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

TL;DR

This paper introduces the Epistemic Support-Point Filter (ESPF), a novel estimator that minimizes maximum entropy to surface what is not proven impossible, unifying possibilistic and probabilistic frameworks within estimation theory.

Contribution

The paper proves the ESPF's optimality as a recursive estimator, unifies possibilistic and probabilistic approaches, and provides numerical validation demonstrating its unique epistemic properties.

Findings

ESPF is the unique optimal epistemic estimator within evidence-only filters.

Possibility and probability are unified as different geometries of ignorance.

Numerical validation shows stress manifests through necessity saturation and surprisal escalation.

Abstract

This paper proves that the Epistemic Support-Point Filter (ESPF) is the unique optimal recursive estimator within the class of epistemically admissible evidence-only filters. Where Bayesian filters minimize mean squared error and are driven toward an assumed truth, the ESPF minimizes maximum entropy and surfaces what has not been proven impossible -- a fundamentally different epistemic commitment with fundamentally different failure modes. Two results locate this theorem within the broader landscape of estimation theory. The first is a unification: the ESPF's optimality criterion is the log-geometric mean of the alpha-cut volume family in the Holder mean hierarchy. The Popperian minimax bound and the Kalman MMSE criterion occupy the p=+inf and p=0 positions on the same curve. Possibility and probability are not competing frameworks: they are the same ignorance functional evaluated under different alpha-cut geometries. The Kalman filter is the Gaussian specialization of the ESPF's optimality criterion, not a separate invention. The second result is a diagnostic: numerical validation over a 2-day, 877-step Smolyak Level-3 orbital tracking run shows that possibilistic stress manifests through necessity saturation and surprisal escalation rather than MVEE sign change -- a direct consequence of the Holder ordering, not an empirical observation. Three lemmas establish the result: the Possibilistic Entropy Lemma decomposes the ignorance functional; the Possibilistic Cramer-Rao Bound limits entropy reduction per measurement; the Evidence-Optimality Lemma proves minimum-q selection is the unique minimizer and that any rule incorporating prior possibility risks race-to-bottom bias.