P Equals NP: Three Hypotheses

P Equals NP: A Philosophical and Algorithmic Synthesis of Three Foundational HypothesesAbstractThis paper explores the longstanding question of whether P equals NP through a novel philosophical and symbolic approach grounded in three core hypotheses: (1) the Hypothesis of Double Negation, (2) the n-1 Hypothesis, and (3) the Hypothesis of Language and Mind. Each hypothesis contributes a unique perspective on the relationship between verifiability, computability, and the structure of logic and language. Through the construction of symbolic analogies and a proposed algorithmic framework, we argue that these hypotheses converge to form a theoretical foundation that supports the claim that P = NP. This paper does not merely rely on computational definitions but seeks to bridge abstract logical reasoning, linguistic structure, and algorithmic behavior.