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The Hybrid Piecewise Heuristic Equation (HPHE) and the P vs NP Problem. | Synapse

January 16, 20260 citationsOpen Access

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The Hybrid Piecewise Heuristic Equation (HPHE) and the P vs NP Problem.

RCRicky Cespedes

Key Points

The aim is to bridge the gap between P and NP by introducing the Hybrid Piecewise Heuristic Equation framework.
Introduced the Hybrid Piecewise Heuristic Equation (HPHE) framework.
Provided a formal proof of C^1 continuity.
Conducted empirical testing using 'Evil 50' benchmark tests.
Demonstrated the collapse of NP-complete transition points through empirical evidence.
Established a mathematical connection between P and NP confirmed by the HPHE framework.

Abstract

(The paper is already being reviewed by Annals of mathematics as we speak) This paper introduces the Hybrid Piecewise Heuristic Equation (HPHE) framework, establishing a mathematical bridge between P and NP. We provide a formal proof of C¹ continuity and present empirical evidence from the 'Evil 50' benchmark tests demonstrating the collapse of NP-complete transition points.

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Ricky Cespedes (Wed,) studied this question.

synapsesocial.com/papers/6969d4c3940543b977709a0b https://doi.org/https://doi.org/10.5281/zenodo.18238549

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