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November 27, 2025Open Access

A Geometric Church–Turing Principle and a Meta-Level Separation of P and NP

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Abstract

Under the Geometric Church–Turing Principle in Universal Variation Theory (UVT), polynomial-geometric complexity classes PUVT and NPUVT are defined, with the Universal Convexity–Gap Theorem and NP-depth Lemma establishing a strict separation PUVT ⊊ NPUVT due to incompatible curvature bounds for NP-complete families.

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Anonymous (2025) studied this question.

synapsesocial.com/papers/694031da2d562116f290721a https://doi.org/10.5281/zenodo.17729212

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Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1A Geometric Church–Turing Principle and a Meta-Level Separation of P and NP2025
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4The Universal Horizon Conjecture: Geometric and Experimental Evidence for P ≠ NPOriginal Research · 2026
5On the Internal Geometry of NP-Completeness: A Partial Order on NPC via Algorithmic Decomposition and Representation-Theoretic ObstructionsOriginal Research · 2026

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