Three bridge outcomes

The legal outcomes for this support problem are:

1. Bridge proved. The implication (SB) holds for every retained first-stage pair, including the declared conjugate sector. The double-ordering commutator gate clears, but the overall causal-product release remains Unresolved.

2. Proved obstructed. A retained pair has both actual support orderings certified and a nonzero commutator. Every symmetric causally factorizing map on the fixed domain is then excluded.

3. Unresolved. A named support calculation, cancellation check, or ordering certificate remains unfinished. Absence of a proof is not an obstruction.

There is no Constructed outcome for ${\mathsf{T}}_2$ within this paper.

Let $\sigma$ be complex-linear flip and $\gamma$ componentwise antilinear conjugation. Retain exactly

Here

is the inherited space of actual first-stage tensors. No tensor is removed, including the strongly separated pairs whose commutator was evaluated as zero in IX-E-2.

{{0.92} Release box. On the supplied information, the bridge release is Unresolved at the inherited boundary-trace certificate (TC) stated below.

A complete conditional support proof is given. For the explicitly specified flat massless zero-Cauchy realization, the bridge is proved, although the proposed solid-ball lower-support assertion is false.

That realization is not silently substituted for the inherited $L={\mathsf{E}}_{0}C$. Verification that the inherited operator has the displayed trace remains necessary.

No certified nonzero two-way pair is produced. No time-ordered replacement or retarded construction is begun. }