When Cached Proofs Certify an Evidence Budget

A cached proof can remain valid while failing to certify a new evidence budget: repricing may make its support unaffordable even when an omitted alternative still fits. We formalize reusable budget certification in finite signed-Horn theories with canonical acquisitions charged once. Complete minimal support frontiers answer exact residual-cost queries; exact whole-proof lookup under arbitrary positive prices requires every minimal support. Under bounded prices and evidence exclusions, cache distortion equals a constrained Hamming covering radius, giving storage bounds and separate thresholds for cost approximation and status coverage. Factored representations can preserve these alternatives compactly: a family with exponentially many minimal supports has a linear-size exact solver, while tree selection can incur a linearly growing cost ratio even after duplicate purchases are removed. On a fixed ProofWriter prefix, independent exhaustive closure verifies 1,864 resource queries and 5,592 budget decisions. Retaining initial infeasibility and minimum-cardinality information resolves 4,240 decisions left unresolved by a one-support cache with its original bounds. Yet 26 feasible budgets still require an affordable witness that the cache omitted. Reusable reasoning therefore requires preserving both the conclusions that certify rejection and the alternatives that enable acceptance after resource changes.