A Cone-Based Certificate for Latent Dimensional Adequacy in Monotone-Output Systems

We establish a geometric falsification criterion for the class of single-latent, monotone-output observable models. A normalized cone-departure indicator quantifies whether observed multi-modal trends are directionally compatible with a scalar latent driver. We prove that persistent departure from the monotonicity cone, beyond explicit noise-dependent thresholds, certifies incompatibility with the order-1 monotone-output realization class. The result is strictly contrapositive: directional coherence does not imply scalar dynamics. A probabilistic extension under sub-Gaussian noise yields exponential decay of false falsification probability. The framework is applied to immunotherapy response monitoring, where…