Corrections to XV-F-patch

{(G1) The support of $K_8$.} The patch's Proposition prop:support placed $\mathrm{supp}{K}_8$ in the solid cone $S_{J^{+}}=\{a=z,b-a\in J^{+}\}$, and its Remark rem:conormal argued that $K_8$ is singular at points with $(b-a{)}^2>0$, where $\mathcal{B}(b-a)$ is locally constant, so that the conormal statement of XIV-H could not be checked. The derivative ${\partial }_{b^{\alpha }}$ inside the bracket of (eq:K8) acts on $\mathcal{B}(b-v)$, and ${\partial }_{\alpha }\mathcal{B}=\frac{1}{2}{x}_{\alpha }R$ (Lemma lem:dB). Hence $\mathrm{supp}{K}_8\subseteq S_{\partial }=\{a=z,b-a\in \partial J^{+}\}$ (Corollary cor:K8supp); the premise of the Remark fails, and the check it declared not performable passes at the level of supports. Item (g) of the patch's Proposition prop:checks is moved to the performed list.

{(G2) The construction of $\mathsf{D}$.} The patch stated that the construction of ${\mathsf{D}}^{\alpha \mu ,I,J}$ from ${\dot{a}}_2$ is XIV-H's and not reproduced. XIV-I displays it II2: $\mathsf{D}$ is the constant bilinear fiber map determined by ${\dot{a_2}}^{\alpha \mu }[G;h]={\mathsf{D}}^{\alpha \mu ,I,J}{h}_I{G}_J$ ((eq:Dfrom) below). The construction is identified; the value of $\mathsf{D}$ depends on $a_2$, which remains open (sec:patch3).

(G3) XII-A and XII-B are non-inputs here. The patch used XII-B's trace reversal to state $\mathfrak{a}=-\text{PPcalnote}$. Under the present evidence contract that sheet is a non-input; the identity is restated as the stand-alone computation ${\mathfrak{a}}^{\alpha \mu ,ab}{r}_{ab}=\frac{1}{2}{\eta }^{\alpha \mu }{\mathrm{tr}}_{\eta }r-r^{\alpha \mu }$ (Lemma lem:fiber), with no second map named. XII-A's Hadamard blocks are not used; the identity of the blocks in ${\mathcal{C}}_{\mathrm{cross}}$ is carried from the patch as open and is not reassessed (sec:reassess).