Scope and legal outcomes

The target is a complex-linear actual tensor map

on one fixed flip-stable comparison domain. An “actual” tensor means an element of the algebraic tensor product of actual functionals, rather than an unquotiented presentation by test functions.

There are three legal outcomes:

1. Constructed: all coefficients exist and every declared interface clause holds on the fixed domain.

2. Proved obstructed: a contradiction excludes every map satisfying that interface on the fixed domain.

3. Unresolved: at least one required consistency, extension, admission, contact, continuity, or overlap obligation remains undischarged.

Failure of one proposed replacement kernel excludes that candidate only. Removing an offending tensor changes the target and does not discharge a claim covering that tensor.

{{0.92} Release box. The domain chosen below contains all of $D_{\mathrm{first}}$ and its conjugates. No offending first-stage pair may subsequently be deleted. The outcome of the supplied-data audit is Unresolved. Free-word coherence does not imply causal factorization. No ${\mathsf{T}}_3$, $R_2$, general free-domain enlargement, G2 release, or repair of VII-C is asserted. }

The inherited hard stop is retained: the causal-product release is Unresolved because the time-ordered extension and its remaining causal, admission, and overlap obligations are unfinished, not because the degree-four free word has failed to descend.