What question did this study set out to answer?

This research aims to establish a definitive proof of the Hodge conjecture by addressing its theoretical constraints.

July 26, 2026Open Access

Yuanxian Proof of the Hodge Conjecture --- A Complete Refinement Scheme for Non-Algebraic Cycle Exclusion Conditions

View Full Paper

Ask AI

Bookmark

This research aims to establish a definitive proof of the Hodge conjecture by addressing its theoretical constraints.
Developed a systematic framework based on Yuanxian T64 theory and topological dynamics.
Identified and analyzed four critical exclusion layers related to algebraic cycles and Hodge classes.
Formally validated the core theorems using Lean 4 without placeholders.
Proved that all rational (p,p)-type Hodge classes are projections of high-dimensional topological cycles.
Established non-existence of non-algebraic Hodge classes, demonstrating the rigid corollary of T64 structure.
Validated core principles through rigorous mathematical proofs and computations.

No takes yet. Share an insight, caveat, or question.

Randomized trial investigates Hodge conjecture outcomes in algebraic varieties, suggesting a new proof framework.

Zhenyuan Acharya (2026) studied this question.

View Full Paper

Ask AI

Bookmark