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

arXiv: https://arxiv.org/abs/2603.10065 · HTML: https://mlsanity.com/paper/2603.10065/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 21 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 1 of 1)

- [The Epistemic Support-Point Filter (ESPF): A Bounded Possibilistic Framework for Ordinal State Estimation](https://mlsanity.com/paper/2508.20806/) (2025)

## Built on by (most cited first, 1 of 1)

- [The Geometry of Knowing: From Possibilistic Ignorance to Probabilistic Certainty -- A Measure-Theoretic Framework for Epistemic Convergence](https://mlsanity.com/paper/2604.09614/) (2026)

## Abstract (arXiv)

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.