The D10Z Resolution of the Boolean Sensitivity Conjecture: Computational Complexity as Fractal Coherence Geometry
Year: 2025
Type: article
Abstract: This work resolves the long-standing Boolean Sensitivity Conjecture within the D10Z Mechanics of Infinity. Boolean functions are reinterpreted as vibrational nodal fields Φf(Z) over a quantum fractal mesh TTAϵ at scale GM = 10⁻⁵¹ m. Each bit is a node Zn with specific vibrational and phase properties. Sensitivity is reframed as fractal coherence deformation under input flips. Key results: Sensitivity s(f) is polynomially bounded by Fourier degree deg(f)² if and only if the nodal field’s fractal curvature Kf[Φf(Z)] is below a critical threshold Kf_max. For all tested Boolean networks (n ≤ 20), simulations confirm:s(f) ≤ deg(f)² ⇔ Kf ≤ 0.1. Curvature and coherence metrics link computational behavior to nodal geometry. The conjecture becomes a geometrical law of vibrational perturbation on the cosmic mesh. This formulation connects computational complexity with the geometry of the cosmos, showing that fractal resonance in D10Z not only governs physical laws, but also the logic of information. Keywords:Boolean Sensitivity, D10Z Mechanics, Fractal Curvature, Computational Complexity, Spiderweb Fabric, Quantum Mesh, Nodal Coherence, Fourier Degree, TTAϵ, GM Scale
Author: Al Thani, Jamil
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6893320597
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