Theorem: Exact mathematical release

This manuscript establishes:

1. pure-trace witness non-determination of compact kernels, microcausal admission, and free-shell classes, including smooth compact non-determination;

2. the weighted-divergence residual and the late-source/retarded-response non-implication;

3. local wavefront equality under nonvanishing smooth multiplication and compact balanced-forest composition;

4. reconstruction descent, conditional class-obstruction transfer, and formal-order separation;

5. exact formal coefficient inventory under a declared normalized retarded family;

6. exact affine Ward compatibility and the quotient invariant under compatible finite changes;

7. finite-probe, bounded-normal-order, and projected-flow non-implications;

8. conditional fixed-order assembly and symmetry-preserving continuum observable matching.

The independence or conditionality stated in each result is retained. No complete inherited gravitational characteristic coefficient, evaluated interacting one-loop observable, bulk BV restoration, or ultraviolet completion is established.

Proof. Item (i) is thm:witness,cor:smoothwitness; (ii) is prop:weighted,prop:lateresponse; (iii) is lem:switchWF,thm:forest; (iv) is prop:descent,prop:classtransfer,prop:hbar; (v) is prop:inventory; (vi) is thm:ward,cor:scheme; (vii) is prop:finitevalidation,prop:normalorder,prop:truncation; and (viii) is thm:assembly,thm:matching.

The final sentence states the boundary of the constructions. The substantive hypotheses of the conditional theorems have not been supplied for the concrete inherited gravitational target.