Auditable Exact Lower Bounds for Trajectory QCQPs via a Rational Riccati Sweep

Exact-rational certification of trajectory quadratically constrained quadratic programs with neighboring-stage quadratic penalties and sampled keep-out constraints. A supplied rational multiplier gives a global lower bound through a bordered positive-semidefiniteness test; a separately checked feasible trajectory gives an upper bound. The paper proves a band-preserving rational Riccati-style sweep, distinguishes general bound verification from exact closure under rational-witness hypotheses, and reports selected numerical proposals and constructed closing families. Current implementations use dense storage. The certificate concerns the rational problem at its sampled states.