Artificial Intelligence and Electrical & Electronics Engineering: AIEEE Open Access
Circulatory Inference, Spectral Rigidity, and Zero-Entropy Computation: An Einstein-Dirac Framework Linking Riemann Zeros, Stability, and Complexity
Abstract
Chur Chin
We propose a unified mathematical framework for stable inference and spectral rigidity based on circulating parameter dynamics. The central idea is that reliable reasoning arises not from convergence or chaotic exploration, but from constrained circulation enforced by geometric and operator-theoretic principles.
We formulate inference dynamics on a curved parameter manifold governed by an Einstein-type equation, where curvature encodes semantic stress and attention density. Circulation emerges naturally from geometric conservation laws via the Bianchi identity. A Dirac-type operator acting on this manifold generates unitary, entropy-neutral evolution, preventing overconfident fixed-point collapse while avoiding chaotic branching.
Within this framework, we establish a zero-entropy impossibility theorem: deterministic circulatory dynamics cannot resolve NP-complete problems in polynomial time unless P=NP. We further connect this circulatory spectral confinement to the Hilbert–Pólya program and formulate a Dirac–Selberg conjecture, interpreting the Riemann zeta zeros as globally consistent phase modes.
The resulting Einstein–Dirac unification links hallucination suppression, complexity-theoretic limits, and number-theoretic spectral rigidity under a common geometric principle: stability arises from curvature-balanced circulation.