Declarations and source provenance

and source provenance

of the work. This is an exact theoretical finite-certificate study. No empirical dataset is used. All action, domain, catalogue, and certificate definitions needed for the finite result are included.

. The quantities $16/3$, $8$, $64$, and $2/3$ are derived analytically. The embedded checker is optional and is not a theorem premise.

status. No successful pdflatex compilation, checker execution, independent Einstein-vertex implementation, numerical integration, or mechanized verification is claimed. The source contains explanatory figures drawn from its displayed objects; it does not claim recovery of unavailable companion figures.

provenance. Companion references identify unpublished registered manuscripts or collections of source records by their supplied identifiers. They are not presented as journal articles with invented titles, dates, or DOIs. The comparison locators and summaries do not constitute independent verification of those manuscripts. No companion theorem enters the central proof.

to the earlier manuscript. The principal finite certificate is unchanged from the supplied version of manuscript II. The revision clarifies the quotient, coverage, successor questions, and non-transfer boundaries rather than claiming a new global contact result.