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What if P + NP = 1? A Multilayer Co-Evolutionary Hypothesis for the P vs NP Millennium Problem

by Rogério Figurelli

Posted: July 8, 2025
Server: Preprints.org
DOI: 10.20944/preprints202507.0640.v1

This paper proposes the symbolic formulation P + NP = 1 as a multilayer co-evolutionary framework for rethinking complexity in the context of the P vs NP Millennium Problem. Rather than advancing a formal proof, it introduces the Wisdom Turing Machine (WTM) as a conceptual architecture for testing this hypothesis through cycles of reflection, intentional curvature, compression, and ethical alignment. The WTM serves as a proof-of-concept platform for exploring how transparent and ethically guided reasoning systems might engage complexity not as an adversary, but as a co-evolving partner in inquiry. The machine is a symbolic extension of Turing’s classical model, designed to provide explainability by design in artificial general intelligence (AGI) and to support co-evolutionary reasoning across complex domains. Inspired by the hypothesis that P + NP =

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