Parametric Neural Lyapunov Verification with a Shared Partition

▎ Independent verification characterizes the disturbance a neural Lyapunov certificate tolerates by rebuilding the branch-and-bound computation at every disturbance size and every candidate level. We show that on every state box the residual is affine in the disturbance size and in the decrease rate, with coefficients that depend on neither, so bounding those coefficients once gives a valid residual bound for every size and rate, and one adaptive partition of the state region serves the whole sweep. The same stored bounds, with validated points, bracket the smallest certificate level that survives a given disturbance size, from above and below and at every size in the interval rather than at the tested sizes alone, at a measured extra cost. On a power-system swing model and a Van der Pol oscillator the shared partition answers the same sequence of checks with 5.75 to 8.42 times fewer bound calls than independent verification. On seven released neural controllers for four plants, from two published pipelines, it uses 2.39 to 15.61 times fewer. In both comparisons it preserves every level the independent run certified. The same stored bounds answer decrease rates at or below the trained rate without a further bound call, and the advantage grew with the state dimension on a family of coupled oscillators. The partition is computation that branch-and-bound verification already performs, kept and reused instead of discarded with the answer.