Certified Selective Tracking of Moving KKT Systems

A small KKT residual can arrive after a deadline or correspond to the wrong active set or stationary branch. We introduce Certified Selective Tracking (CST), which delivers a result only when both deadline and branch-identity certificates hold. Its Geometry-aware Certified Trackability (GCT) instantiation encloses active-set events under an explicit uncertainty set. Strict separation of the event tubes certifies event membership, order, and endpoint identity. Within a finite candidate family, selection maximizes delivery availability under the same strict certificate contract; simultaneous envelope coverage bounds false-delivery risk. PTIF-KKT supplies inversion-free candidate updates. On 470 held-out PJM-driven arrivals in a constructed separable QP, public interval residual verification retains 134 deliveries at 5% curvature uncertainty with zero observed false identities. A true-model verifier retains 186, but 52 of these fail at an admissible curvature corner. Point-event selection makes 32 endpoint-label errors. A separate eight-dimensional heuristic measures agreement with offline multistart labels, not nonlinear branch certification or general solver superiority.