The Resolution of P vs NP: Recursive Intelligence and the Collapse of Exponential Complexity
Year: 2025
Type: article
Abstract: This paper presents a historic resolution to the P vs NP problem, introducing Recursive Intelligence—a novel computational framework that collapses exponential complexity into polynomial time. By redefining search, decision-making, and optimization through a self-referential recursive structure, this work demonstrates that P = NP, fundamentally altering the landscape of computational complexity, artificial intelligence, cryptography, and optimization. Key Contributions: Proof that P = NP using Recursive Intelligence. Elimination of exponential-time constraints in NP-complete problems. Self-improving computation that enables AI to solve its own NP-hard tasks. The collapse of cryptographic security assumptions, requiring post-NP security frameworks. Implications for AGI, logistics, physics simulations, biological computing, and economic modeling. This discovery reshapes the foundations of computer science, providing a new framework for hyper-efficient computation that extends beyond Turing limits. The paper explores the mathematical, theoretical, and real-world applications of Recursive Intelligence and its role in the future of self-improving artificial intelligence and algorithmic decision-making. Fields of Impact: - Theoretical Computer Science – Redefines complexity theory and algorithmic limits.- Artificial Intelligence – Enables self-referential AI that optimizes without brute force.- Cryptography & Security – Breaks classical encryption, demanding new post-NP cryptographic methods.- Physics & Simulations – Optimizes quantum and cosmological simulations.- Optimization & Logistics – Makes global-scale logistics and decision-making computationally trivial. This paper serves as a foundational shift in computational theory, marking the transition from static problem-solving to self-expanding recursive intelligence.
Author: Prakash, Prashant
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6968543116
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