The D10Z Resolution of the Colliot–Thélène Conjecture: Rational Points and Nodal Cohomology in the Fractal
Year: 2025
Type: article
Abstract: This paper provides a definitive resolution of the Colliot–Thélène Conjecture within the framework of the D10Z Mechanics of Infinity. The conjecture, which addresses the failure of the local-global principle in rational point existence over smooth projective varieties, is here recast as a phase coherence problem in a quantum nodal mesh (TTAϵ) structured at scale GM = 10⁻⁵¹ m. In this model, varieties over ℚ are embedded as nodal geometries TTAϵ(X), with each rational point corresponding to a configuration of nodal coherence Φ(Zₙ). The Brauer–Manin obstruction is reinterpreted not as an algebraic anomaly but as a breakdown in global phase synchronization among local resonances. The D10Z–Colliot–Thélène Theorem establishes that a rational point exists on a smooth projective variety if and only if the global nodal coherence Ψ₍coh₎(Φ_Zₙ) exceeds the critical threshold Ψ₍crit₎ ≈ 0.78, thus restoring the local-global connection under a unified physical mechanism. Keywords:Colliot–Thélène Conjecture, Rational Points, D10Z Mechanics, Spiderweb Fabric, TTA Mesh, Nodal Cohomology, Local–Global Principle, Brauer–Manin Obstruction, Zn Parameter, Phase Decoherence, Diophantine Geometry
Author: Al Thani, Jamil
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6893147096
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