Scope and remaining physical questions

11 Scope and remaining physical questions

The conditional finite-programme result combines explicit coherent resource gates, a massive writer, transported-trap reset, retained receivers and a common autonomous controller. Its archival conclusion follows from the complete current and transfer estimates. The theorem does not need a freely sampled history or a collapse of the full wave at each declaration.

The assumption of initial equilibrium remains substantive. A real stationary wave gives zero Bohmian velocity, and therefore preserves any initial position law: dynamics in this class cannot establish universal relaxation to equilibrium. The independent ready stock also remains supplied. A local reset transfers correlations to retained receivers; it does not manufacture conditional independence from an arbitrarily exposed microscopic past.

The interaction catalogue is deliberately mathematical. Positive kinetic energy, smooth bounded coefficients and confinement give a well-defined semibounded model. They do not prove relativistic locality, construct the catalogue from established microscopic interactions, or price all fabrication, preparation and calibration requirements. Those are physical-realization questions beyond this theorem. The protection result covers bounded internal nuisance operators on its commuting spatial-spectator domain; arbitrary new read interactions and unbounded coordinate disturbances require separate analysis.

The resource limit fixes the finite programme and horizon first. Increasing mass, separation and gap yields arbitrarily small declared errors, with growing costs. It does not yield an unlimited memory or perfect clock at finite resources. Recombining every retained branch is a different experiment and can intentionally erase record separation. A first-crossing formula for the specified pointer likewise does not construct a timestamp reader; the latter needs its own interaction and error analysis.

The main proofs are inherited from the cited version 2 manuscript and are given in full in the present scope. Targeted algebraic and numerical checks have been repeated, but neither those checks nor AI-assisted internal review constitute independent specialist verification. Independent review of the operator domains, derivative estimates and whole-history coupling remains valuable before journal submission. The present revision does not claim that the broader measurement or Born-probability programme has been resolved.