M15: A Multiscale Post-Hoc Protocol for Auditing the Geometric Fidelity of Latent Projections

Low-dimensional (2D) visualization of semantic latent spaces or influence networks is acritical tool for decision-making in analytical, forensic, and institutional contexts. However,these visual maps typically lack formal geometric fidelity guarantees. We present a multiscalepost-hoc protocol to audit the geometric fidelity of 2D latent projections, combining threecomplementary layers: (i) the Mantel Test for global metric fidelity, (ii) a 0-dimensionalpersistence profile (PH0 Profile) over the Minimum Spanning Tree (MST) for hierarchicaltopological stability, and (iii) a Fissure Index based on community permutations to detect localsemantic-structural dissonance. An adversarial benchmark of 1,000 Monte Carlo simulations(10 scenarios, N = 100 nodes) and a comparative ablation study against classical metrics(Venna & Kaski, 2001; Lee & Verleysen, 2007) demonstrate that the combined classifierachieves 95.9% accuracy, 96.1% sensitivity, and 95.0% specificity. An anonymized case studyon empirical data (N = 457 actors) illustrates the protocol’s application, without constitutinga causal validation or generalization beyond the studied domain.