Manuscript XI-F@2 · XI-F-v2.tex · section · f4899be0

Decision, exclusions, and handoff

Decision, exclusions, and handoff · lines 1385–1447

Gate	Ending	Exact scope
F1	Proved obstructed	The frozen representative of $C_{3} (f, g)$ has $\pm d t \in WF$ at $Σ$ in a metric slot (Theorem thm:F1); it leaves $F_{mc, pol}$ , and XI-E's admission map does not apply. Mechanism: zero Cauchy data for the second coefficient together with an unswitched, unramped cubic source. Not finite rank; not a loop. The on-shell class is open.
F2	Constructed	De Donder variation $2 D^{*} D s_{ξ}$ from XI-B's fermion, divergence $- □ D s_{ξ}$ , response $K ζ_{gf} [s_{ξ}]$ , $ζ_{gf} = - E_{0}^{R} D s_{ξ}$ , coefficient $- 1$ (Lemma lem:gf, Proposition prop:gfprops). Ghost term has no metric leg at this order.
F3	Constructed	$u_{3}$ obeys the X-A second-order law with $ζ = ζ_{gf}$ (Theorem thm:u3law); the cubic-completed coefficient shifts by $A_{1} [K ζ_{gf}]$ plus the named Einstein-shell term (Theorem thm:F3); zero when $A γ = 0$ on $U$ and $D_{f} \cap J^{+} (supp ξ) \subset P_{g}$ ; ledger $- I + 0 + I + 0 + 0 + 0 + 0 = 0$ on the witness; remainder supported in (eq:remsupport), no ramp term.
F4	Recorded	Not a Ward identity; not an automorphism; no quantum version in $E_{H}$ ; affine numbers untouched.

Gate	Constructed only if	Obstructed if	Result
F1	$C_{3} \in E_{H}$ with the XI-E embedding	kernel leaves the copied wavefront class	Obstructed: timelike conormal at $Σ$
F2	de Donder variation computed in the coefficient $- 1$	—	Constructed
F3	plateau sum proved, support stated	interior pairing nonzero on the witness	Constructed: sum $= 0$ ; the sheet's $I$ was a double count

The worst ending among the two gates governs: Proved obstructed, at the admission gate. The plateau sum is constructed as a classical identity and could not be quantized in $E_{H}$ even if its sum were nonzero.