Gödelian Constraint on Epistemic Freedom (GCEF): A Topological Theory of Embedded Cognition and Epistemic Singularities

This paper introduces the Gödelian Constraint on Epistemic Freedom (GCEF), a formalframework for understanding the limits of knowledge faced by embedded cognitive agents.Drawing from Gödel’s incompleteness theorems, Turing undecidability, Kolmogorov complexity,Lawvere’s fixed-point theorem, and insights from physics, cognitive science, and epistemology,GCEF proposes that certain classes of problems—termed E-class—are structurally unverifiablefrom within the systems they arise. These problems exhibit a topological occlusion: the globalstructure required to resolve them lies beyond the modeling capacity of any agent constrained tolocal information and recursive cognition. I argue that this constraint is not merely technicalor practical but topological and epistemologically generative. From the interpretation crisis inquantum mechanics to the enduring resistance of P vs NP and the continuum hypothesis, I showthat E-class problems reveal a structural horizon of epistemic embeddedness. GCEF provides ametatheoretical account of why certain problems remain persistently intractable and why agentsmust simulate coherence and freedom under conditions of occlusion. The result is a unifiedaccount of epistemic failure, simulation, and symbolic constraint across disciplines—and a callfor new formal tools to chart this topology.