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April 19, 20260 citationsOpen Access

Establishing the Identity of Time Complexity Classes P Versus NP

Formal Submission for the Problem Solution P versus NP

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Authors

ACAlejandro Armando CAPARÓ

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Overview

Formal submission establishes P versus NP relationship using structural resonance, indicating NP problems can be solved in polynomial time.

Key Points

  • To establish the identity of time complexity classes P and NP using the principle of Structural Resonance.
  • Defined time complexity classes and the traditional assumptions about P and NP.
  • Introduced a Resonance Operator to analyze NP-complete problems.
  • Demonstrated through mathematical foundations how topological disconnect affects problem-solving.
  • Showed that NP-complete problems can be solved in polynomial time.
  • Illustrated the gap between finding and verifying solutions is a topological issue rather than a logical one.
  • Provided a new perspective on the relationship between problem topology and solution space.
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Cite This Study

Alejandro Armando CAPARÓ (2026) studied this question.

synapsesocial.com/papers/69e474b6010ef96374d902c8https://doi.org/10.5281/zenodo.19633596
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Also Consider

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

  1. 1Formal Submission for the Problem Solution P versus NP2026
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