Certified localization of reaction deletions in autocatalytic networks: ranked support witnesses, witness selection, and exact robustness laws

A reflexively autocatalytic and food-generated (RAF) set is the standard combinatorial model of a self-sustaining reaction network. We study what happens to the maximum RAF of a finite catalytic reaction system when reactions are deleted, from three directions. First, we introduce ranked support witnesses: for every reaction of the baseline maximum RAF, a set of producer parents whose ranks decrease along reactant edges, together with one unrestricted catalytic parent. We prove that the part of the baseline not reachable from a deletion along selected edges survives every deletion, and that the exact new maximum RAF is recovered by one residual computation inside the reachable cone. This localizes any deletion query to a source-checkable region and admits an exact charge-model theorem: on an explicit unbounded family, a packet evaluator beats a specified fresh evaluator by any prescribed constant factor. Second, we ask which witness to store. The reachable cone always contains the true loss, and the excess above that intrinsic floor is the only thing witness selection can change. Every single deletion admits a perfect witness, the true loss equals the intersection of all witness cones, singleton dependence is a preorder, and synergistic loss under combined deletions prevents any one witness from being perfect for every singleton. Weighted selection is exactly separable on a one-layer source class, becomes NP-complete after one downstream aggregator through an exact reduction from set cover, is repaired by portfolios that keep exact answers through a residual solve and admit the classical greedy coverage guarantee, and yet can require $2^{k}$ witnesses for universally exact regions on a source with $2k+1$ reactions although two suffice for all singletons. Third, for independent random deletion we derive exact robustness laws: the first derivative of expected surviving size is the total singleton loss; the second derivative is twice the sum, over pairs, of overlapping singleton damage minus cooperative pair damage; on functional sources with one alternative catalytic site, two forward exposure sets decide survival under every availability set, yield the complete classification of inclusion-minimal external cuts, an exact objective for choosing one catalyst addition, and an exact variance formula whose overlap count is the obstruction to concentration. Disjoint catalytic modules and a common gateway separate size bias from collective criticality and concentration from persistent fluctuations. The finite statements are compiled in Lean 4 against Mathlib with warnings promoted to errors and no admitted proofs; the few hand-proved consequences are listed explicitly. The results concern structural RAF survival, not kinetic persistence.