidence contracts.
Where it sits in the release
The third source-refresh paper. Its contribution is the explicit separation and composition of exact preparation, source interpretation, local transition, and finite evidence contracts.
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