PA-1 Pairwise Theta Measure and Sorkin Interference: A Reproducible Algebraic Verification in the Theta-Field Observer-Rendering Framework

This paper isolates and verifies a single formal consequence of the PA-1 addition to the Theta-field observer-rendering framework. PA-1 states that the measure assigned to an unresolved finite set of alternatives is generated by a pairwise kernel, μ(S) = Σᵢ,ⱼ∈S Dᵢⱼ. Using Sorkin's hierarchy of interference functionals, the paper proves that PA-1 allows ordinary second-order interference generically, while forcing all third-order and higher interference terms to vanish identically. The result is conditional: it does not prove that nature is governed by PA-1, and it does not constitute an empirical validation of the Theta-field program. It proves the algebraic implication PA-1 ⇒ Iₙ = 0 for all n ≥ 3 and reports an exact-rational Python audit confirming the cancellation on deterministic and randomized finite kernels. The paper includes the complete executable verification script, raw computational output, limitations, and an external-audit requirement.