Abstract

XV-F-patch-ii completes XV-F-patch at the level of frozen objects. It asks whether the four gaps recorded in the patch's F0 verdict—the residual codomain, the generators and module action of the presentation package, the ingredients of the six operational entries, and the parametrization and presentation-level form of the correction class—can be closed under the original F0 rule, which passes a core item only when its frozen member is identified, never when a parameter family is displayed.

Five gates are run. Q1: a residual bundle $E_{\mathrm{res}}$ of rank ten, with the metric slot at $z$ and the scalar slot at $y$, its density, and its duality pairing are specified as a convention adopted here, no sheet defining them; the index bookkeeping of the displayed entries supports the choice, and it is proved that smooth residual testing erases every covector with nonzero $z$-component. Q2: the six entries are enumerated; the $K_5$ placements have XIV-I's chart module with its reconstruction rule but without reproduced generators; for the supported sector it is proved that, for every completion of the undefined data obeying XIV-H's bound $|\alpha |+|\beta |\le 2$, $K_6+K_8+K_9$ is a normal jet of order at most three along the null incidence $\{q_{+}=0,r_{+}=0\}$, which reproduces XIV-J's normal order exactly, and that ${\partial }_{\alpha }\mathcal{B}=\frac{1}{2}{x}_{\alpha }R$, so $K_8$ is carried by the null incidence, correcting a remark of the patch; $K_{47}$ has no presentation space in any sheet, and Q2 fails there. Q3: the construction of $\mathsf{D}$ from ${\dot{a}}_2$ is displayed in XIV-I and identified; $\mathsf{A}$, ${\sigma }_{\epsilon }$, $f$, $a_2$, ${q^{L,I,J}}_{\alpha \beta }$, $\mathsf{P}$, $\mathfrak{b}$, $g$, ${E^{\mathrm{A}}}_m$ are open, each reduced to a named sheet and sentence. Q4: XIII-C's three roles remain roles; the correction class as maps on presentations is not defined by the sheets, and the lift of the collision sets is refused. Q5: the list of cross-line products proved on $U_{\mathrm{can}}$ with an operational domain is stated to be empty. The verdict is Unresolved at F0, at Q2; F1 is not entered; no lift, null-defect test, characteristic prescription, or admission is asserted.