On the Nature of Logic and the P vs NP Prob-lem

We prove P = NP by demonstrating that NP-completeness arises from an avoidable computational overhead: the exponential cost of constructing higher-order logical (HOL) frameworks from first-order primitives. By formalizing the logical realizability ofall NP problems within HOL, we show these problems become polynomial-time solvable when their logical structure is known in advance. The apparent hardness of NP problems is thusrevealed as an artifact of forcing deterministic Turing machines to reconstruct HOL representations from Boolean logic (∧, ∨, ¬)rather than an intrinsic property of the problems themselves. Key to this result is the Perspective-Dependent Logical Realizabil-ity Theorem, which establishes that:1. Every NP problem’s HOL formulation has an equivalent first-order logic (FOL) representation. 2. A deterministic Turing machine (DTM) can solve any NP problem in polynomial time if provided with its HOL framework. 3. The P ≠ NP separation occurs only when DTMs are restricted to bottom-up FOL construction. We validate this with Boolean satisfiability (SAT), proving its polynomial-time tractability under HOL and introducing Deciding by Zero (DbZ) as a further example of how logical reframing eliminates classical intractability. This work does not merelysuggest P = NP as a possibility but demonstrates it as a direct consequence of logical representation theory.