Theorem: Classical route release

On the unchanged cubic-only sheet, for the detecting fixed data of Section sec:witness:

1. Every shell-descending action in ${\mathfrak{K}}_{\mathrm{loc},\mathrm{R}}(f,g,W)$ induces the trivial representation on ${{\mathcal{F}}^{\mathrm{sol}}}_{\mathrm{mc},\mathrm{pol}}$.

2. The copied auxiliary pairing is not a cocycle for that representation.

3. No slot action or integrated compensating functional in the frozen class satisfies the cancellation target on the complete gauge-fixed free shell.

4. The admitted cochain ${\mathcal{C}}_{\xi }=-{\mathfrak{B}}_{\xi }[D\gamma ,\varphi ]$ provides an algebraic parameter-dependent cancellation, not an integrated completion in the class.

The ending for the named integrated class is Proved obstructed. The result claims nothing about completions outside the parameter-local/one-retarded, shell-descending class.

Proof. Theorem thm:triviality, Proposition prop:C-admission, Lemma lem:bracket, and Theorem thm:obstruction.