Temporal Dynamics of Distinguishability Collapse: On the Breakdown of the Schwartau Inequality under Generative AI

This paper establishes the Temporal Information Collapse Theorem (Theorem 4.X), the dynamic counterpart of the Distinguishability Collapse Theorem [Rouxel 2026]. Under compression of adversary adaptation tempo below the structural floor of defender observation tempo, mutual information between the sampled trajectory and adversary intent, conditional on the confusable class, is bounded by the bilateral density ratio of the Dual-Use Trajectory Realizability Hypothesis. 
In the strong-collapse regime the bound vanishes; in the prior-dominated regime it reduces to the Axelsson base-rate bound. 

By the Data Processing Inequality, this impossibility is architecture-invariant: no sample-based detector — reconstructive or otherwise — recovers intent 
information from a collapsed channel. Two sampling-theoretic mechanisms realize the collapse: aliasing (Nyquist-Shannon violation) and sub-resolution (Slepian-Pollak-Landau dimensionality). A complementary Wienerian statistical floor (Theorem 5.0) bounds observation tempo from below, closing the viable observation window under sustained genAI compression. Schwartau's P_t > D_t + R_t inequality is shown to be a special case of the detectability condition, structurally unsatisfiable in the collapse regime.

Paper 2 of the Distinguishability Collapse Theorem series.