Authors : Ahmed Mohammed Al-Fahdi

Volume/Issue : Volume 10 - 2025, Issue 5 - May

Google Scholar : https://tinyurl.com/3cpss3m4

DOI : https://doi.org/10.38124/ijisrt/25may1171

Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.

Abstract : This paper is built upon analyzation over cumulative information while writing previous papers (part-1 & part- 2) entitled as “Modular Square One-Way Function& Square Root Algorithm”. In that papers the square root algorithm was analyzed. Such analyzation focus on the randomness characteristic of such algorithm aiming to find kind of regularity . The methodology was by rounding the rational numbers of nonperfect square root and normalizing it yield to what is innovatively called modular factor symbol similar to Legendre symbol. It is noticeable that the 1⁄2 factor play a genuine role for such analyzation. This yield analyzing related hypothesis and phenomena with similar factor such as Riemann nontrivial zetta zero laying at real part (1⁄2) in number theory. It is something related to what is called random matrix theory (RMT). In addition, in cosmic there is a surprising relation to what is called chaotic quantum system with Riemann spectrum (Riemannium). This leads us back to what is called Gaussian Unitary Ensemble (GUE). It is somthing rlated to the distribution of the prime number. Analyzing such topics is something genuine to the deep number theory, quantum physics, quantum algorithm which is the recent topics for the quantum mechanics, cryptographic, artificial intelligence (AI)

Keywords : Square Root Algorithm, Quantum Algorithms, Gaussian Unitary Ensemble (GUE), Planck-Scale Physics, Quantum Physics, Zetta Function, Imaginary Part of Riemann Zetta Zeros, Riemannium, Hilbert-Polya Conjecture, Hermitian Operator, Chaotic Quantum System, Prime Numbers Distribution, Schwarzschild Radius, Schwarzschild Mass, Mass-Energy Equivalence, Dark Matter Bridges, Spatial Agglomeration, Graviton, Higgs Field, Casimir Energy, Black Holes.

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