What question did this study set out to answer?

The study aims to establish a geometric framework to differentiate complexity classes, particularly P and NP-complete problems.

April 17, 2026Open Access

The Universal Horizon Conjecture: Geometric and Experimental Evidence for P ≠ NP

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This research demonstrates a geometric distinction for P and NP-complete problems, suggesting a universal obstruction in computational complexity.

The study aims to establish a geometric framework to differentiate complexity classes, particularly P and NP-complete problems.
Developed a geometric framework for computational complexity using energy descriptors.
Conducted topological analysis via Wasserstein distance and persistent homology.
Analyzed NP-complete problems like 3-SAT, MAX-CUT, and Vertex Cover.
Utilized statistical tests to confirm the significance of findings.
A universal ring geometry was confirmed with an inner radius approximately 0.31.
Wasserstein distance revealed a clear topological distinction between P and NP-complete problems.
All p-values were less than 0.001, confirming statistical significance.

Radu-Daniel Derscariu (2026) studied this question.

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This research demonstrates a geometric distinction for P and NP-complete problems, suggesting a universal obstruction in computational complexity.