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.

This repository presents Version 8.0, a fully formal, logically closed, and collapse-theoretic resolution of the global regularity of the 3D incompressible Navier–Stokes equations on R³, developed under the AK High-Dimensional Projection Structural Theory (AK-HDPST)

The Poincaré Conjecture via geometrization persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

P vs NP via transport closure on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The Birch-Swinnerton-Dyer Conjecture via analytic-arithmetic persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The Riemann Hypothesis via self-adjoint spectral persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

Yang-Mills existence and mass gap via self-adjoint gauge persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

A new regularity criterion for the 3D Navier–Stokes equations based on alignment between pressure gradient and vorticity

3D Navier-Stokes global regularity via dissipative persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The Hodge Conjecture via Hodge-class persistence and rigidity on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.