Theorem: Combined IX-D-ST release

Under the stated inherited inputs, the four ordered parts establish:

1. laboratory-local causal interfaces, support inclusions, the free-word scalar non-lift, and separation of causal factorization from free coherence;

2. the first-stage commutator identity, fixed-domain obstruction criterion, and exact algebraic finite-relation extension criterion;

3. the direct-plus-reflected evaluation (eq:imag), exact vanishing on the entire strongly separated two-way class, and a nonzero observation-spacelike control without an inherited two-way certificate;

4. exact support of $W_g$, the null-sphere lower-support theorem and bridge under (TC), and a fully specified flat realization verifying that certificate;

5. a common finite destructive-clock, certificate, locality, and regular reference-preserving transport interface.

Each stage is a local Grade S interface package. For the weak inherited operator, (TC) remains an explicit verification obligation. If its same-adjoint identification is supplied, the commutator gate clears.

In both cases, the complete sharp causal-product release is Unresolved: no sharp ${\mathsf{TO}}_2$, ${\mathsf{T}}_2$, normalized $R_1$, or $R_2$ is constructed.

Proof. The stage releases are Theorems thm:Drelease, thm:Erelease, thm:E2release, and thm:E3release. The operational section proves every finite interface clause independently of the absent time-ordered map. The same-adjoint audit distinguishes the two bridge statuses without changing the fixed causal target. Requirement req:analytic has not been discharged in either branch.