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THE EL-RAKHAWI DOCTRINE OF ADVANCED COMPUTING ENCYCLOPEDIA OF QUANTUM INTELLIGENCE AND SCIENTIFIC COMPUTING From AI-Native Operating Systems to Hybrid Quantum-Classical Architectures - A Unified Framework for the Computational Singularity

mohamed kamal arafa el-rakhawi

Published Oct 20, 2026• 0 citations
Publisher

Abstract

THE EL-RAKHAWI DOCTRINE OF ADVANCED COMPUTING by Dr. M.K.A. El-Rakhawi (DOI: 10.5281/zenodo.23494755) presents a unified framework across five parts. Part I covers AI-Native OS with resource allocation R(t)=argmax_R U(R,t) subject to capacity constraints, and compiler optimization min T(code) under power/energy budgets. Part II addresses HPC with peak performance P_peak=N_cores·F_clock·OPS/cycle and scalability S(P)=T(1)/T(P) per Amdahl's law. Part III explores QML via |ψ⟩=α|0⟩+β|1⟩ and hybrid VQAs θ*=argmin_θ ⟨ψ(θ)|H|ψ(θ)⟩. Part IV details SciML with PINNs loss L(θ)=λ_PDE·L_PDE+λ_BC·L_BC+λ_IC·L_IC+λ_data·L_data where adaptive λ_i mitigate gradient pathology, and distributed training T_total=max(T_compute,T_communication_overlap)+T_synchronization reflecting communication-computation overlap. Part V establishes unified theory bounded by Bremermann's limit C_max≤(2E)/(πℏ), establishing strict physical ceiling for any computational substrate. Legal framework excludes abstract ideas/algorithms per Alice Corp. v. CLS Bank (2014) and 35 U.S.C. §101, protecting only concrete implementations, system architectures, and applied methods. Protected under international copyright.

DOI
10.5281/zenodo.23494754

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