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

Moriba Kemessia Jah

cs.ITMar 10, 2026

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

Authors: Moriba Kemessia Jah

Organizations: Black Swan Research Group, GaiaVerse, Ltd. · Jah Decision Intelligence Group, Aerospace Engineering & Engineering Mechanics, The University of Texas at Austin

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.

Figures & tables

Step	$\sigma_{k}$	$\log\det$	$N_{t}$	Regime	Claim A		Claim B
					rand	swap	rand	swap
1	0.970	$-17.80$	–	C	P	P	P	P
2	0.941	$-13.33$	–	C	P	F(0.025)	P	F(0.019)
3	0.913	$-9.42$	–	C	P	F(0.028)	P	F(0.020)
4	0.885	$-6.07$	–	C	P	P	P	P
5	0.859	$-3.13$	–	C	P	F( $<$ 0.001)	P	P

Table 1: Lemma 3 diagnostic, steps 1–18: initial contraction, diffusion, first collapse. P/F = pass/fail; parenthetical = gap magnitude (nats). C = contraction (

\log\det<0

), D = diffusion (

\log\det>0

Step	$\sigma_{k}$	$\log\det$	$N_{t}$	Regime	Claim A		Claim B
					rand	swap	rand	swap
19	0.561	$-50.89$	82	C	P	F(0.060)	P	F(0.046)
20	0.544	$-53.16$	82	C	P	P	P	P
21	0.528	$-56.15$	82	C	P	P	P	P
22	0.512	$-58.63$	81	C	P	P	P	P
23	0.496	$-61.02$	81	C	F(0.051)	F(0.175)	P	F(0.113)

Table 2: Lemma 3 diagnostic, steps 19–52: deep contraction, second collapse, re-stabilization.

N_{t}=N_{\mathrm{target}}

; † marks the second stress event.

Epistemic Uncertainty

Epistemic uncertainty is uncertainty arising from limited knowledge or model support, rather than irreducible randomness in data.

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The Geometry of Knowing: From Possibilistic Ignorance to Probabilistic Certainty -- A Measure-Theoretic Framework for Epistemic Convergence

Moriba Kemessia Jah

Black Swan Research Group, GaiaVerse, Ltd., Austin, TX 78728, USA · Jah Decision Intelligence Group, Aerospace Engineering & Engineering Mechanics The University of Texas at Austin, Austin, TX 78712

Imprecise Probability Epistemic Uncertainty Uncertainty Quantification

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This paper develops a measure-theoretic framework establishing when and how a possibilistic representation of incomplete knowledge contracts into a probabilistic representation of intrinsic stochastic variability. Epistemic uncertainty is encoded by a possibility distribution and its dual necessity measure, defining a credal set bounding all probability measures consistent with current evidence. As evidence accumulates, the credal set contracts. The epistemic collapse condition marks the transition: the Choquet integral converges to the Lebesgue integral over the unique limiting density. We prove this rigorously (Theorem 4.5), with all assumptions explicit and a full treatment of the non-consonant case. We introduce the aggregate epistemic width W, establish its axiomatic properties, provide a canonical normalization, and give a feasible online proxy resolving a circularity in prior formulations. Section 7 develops the dynamics of epistemic contraction: evidence induces compatibility, compatibility performs falsification, posterior possibility is the min-intersection of prior possibility and compatibility, and a credibility-directed flow governs support geometry contraction. This is not belief updating. It is knowledge contraction. Probability theory is the limiting geometry of that process. The UKF and ESPF solve different problems by different mechanisms. The UKF minimizes MSE, asserts truth, and requires a valid generative model. The ESPF minimizes maximum entropy and surfaces what evidence has not ruled out. When the world is Gaussian and the model valid, both reach the same estimate by entirely different routes -- convergent optimality, not hierarchical containment. We prove this (Theorem 9.1) and compare both on a 2-day, 877-step orbital tracking scenario. Both achieve 1-meter accuracy. The UKF is accurate but epistemically silent. The ESPF is accurate and epistemically honest.

Abstract

Epistemic Uncertainty

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