Status ledger and debugging corrections

{}1.12 {@{}p{0.30}p{0.65}@{}} Result & Current status

Result & Current status, continued

Switch-correction degree audit & Established from the displayed monomials: Proposition prop:monomials. The bulk $J_3$ homogeneity and local-polynomial structure remain explicitly imported premises.

Real polarized completion & Established on the stated inherited completion domain: Theorem thm:Opol. Defined by three diagonal completion evaluations.

Compact kernel $t_{\mathrm{D}}$ & Established under the stated root/kernel inputs: Theorem thm:trep. Defined on general tests by (eq:t-test); no arbitrary distributional product is presumed.

Ambient support and tensor symmetry & Established for this kernel: (eq:t-support) and Theorem thm:trep. Reaching $t=0$ is compatible with ambient compactness. Boundary regularity is not determined.

Finite-order seminorm estimate & Established for some finite orders: Proposition prop:estimate. The root order contributes; the source order two is not substituted for the full distributional order.

Complex extension and witness equality & Established: Theorem thm:Opol(5)–(6). The definitions coincide with revised XVI-E/F. The supplied current XVI-G chain closes the old witness compatibility item.

Witness contraction to $j_{\lambda }$ & Established as a scalar distributional equality: Proposition prop:tmatch. Partial evaluation only, not identification of the full kernel with a one-variable density.

Witness decay and resonance & Imported from current XVI-G and transferred by (eq:t-to-j). Their original fixed-width and scalar-family hypotheses remain unchanged.

Free-shell class & Defined for the constructed compact kernel. Comparison with the matching frozen XI-G class remains unresolved; no all-free-triples equality is proved.

Full-kernel wavefront/admission & Unresolved. Neither the full kernel's wavefront set nor its trisolution's wavefront set is calculated. The admission criterion is not applied.

Switch representative & Conditional consistency deduction: Proposition prop:switch. Uses the explicitly reproduced XI-G slot identities. Trisolution preservation is not admission.

BRST/BV observability & Not established. No differential or closure/descent calculation is specified.

Scalar two-point pairing & Definable for specified ${\mathsf{H}}_2$ by (eq:scalar-pairing). No two-point distribution is selected or evaluated.

Prepared quantum product & Not constructed. No Hadamard choice, time-ordered product, extension, scaling degree, or counterterm is supplied.