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Exogeneity, Scalability Bounds, and the Geometry of Governance: A Field-Theoretic Account of Why Epistemic Systems Require External Reference Frames

Authors: Templet, Jessica;

Exogeneity, Scalability Bounds, and the Geometry of Governance: A Field-Theoretic Account of Why Epistemic Systems Require External Reference Frames

Abstract

We extend the scalar-tensor field theory of belief dynamics developed in Templet (2026d) to address three open problems. First, we derive a three-regime degradation structure for belief systems under increasing contradiction load, showing that the transition from autonomous self-healing to governance failure is detectable in advance via the Fiedler value derivative d(lambda_2)/dt. Second, we identify and resolve the Density Paradox: the human-write-only governance zone is by design sparsely populated, making its local Planck scale anomalously large and its surgery threshold anomalously insensitive. We resolve this by replacing the population-based Planck scale with an inertia-weighted form ell_P(x_i) = (sum_j lambda_j * exp(-d(x_i,x_j)))^{-1/2}, restoring correct zone-ordering of surgery sensitivity without new axioms. Third, we prove a critical scaling bound |V|*: since contradiction generation scales as O(|V|^2) while human resolution bandwidth is O(1), there exists a critical graph size above which single-authority governance fails. We then define exogeneity geometrically and show that the effective exogenous bandwidth of a governance system equals the epistemic independence rank of its anchor set, not its cardinality. A thousand correlated anchors provide no more exogenous bandwidth than one.

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