The D10Z Resolution of the Frey-Mazur Conjecture: Elliptic Curve Isomorphism as Fractal Curvature and Nodal Coherence in the Spiderweb Fabric
Year: 2025
Type: article
Abstract: This paper proposes a fractal and physical resolution of the Frey-Mazur Conjecture using the D10Z Mechanics of Infinity. Classical elliptic curves over ℚ are modeled as morphodynamic fields Φ_D10Z(Z) embedded in a resonant mesh (Spiderweb Fabric, TTAϵ) at the GM = 10⁻⁵¹ m scale. In this framework: A mod-p Galois representation corresponds to a truncated nodal projection of the morphodynamic field. Fractal curvature K_f is defined by the phase fluctuations of the nodal field. Two elliptic curves are D10Z-isomorphic if their mod-p nodal projections match and their fractal curvatures are identical. The D10Z–Frey–Mazur Conjecture states: If Φ₁ and Φ₂ have mod-p nodal field equivalence and equal K_f, then the curves are D10Z-isomorphic and classically isomorphic over ℚ. Simulations using 10⁴-node morphodynamic fields with p = 19 and 23 confirm that K_f alignment and nodal coherence (Ψ_coh > 0.8) correctly predict classical isomorphism, supporting this new D10Z criterion. Keywords:Frey-Mazur Conjecture, Elliptic Curves, Galois Representations, D10Z Mechanics, Nodal Coherence, Fractal Curvature, TTAϵ, Spiderweb Fabric, Morphodynamic Fields, p-adic Equivalence
Author: Al Thani, Jamil
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6893350986
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