Verification boundary

The following are reported computational results, with exact certificates in the archive (Appendix app:script):

• the $1065$-entry specialization of M.1 and the support counts;

• the numerator ranks $d_N$, reconstruction certificates and relation vectors of M.2;

• the general-$h$ ranks $\dim U_N$ and the background/plateau kernels of M.3;

• the collapse ranks, self-adjoint subspaces, Helmholtz certificates, and matching preimages of M.4;

• the symbolic/numerical cross-checks of work package A (Lemma lem:wpA-comp); the top-order residues, coefficient files and scale-tensor collapse certificates of work package B; the time-only kernels, route 1/route 2 agreement and matching probes of work package C (Lemma lem:to-comp);

• the audit-3 checks: the separating functional on the archived target vectors, its pure-gauge sympy verification and the recollapse of $C_{\mathrm{top}}$ (Proposition prop:wpB-sep); the numerical variable-regulator pairing (Lemma lem:wpA-comp); the Beta-integral convolution of Lemma lem:bv(c).

The analytic statements (Lemma lem:bv, Lemma lem:wpA-varreg, Theorem thm:wpA-Sbv, Proposition prop:wpB-sep, Propositions prop:relations, prop:Gsplit, prop:collinj, Lemma lem:helm, Lemma lem:wpB-dw, Theorem thm:wpB-B0, Lemmas lem:to-intertwine and lem:to-indep, Corollaries cor:wpB-timeonly and cor:wpB-MC) are written proofs. The outputs are reproduced verbatim in Appendix app:out.