Structural Support Certificates for Graph-Query Inference in Mechanism Posteriors

Modern scientific discovery systems can propose more mechanistic hypotheses than laboratories can test. We cast downstream selection as certified graph-query inference in a finite locally factorized posterior over admissible mechanisms: for $A \rightsquigarrow B$, structural support is the posterior mass of mechanisms in which $A$ reaches $B$ by a directed path, not a direct-edge score, retrieval confidence, or MAP-graph decision. Exact support is global because exterior factors can reweight local mechanisms and witness paths may leave any bounded neighborhood; for path cutoff $L$ and locality radius $m$, truncated support is a convex combination of exact boundary-conditioned local supports. Optimizing over locally admissible blanket states and adding a certified long-path remainder gives $p_{AB} \in [\\ell_{L,m}, \min\{1, u_{L,m} + \bar{r}_L\}]$. For coupled rivals, the same calculations yield joint feasible sets used by a robust resolve-or-abstain rule. On controlled and biologically scaffolded finite-posterior records, the implementation has zero endpoint containment misses and zero false fixed-model resolutions, and joint feasible sets resolve 14/24 coupled-rival cases versus 6/24 for scalar boxes.