The fifth pass: one identification, three refusals, four candidate displays

adapted chart (D0.1, D0.5). XIV-I, lines 828–855 Ichart: the two placements are

diffeomorphisms onto their images; near the null cone $q_{\pm }={d_{\pm }}^2$ and ${\zeta }_{\pm }\in {\mathbb{R}}^3$ are ordinary coordinates; with $u_{+}=a$, $u_{-}=z$, the adapted chart is $w_{\pm }=(u_{\pm },{\zeta }_{\pm },q_{\pm },r_{\pm },y)$, of dimension sixteen, and ${\mathcal{A}}^m(V)$ is defined on it. The particular choice of ${\zeta }_{\pm }$ is not reproduced. This relates the chart domain $V$ to $W$; it does not identify $V$ with $W$ and does not lift ${\Delta }_I$ to $W$.

refusals (D0.8). XIV-H, lines 1661–1667 Hrefuse; XIV-I, Proposition prop:canonical, lines 1492–1496 Irefuse; XIV-J, lines 1305–1309 Jrefuse: each states that no equality $U_{\mathrm{can}}=W\setminus \overline{{\mathcal{N}}_{\mathrm{att}}}$ is asserted. $U_{\mathrm{can}}$ remains the inherited domain on which the specified products have already been proved. XIII-C's ${\mathcal{U}}_{\Gamma }$ is the open set on which the Hörmander sum condition holds, and XIII-C states that this does not identify ${\mathcal{U}}_{\Gamma }$ with the complement of the collision diagonals.

map (D0.13). XIV-H writes Hfiber

so that $\mathsf{A}$ is the coefficient matrix of XIV-H's linear fiber map $a_1$; $a_1$ itself is not reproduced. XII-D, lines 519–525 XIIDfiber, and XII-A, lines 974–976 XIIA, display

The candidate is ${\mathsf{A}}^{\alpha \mu ,I}={\mathfrak{a}}^{\alpha \mu ,ab}$ with $I$ the symmetric pair $(ab)$; no sentence in XIV-H states that its $a_1$ is XII-D's.

weight (D0.13). XII-D, lines 545–552 XIIDweight, takes an arbitrary $f\in {C^{\infty }}_c({\mathring{M}}_T)$ on the open slab and sets

On the XII sheet $f$ is a compactly supported test weight, not a missing formula. Whether XIV-H's $f$ in (eq:K5a)–(eq:K9) is this $f$ is a candidate (sec:candidates).

{Quadratic coefficient (D0.13, $K_6$).} XII-E, lines 401–403 XIIEa2:

XIV uses ${\dot{a}}_2$ in the definition of $\mathsf{D}$ in (eq:K6) and does not record its expansion; Lemma lem:a2 computes the derivative of (eq:a2).