Abstract

XV-F continues XV-E at its gate E0. Its first task is to resolve the source gap that XV-E documented: either recover, from the supplied record, the core definitions needed to state the preliminary lift of the frozen six-branch joint target and its correction class, or report exactly which items remain unavailable.

Five retrieval passes are recorded. The second reproduces XIV-H's coordinate-response line, the $K_8$, $K_9$ kernels, XIII-C's collision sets and partial-diagonal class, and XII-A's Hadamard matrix; the third returns locators only; the fourth reaches the registered full texts and reproduces XIV-I's reconstruction rule, XIV-I's retarded kernel $R$ and its square, XIV-J's grouped cross-line operator, mixed vertex Hessian, and output convention; the fifth yields exactly one identification—XIV-I's adapted chart $w_{\pm }=(u_{\pm },{\zeta }_{\pm },q_{\pm },r_{\pm },y)$ in terms of $(a,b,z,y)$—three located refusals of the equality $U_{\mathrm{can}}=W\setminus \overline{{\mathcal{N}}_{\mathrm{att}}}$, and four candidate displays from the XII sheet (the fiber tensor $\mathfrak{a}$, the observation weight $f$ as a compactly supported test function, XII-E's quadratic coefficient $a_2$, and the scalar stress tensor $T_0$). Every reproduced display is checked. New checks: in the adapted charts both $K_5$ placements and $K_6$ have exactly the form of the reconstruction rule with explicit coefficients; the fiber map $\mathfrak{a}$ is minus the trace reversal; the derivative ${\dot{a}}_2$ is recomputed; the polarization of $T_0$ matches the displayed Hessian for one normalization and is off by a factor two for the other; the advanced kernel ${E^{\mathrm{A}}}_m$ is constructed and shown unique for all $m\ge 0$, conditionally on a declaration the XIV texts do not contain. Three corrections to the circulated draft are recorded: the argument of the reconstruction coefficients is the chart point; with chart-function coefficients the generating family is not free, and XIV-J's null relation is an instance of this dependence; and no manuscript contains the symbol $\hat{H}$ returned by the fourth pass. The tensor $\mathsf{A}$, the symbols ${\sigma }_{\epsilon }$, ${\dot{a}}_2$, $\mathsf{D}$, the ingredients of $K_8$, $K_9$, the normalization of the polarized stress, the displays of the target contraction, joint-map class and canonical domain, the residual bundle, the presentation-level correction class, the lift of the collision sets, and all candidate identifications remain unsupplied. The graph-level outcome is Unresolved at F0.

The mathematics on the finite normal-jet module with punctured reconstruction is unchanged: the disjoint classification of null relations; jet-detection as “some extension carries a defect”; the affine space of descending extensions over the reconstruction-fixed freedom, infinite-dimensional in XV-D's example; and the theorem that a normal-order bound alone never makes the puncture-supported ambiguity finite-dimensional. Two phrasing errata to XV-E are recorded. Nothing is transferred to the inherited graph.