Single shared SDP for all target classes

1. Integration point: modify a neural-network robustness verifier after interval bound propagation and before the SDP solver. The network forward equations, perturbation set, and lifted quadratic constraints remain unchanged; only the objective and output-layer constraints are changed. For each correctly classified sample (x,y), create one SDP instance with shared variables for z_0,...,z_K and one scalar t. Add K-1 linear constraints t <= z_K[y]-z_K[j] instead of launching K-1 independent targeted instances. 2. Pseudocode: compute interval bounds and the existing SDP relaxation R_SDP(x,epsilon); allocate t; for j in classes excluding y, add_constraint(t <= logit_y - logit_j); solve minimize(t); return certified = (t_star >= 0). If the solver supports multiple right-hand sides, batch the K-1 output constraints in one matrix. 3. Computed from the paper's mathematics: the epigraph reduction and the nonnegative-certificate test. Estimated empirically: solver factorization reuse, memory, and whether shared presolve actually reduces time; compare against separate targeted solves. 4. First experiment: use a small 4-layer ReLU MLP or CNN on MNIST and CIFAR-10, then an ImageNet-100 classifier with the same verifier and epsilon. Measure total certification time, peak memory, certified accuracy, and t_star against K-1 separate SDP runs. The expected signal is near-identical certificates and at least a 2x speedup for 100 classes, with larger gains when SDP setup or factorization dominates.