Which Local Guarantees Compose? A Universal Factorization Theorem for Graph-Indexed E-Certificates on Adaptive Execution Graphs

Adaptive agentic systems generate random execution graphs through routing, joining, filtration change, and stopping. We ask which local uncertainty objects remain valid under such adaptive composition. First, ordinary local marginal-coverage and expected-risk guarantees are not closed under predictable routing, even on finite depth-(2) graphs. Next, when local null classes are generated by finitely many bounded predictable constraints, every pointwise-admissible local e-certificate is fiberwise quasi-surely affine in the local constraints, and along any admissible law the coefficients admit a predictable selection. Under trace-generated normal form, serial precision, admissible same-null joins, and conditionally valid lifts, every universally valid graph calculus factors through a game-martingale serial update, weighted arithmetic averaging at same-null joins, and, under value-based lifts, adjusters across filtration changes. For the canonical full-betting factorization we obtain an exact log-evidence tax at symmetric joins and a lift-dependent lower bound. Rank-based conformal e-predictors and bounded-risk local modules therefore compose globally once expressed through the common local e-certificate interface.