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

This preprint proposes the Gödelian Constraint on Epistemic Freedom (GCEF), a unifying theoretical framework for understanding why certain problems across mathematics, cognition, physics, and artificial intelligence resist resolution by embedded agents. Drawing from Gödel's incompleteness theorems, Turing uncomputability, Lawvere's fixed-point theory, and thermodynamic constraints on cognition, GCEF argues that epistemic occlusion is not incidental — it is structural.

The central claim is that embedded agents cannot construct complete models of the systems they inhabit due to topological constraints, recursive simulation limitations, and energy-bound inference. This gives rise to a novel problem class — “E-class” problems — characterized by local verifiability but global inaccessibility.

The paper traverses foundational mathematics, alignment theory, cognitive science, ethics, and governance, offering speculative applications in climate policy, AGI safety, and epistemic instability. While deeply interdisciplinary, the argument is rigorously formal in its core logic and invites further development through homotopy theory, sheaf-theoretic modeling, and higher-order categorical semantics.

GCEF is not a replacement for existing theories of bounded rationality or computational complexity; it is a topological frame that explains why these limits recur across domains. The work is intended as a provocation, not a conclusion — an initial topology of embedded knowing in an era approaching epistemic singularity.

Related Work:
For a speculative, narrative exploration of the implications of GCEF—written for a broader philosophical audience—see:
“Transcendence is Entropy in Drag” (Substack essay): https://substack.com/home/post/p-168720593