Work

Formal Submission for the Problem Solution P versus NP

Year: 2026

Type: article

Abstract: This submission establishes the identity of the time complexity classes P versus NP through the principle of Structural Resonance. It demonstrates that the gap between finding a solution and verifying it is not a fundamental property of logic, but a result of a topological disconnect. By applying a Resonance Operator (R) NP -complete problems are shown to be solvable in polynomial time. 1. Mathematical Foundations The traditional assumption of a divergence between finding a solution (P) and verifying it (NP) is a result of a disconnect between the topology of the problem and the solution space. This proof demonstrates that an NP complete problem is solvable in polynomial time by applying a Resonance Operator R.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.19633595

Author: CAPARÓ, Alejandro Armando

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7154783000

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