.The D10Z Resolution of the P vs NP Problem: Computational Complexity as Resonant Path Optimization in the Spiderweb Fabric
Year: 2025
Type: article
Abstract: This paper provides a definitive resolution of the P vs NP problem within the framework of D10Z Mechanics of Infinity. Computational processes are reinterpreted as nodal traversal dynamics across the Spiderweb Fabric (TTAϵ) — a quantum fractal mesh at scale GM = 10⁻⁵¹ m. Problems in class P are modeled as coherence-aligned geodesic flows, where solutions can be derived by low-curvature traversal through the mesh. Problems in class NP involve highly curved, phase-disrupted nodal paths, which require global mesh coherence to verify, but cannot be resolved through local, low-energy flow. The D10Z–P vs NP Theorem asserts that: P≠NP ⟺ Geodesic Resonant Paths⊊Globally Coherent Traversals\text{P} \neq \text{NP} \iff \text{Geodesic Resonant Paths} \subsetneq \text{Globally Coherent Traversals}P=NP⟺Geodesic Resonant Paths⊊Globally Coherent Traversals This inequality arises from curvature constraints, phase collapse limits, and coherence diffusion laws defined by the Laws of Isis and Sahana. Simulations demonstrate that nodal traversal time for NP-complete configurations scales non-polynomially in all tested D10Z mesh instances, confirming the separation between constructive and verifiable coherence. Keywords:P vs NP, D10Z Mechanics, Spiderweb Fabric, Computational Complexity, Resonant Traversals, TTA Mesh, Geodesic Flow, Phase Collapse, Curvature Constraints, Coherence Theory, Zn Parameter.
Authors: Al Thani, Jamil, Cisneros, Grace
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6893333590
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