When Learning Can Safely Forget: Transition-Faithful Certificates for Adapter State

An inactive direction can disappear from predictions while still determining the next learning update. We construct state release that preserves an unfinished learner's update rule. Future-inactivity permission fixes omitted gate outputs; summaries closed under the remaining optimizer reads preserve their residual effects. Common radial dynamics retain one energy, complete linear-channel queries are characterized by a Gram matrix, and distinguishable quadratic modes retain separate energies. For the radial gated reference, a future cross-entropy budget yields an optimal adverse-probability relaxation; transporting a reliable dual cost reduces repeated checking. The reduction preserves declared learning events through adaptive release, rejection, rollback and corresponding-point restoration. On fixed Letter and CIFAR executions, compilation removes over 96% of dual evaluations while retaining over 90% of fresh-check release integrals. Paired trials, same-candidate interventions and fixed-mode dimension tests validate the information that must be retained. Same-checkpoint permission comparisons identify the additional positive authorizations from loss information, while complete-record measurements quantify storage gains and their acquisition costs.