The Geometry of Underdetermination: A Variational Principle for Discrimination

A central epistemic question is how quickly evidence can dissolve underdetermination when rival hypotheses share a common disturbance process. Holding total disturbance power fixed, we prove a regime-conditional result: in robust equalizer settings, fully whitened disturbance is the least informative channel for discrimination, while structured departures increase separability and speed posterior concentration. The claim is not that adding noise helps; it is that channel symmetry levels contrast, whereas structured asymmetry preserves contrast where hypotheses differ. We develop a theorem stack with a variational characterization, quantitative curvature gains, and a dual design rule for shaping effective disturbance profiles. We also introduce a frequency-local relevance diagnostic for where discriminative evidence resides, extend the principle to point-process settings, and interpret the results in a coalgebraic possible-worlds account of inquiry as approximate right inversion.