A Global and Unconditional Resolution of the P vs NP Problem via Formal Complexity-Class Bridge
Year: 2025
Type: conference-paper
Abstract: This paper presents a complete resolution of the P vs NP problem using the Global Bridge Framework as its analytic foundation. By constructing a dedicated Projection API for NP verification structures, we embed nondeterministic certificate spaces (e.g., 3-SAT spike encodings) into holomorphic annulus spaces H∞H_\inftyH∞ and analyze the corresponding lifted operators. We prove that NP-complete languages induce three independent analytic obstructions: Norm divergence — certificate kernels have ℓ1\ell^1ℓ1-norms growing as 2n2^n2n. Radius-of-convergence growth — natural boundary behavior violates Montel compactness. Categorical obstruction — nondeterministic coalgebras fail to embed into deterministic algebras. Each obstruction independently breaks the fixed-point correspondence of the bridge, preventing a deterministic polynomial-time fixed point in the analytic host space. This forces class separation, giving P≠NP\mathbf{P} \neq \mathbf{NP}P=NP. The result is CSP-compatible: all fixed-point and contraction arguments are formally verifiable within the Global Bridge framework [Global Bridge DOI: https://doi.org/10.5281/zenodo.16751646]. This work provides a rigorous analytic–categorical proof of P≠NP\mathbf{P} \neq \mathbf{NP}P=NP, extending the reach of the Global Bridge to computational complexity. Note on Related Work:This result complements my earlier paper Φ‑Field Resolution of P vs NP: Computational Complexity as Recursive Emergence Transcendence (https://doi.org/10.5281/zenodo.16623960), which established the separation P≠NPP \neq NPP=NP classically and P=NPP = NPP=NP in recursive emergence frameworks. The present work, by contrast, gives a CSP‑compatible separation via the Global Bridge and Projection API, operating entirely within classical analytic and categorical methods. The Φ‑Field resolution uses a trans‑classical mechanism (recursive emergence), whereas the current proof remains entirely inside the CSP framework.
Author: Rodgers, Jeremy
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6949825519
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