Declarations

scope. All constructions are classical, at ${\hslash }^0$. The antibracket is the classical antibracket of local functionals on smooth configuration spaces. No quantum antibracket, quantum master equation, ${\star }_H$ on antifields, state, or loop is constructed.

scope. The relative complex lives on ${\mathfrak{F}}_W$, whose ghosts are supported where both backgrounds are trivial and whose antighosts and antifields are compactly supported in the open slab. Its intersection with XII-A's shell has zero ghost sector. The observable identities are evaluations on the named bosonic sets, not quotients and not closure on ${\mathcal{C}}_{\mathrm{sol}}$.

recorded. XIV-A's ${\mathfrak{F}}_W$ is fixed as a subspace of its $\mathfrak{F}$, with compact antighost; nothing in XIV-A used a noncompact antighost. The free-shell ghost theorem is stated for the ghost $c$ by the $W$-support and for the antighost by compact support in the open slab; the antighost rule on the intersection is the inherited $s_0\bar{c}=ib$, not zero. The Koszul–Tate sector is identified with the equations of the gauge-fixed interacting action, which coincide with the free shell only at order ${\kappa }^0$.

scope. XIV-A supplies the sheet, the kinematic rule, the extended action, the breaking functional and its witness, the relative identity, the gauge-fixed form, and the observable ledger. XIII-A supplies the non-ideal theorem and ordering counterexample. XIII-D supplies the class exclusion and the cochain. XII-A and XI-B supply the carrier, the free rule, and the uniqueness input. XII-C supplies the exact metric Euler derivative used in the Koszul–Tate witness. The algebra ${\mathfrak{A}}_W$, the nilpotence and its failure off ${\mathfrak{F}}_W$, the Koszul–Tate identification, the free-shell ghost theorem, the separation lemma, and the two obstructions are proved here.

. No successful pdflatex execution, proof-assistant check, independently executed symbolic computation, independent referee review, or journal acceptance is asserted. The value $-8I$ is copied from XII-F and not recomputed.