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This work aims to establish a comprehensive empirical basis for the Universal Horizon Conjecture that asserts P ≠ NP.

April 22, 2026Open Access

The Universal Horizon Conjecture: Multi-Metric Geometric, Topological, and Thermodynamic Experimental Evidence for a P ≠ NP Barrier in 3‑SAT

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Experimental validation finds P ≠ NP barrier in 3-SAT, indicating fundamental physical limitations.

This work aims to establish a comprehensive empirical basis for the Universal Horizon Conjecture that asserts P ≠ NP.
Utilized multi-metric analysis integrating static geometry, topology, thermodynamics, and information theory.
Conducted experiments using persistent homology, replica exchange, and alpha complexes to analyze 3-SAT.
Evaluated fragmentation and complexity through statistical methods and thermodynamic properties.
Identified 438 persistent two-dimensional holes in 3-SAT indicating a topological distinction from 2-SAT.
Demonstrated strong fragmentation in 3-SAT via overlap gap ratios, confirmed by statistical tests.
Found direct experimental evidence for a thermodynamic barrier with low temperature signatures in 3-SAT.

Radu-Daniel Derscariu (2026) studied this question.

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