Final release statement.

release statement.{ The prepared witness-response theorem is proved, including no-decay uniqueness, polarization, explicit identification, the traceless contraction, and the scalar completion check.

The coordinate Cauchy problem has a unique explicit solution, and a restricted auxiliary operator extension exists. Their identification with the inherited coordinate prescription is stated precisely and remains conditional.

The supplied XVI-F-v3 equality $I_{\mathrm{cand}}=Q_{\lambda }$ is recorded as proved there. It is not misreported as an unresolved residual, nor used to silently rename the coordinate field.

The inherited-completion and class-admission programme remains Unresolved. This manuscript is complete as a response proof and a domain-sensitive compatibility interface, not as a proof of the unresolved quantum coefficient. }