The Epistemic Support-Point Filter: Jaynesian Maximum Entropy Meets Popperian Falsification

Abstract: The Epistemic Support-Point Filter (ESPF) was designed around a single epistemological commitment: be quick to embrace ignorance and slow to assert certainty. This paper proves that this commitment has a precise mathematical form and that the ESPF is the unique optimal filter implementing it within the class of epistemically admissible evidence-only filters. The ESPF synthesizes two complementary principles acting at different phases of the recursion. In propagation, it enacts Jaynesian maximum entropy: the support spreads as widely as the dynamics allow, assuming maximal ignorance consistent with known constraints. In the measurement update, it enacts Popperian falsification: hypotheses are eliminated by evidence alone. Any rule incorporating prior possibility is strictly suboptimal and risks race-to-bottom bias. The optimality criterion is possibilistic minimax entropy: among all evidence-only selection rules, minimum-q selection minimizes log det(MVEE), the worst-case possibilistic entropy. Three lemmas establish the result: the Possibilistic Entropy Lemma identifies the ignorance functional; the Possibilistic Cramér-Rao Lemma bounds entropy reduction per measurement; the Evidence-Optimality Lemma proves minimum-q selection is the unique minimizer. The ESPF differs from Bayesian filters by minimizing worst-case epistemic ignorance rather than expected uncertainty. The Kalman filter is recovered in the Gaussian limit. Numerical validation over a 2-day 877-step Smolyak Level-3 orbital tracking run confirms the regime structure under both nominal and stress conditions.