Abstract
A local numerical reference is useful only when a justified flow image enters its domain. In autonomous source refresh, that obligation involves the state of the apparatus, not merely its selected output registers. We study a supplied 44-coordinate source model and give a conditional composition theorem that retains the original state and time, the interaction contrast, accumulated pulse area, mechanical histories, and passive transport records. Exact normal-mode reconstruction distinguishes interval wrapping from physical uncertainty. For an inactive router with positive momentum, we derive the attained position extrema and a restricted forward marginal-hull equality: retaining correlations does not remove the genuine spread of this particular projection. A separate guarded receiving domain admits the wider router record while preserving the original time and other 43 coordinate requirements. Source-local factorization then transfers the reference observables without deleting a physical coordinate or replacing an evolved state by a stored center. Smooth continuation, exact negative free transport, and a source-matched integral left-entry layer are composed under prospective whole-path guards. A positive moment expansion supplies directed bounds for the isolated reference, with its interior momentum trace distinguished from the archived cutoff convention. Fresh bounded calculations reproduce 18 accepted and three rejected candidate comparisons at each of two scale labels under their separately declared input hypotheses; these are not service probabilities. The result closes a local conditional implication, not physical initialization, complete two-use validation, global floating-program accuracy, or a common-origin derivation.
Where it sits in the release
The second source-refresh paper. It closes a local conditional implication about entering a numerical reference domain — not physical initialization, complete two-use validation, or global floating-program accuracy.
Download paper (Zenodo) — CC-BY-4.0.