Proposition: Checks performed and not performable

The following mutual-consistency checks among reproduced items pass: (a) the reconstruction rule against XIV-J's two values (Lemma lem:recrule(i)) and, under $q$-linearity, against its null relation (Lemma lem:recrule(ii)); (b) (eq:R) against the pole chart (Lemma lem:R); (c) the display (eq:RR) (Lemma lem:RR); (d) the adapted chart against $\dim W=16$ and the pullback domain of (eq:cross) (Lemmas lem:chart, lem:cross); (e) the supports of $K_6$, $K_9$ and the singular locus of $\mathcal{B}$ against the base of ${\Lambda }_{\mathrm{resp}}$ (Proposition prop:support); (f) XII-B's trace reversal against XII-A's ${\mathcal{P}}^2=\mathrm{id}$ and XII-D's $a_1=-\mathcal{P}$ (Lemma lem:fiber); (g) the form of both $K_5$ placements and of $K_6$ against the reconstruction rule in the adapted charts (Proposition prop:K5chart); (h) the displayed Hessian against the polarization of $T_0$, which passes for exactly one of the two normalizations (Lemma lem:polar). The following cannot be performed from the record: (i) the conormal statement for $K_8$ against its singular support (Remark rem:conormal); (j) XIV-J's blocks against XII-A's (eq:Hblocks); (k) the candidate identifications (a)–(g) of Proposition prop:reduction; (l) freeness of ${\mathcal{K}}_{\mathrm{int}}$, which depends on the unreproduced coefficient class (Lemma lem:recrule(iii)–(iv)).

Proof. Each item cites the result that establishes it or the passage whose absence prevents it.