What question did this study set out to answer?

The aim is to provide a constructive proof of the Hodge Conjecture through YuanXian Theory.

May 10, 2026Open Access

YuanXian Theory: A Constructive Proof of the Hodge Conjecture

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Randomized trial finds a new constructive proof for the Hodge conjecture using YuanXian Theory, suggesting a novel mathematical framework.

The aim is to provide a constructive proof of the Hodge Conjecture through YuanXian Theory.
Constructed the Hodge-Laplacian operator on the 64-dimensional torus with TCSC symmetry.
Established spectral correspondence between the kernel of this operator and Hodge classes.
Developed a bidirectional verification pipeline between SageMath and Lean 4.
Confirmed the correspondence between the Hodge-Laplacian operator's kernel and Hodge classes.
Demonstrated that the Hodge Conjecture follows from spectral theory in the defined framework.

Zhenyuan Acharya (2026) studied this question.

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May 10, 2026Open Access

View Full Paper

Ask AI

Bookmark

Authors

Randomized trial finds a new constructive proof for the Hodge conjecture using YuanXian Theory, suggesting a novel mathematical framework.

The aim is to provide a constructive proof of the Hodge Conjecture through YuanXian Theory.
Constructed the Hodge-Laplacian operator on the 64-dimensional torus with TCSC symmetry.
Established spectral correspondence between the kernel of this operator and Hodge classes.
Developed a bidirectional verification pipeline between SageMath and Lean 4.
Confirmed the correspondence between the Hodge-Laplacian operator's kernel and Hodge classes.
Demonstrated that the Hodge Conjecture follows from spectral theory in the defined framework.

Zhenyuan Acharya (2026) studied this question.

View Full Paper

Ask AI

Bookmark