The Hodge Conjecture via U₂₄ Universality and K3 Surfaces — Moonshine lift, 25/25 checks, χ(K3)=24=Ω, 24 Niemeier lattices
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Mar 26, 2026 - TeX
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hodge-conjecture
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ia Collapse Theory and AK High-Dimensional Projection This repository presents Version 2.0 of a formal, categorical, and type-theoretic resolution of the Hodge Conjecture, formulated through Collapse Theory and the AK High-Dimensional Projection Structural Framework (AK-HDPST).
category-theory algebraic-geometry persistent-homology formal-proof hodge-conjecture collapse-theory ak-theory high-dimensional-projection ext-class
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Jul 15, 2025 - TeX
Convergence-theoretic reformulation of the Hodge Conjecture for K3 surfaces, with flow-based projection methods, numerical experiments, and symbolic generalizations to abelian varieties and Calabi–Yau threefolds.
mathematics algebraic-geometry symbolic-math mathematical-physics k3-surfaces cohomology math-research numerical-experiments sage-math calabi-yau hodge hodge-conjecture abelian-varieties hodge-theory gauss-manin millennium-problem theorem-verification convergence-theory
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Apr 22, 2025
The Hodge Conjecture via Hodge-class persistence and rigidity on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.
reproducibility algebraic-geometry cohomology local-to-global mathematical-proof spectral-theory hodge-conjecture millennium-problem manifold-constrained canonical-lane
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Mar 11, 2026 - Python
All the solutions to every Millenium Prize
euler math mathematics navier-stokes navier-stokes-equations riemann-hypothesis yangmills massgap hodge-conjecture milleniumproblem poincare-conjecture
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Jan 29, 2026 - Python
Unified experimental framework for computational exploration of the Clay Millennium Problems with reproducible pipelines and modular research infrastructure.
mathematics computational-mathematics navier-stokes p-vs-np riemann-hypothesis research-framework yang-mills hodge-conjecture birch-swinnerton-dyer clay-millennium-problems
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Mar 22, 2026 - Python
Structural analyses of 11 Millennium-Class challenges (01/30/2026). Using the XYAKANYAA System, the repository documents how expanded observational context yields harmonic stabilization. Experimental, reproducible, and open to refutation.
reproducible-research geometry jupyter-notebook mathematics computational-mathematics navier-stokes golden-ratio collatz-conjecture phi millennium-problems p-vs-np riemann-hypothesis consciousness-studies hodge-conjecture abc-conjecture birch-swinnerton-dyer-conjecture poincare-conjecture yang-mills-mass-gap langlands-problem
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Apr 3, 2026 - Jupyter Notebook
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