Abstract

We formulate the binary causal-extension problem on a fixed actual tensor domain inherited from IX-Free-2 and prove its algebraic consistency tests, its first-stage commutator identity, its double-ordering obstruction, an algebraic extension criterion, and the conditional unnormalized subtraction theorem. We correct the double-ordering geometry: two support orderings require causal disjointness, not overlapping functional supports. Neither full support of the locked contraction kernel nor injectivity of the first-stage maps determines the commutator.

The release outcome is Unresolved. The supplied information does not specify the restriction of $K-\overline{K}$ needed to evaluate the decisive causal test, an old time-ordered map on a nonzero comparison subspace, or the sharp distributional extension and continuity data. Consequently this manuscript does not claim a constructed causal product or a universal obstruction. Its proved results identify exactly what a subsequent construction or no-go proof must discharge. Degree-four free descent is not reopened.