The MorphoEvoShorQS algorithm represents a hybrid approach to integer factorization, integrating ... more The MorphoEvoShorQS algorithm represents a hybrid approach to integer factorization, integrating classical methods such as Trial Division, Pollards Rho, and the Elliptic Curve Method (ECM) with a novel correlated oscillatory loop inspired by Shors quantum algorithm and the Quadratic Sieve (QS). This paper elucidates the algorithms design, theoretical foundations, and performance on large composite numbers, including a 100-digit composite number. We analyze its computational efficiency, explore its implications for cryptography, and discuss its impact on physics, computer science, and related fields. The algorithms ability to factor large numbers efficiently suggests potential vulnerabilities in cryptographic systems like RSA and provides insights into the computational complexity of quantum-inspired classical algorithms. We also examine the theoretical connections to quantum mechanics and evolutionary computing, highlighting future research directions and interdisciplinary applications.
The MorphoEvoShorQS algorithm represents a hybrid approach to integer factorization, integrating ... more The MorphoEvoShorQS algorithm represents a hybrid approach to integer factorization, integrating classical methods such as Trial Division, Pollard's Rho, and the Elliptic Curve Method (ECM) with a novel correlated oscillatory loop inspired by Shor's quantum algorithm and the Quadratic Sieve (QS). This paper elucidates the algorithm's design, theoretical foundations, and performance on large composite numbers, including a 100digit RSA challenge number. We analyze its computational efficiency, explore its implications for cryptography, and discuss its impact on physics, computer science, and related fields. The algorithm's ability to factor large numbers efficiently suggests potential vulnerabilities in cryptographic systems like RSA and provides insights into the computational complexity of quantum-inspired classical algorithms. We also examine the theoretical connections to quantum mechanics and evolutionary computing, highlighting future research directions and interdisciplinary applications.
This paper presents an elegant, unified framework that integrates classical field theory, nonline... more This paper presents an elegant, unified framework that integrates classical field theory, nonlinear dynamics, and quantum mechanics within a cohesive mathematical model. By incorporating effective mass terms, nonlinear reaction dynamics, diffusion/dissipation processes, and higher-order spatial derivatives, the framework captures emergent features that bridge the gap between classical and quantum regimes. The model demonstrates how a system of coupled partial differential equations can describe a wide spectrum of physical phenomena, providing new insights into the interplay between classical behavior and quantum corrections.
This work presents an integrated framework that combines the mathematical principles underlying Q... more This work presents an integrated framework that combines the mathematical principles underlying Q.C. System with the detailed mechanics of the I.R.I.S. Intelligence system. It further incorporates the conceptual and practical aspects of Morpho Field theory-addressing spatial and temporal interactions. The novel quantum computer architecture, QC Amalgamation 1.0, is optimized for solving complex, multi-dimensional problems. The paper explores mathematical models, computational simulations, and practical applications across material science, healthcare informatics, and beyond. In conclusion, we discuss how this convergence may usher in a new era of prosperity and ingenuity for mankind.
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Papers by Anthony Castro