Structural Support Certificates for Mechanistic Hypothesis Selection

Modern scientific discovery systems can propose more mechanistic hypotheses than laboratories can test. We study the downstream selection problem: after upstream retrieval, extraction, expert modeling, or curation has fixed a finite locally factorized posterior over admissible mechanisms, when does the posterior evidence justify acting on one structural hypothesis rather than its rivals? For a query $A⇝B$, we define *structural support* as the posterior mass of mechanisms in which $A$ reaches $B$ by a directed path. This is not a retrieval rank, direct-edge score, or MAP graph decision: support can be distributed across many compatible mechanisms. Our main result is a local certificate for this global support quantity. 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 gives a boundary range $$\begin{gathered} [ \\ el{l}_{L,m},u_{L,m}] \end{gathered}$$, and a certified tail bound ${\bar{r}}_L$ accounts for longer witnesses: $$\begin{gathered} p_{AB}\in [ \\ el{l}_{L,m},\min \{1,u_{L,m}+{\bar{r}}_L\}] \end{gathered}$$. For coupled rivals, the same boundary-conditioned calculations yield a joint feasible set rather than only independent coordinate intervals. We convert these certificates into resolve-or-abstain decisions: an action is resolved only when it wins throughout the certified support set. Under valid certificates, a resolved action is the unique strict utility maximizer inside the declared fixed model, action set, and utilities; otherwise, the solver abstains and reports whether boundary, tail, computation, evidence, or outer-model uncertainty blocks resolution. On controlled and biologically scaffolded finite-posterior records, the implementation has zero endpoint containment misses and zero false fixed-model resolutions. In a coupled-rival diagnostic, joint feasible sets resolve $14/24$ cases versus $6/24$ for scalar boxes, with no false commitments.