We introduce the first persistence diagram classifier with computable per-prediction correctness guarantees. Each prediction is accompanied by a certificate—a scalar inequality checkable in O(1) from training statistics alone—that, when satisfied, ensures the prediction is correct with probability at least (1 - alpha). The certificate is made possible by establishing a learnable, closed-form lower distortion bound on the persistence landmark embedding of Mitra and Virk. Existing vectorizations (persistence images, landscapes, kernels) provide only Lipschitz upper bounds, leaving no guarantee that topologically distinct diagrams remain distinguishable after embedding. Our PLACE fills this gap through bi-Lipschitz guarantees. We formulate supervised metric learning as population RatioCut minimization over scale measures and kernel weights, solving via alternating projected gradient descent with provable convergence. The learned metric achieves competitive classification accuracy on graph benchmarks while providing what no other method can: a positive distortion certificate for every prediction.