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This work aims to provide a geometric interpretation of the Hodge Conjecture through the lens of △-ontology.

May 29, 2026Open Access

The Hodge Conjecture in △-Ontology: A Geometric Explanation via Infinium Self-Similarity (Most Complete Version, May 2026)

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This work aims to provide a geometric interpretation of the Hodge Conjecture through the lens of △-ontology.
Explores cohomology types using △-mosaics based on the infinium △₁ₓ₁.
Establishes connections between the Hodge classes and algebraic cycles through self-similarity.
Formalizes the infinium in homotopy type theory to connect to the Langlands program.
Demonstrates that all types of cohomology can be represented using △-mosaics.
Shows the relationship between the Beilinson regulator and the spectral gap λ₁.
Provides explicit examples illustrating the application for various geometrical structures.

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Conceptual work explains the Hodge Conjecture using △-ontology, suggesting new insights for algebraic geometry.

Alexey (KAMAZ) Petrov (2026) studied this question.

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