Declarations

scope. The new proofs are conditional distributional comparisons, linear-algebraic repair criteria, formal-order statements, and explicit finite-dimensional counterexamples. They construct no native gravitational quantum coefficient. Elementary comparison channels and contact distributions are not released as clock quantizations.

scope. The cited unpublished versions and supplied excerpts provide documentary scope and motivation. Their unprinted proofs, artifact outputs, archive hashes, and rebuild reports are not premises of Theorem thm:main. No exhaustive scan of the manuscript series is claimed.

. The comparison manuscripts bearing Oai identifiers are cited under their supplied N. Cheung attribution. The separate catalogue is cited under its supplied OpenAI attribution. No identity of those authorship records or independent catalogue authentication is asserted.

qualification. The Enter-calculus journal metadata are reproduced from the supplied accepted-article record. Independent authentication of that publisher record is not claimed here. A signed submission should check its final publication metadata and provide stable copies of all cited unpublished versions.

. The source contains one internal bibliography and uses standard pdfLaTeX packages without external figures or input files. No successful pdfLaTeX run, proof-assistant verification, independent symbolic or numerical execution, native program compilation, referee decision, or acceptance is asserted.

. The submission format is anonymous. Citation of N. Cheung does not establish authorship of this manuscript. A signed submission must supply authorized author and affiliation metadata.

boundaries. No quantum evolution without an external time, invariant physical speed, derived metric, Einstein dynamics, de Sitter state, ultraviolet completion, or inherited characteristic quantum admission is concluded.