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This work aims to redefine the Hodge Conjecture's unsolvability by analyzing its underlying elements.

July 7, 2026Open Access

Why the Hodge Conjecture Remained Unsolved for a Century: Not "Complexity" but the Wrong Primitive Element. A View from Δ‑Ontology After the Synthesis of Energy Economy, Genetic Reconstruction, and the Ten Bridges Theorem

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This work aims to redefine the Hodge Conjecture's unsolvability by analyzing its underlying elements.
Utilized Δ-ontology to explore energetic, genetic, and architectural perspectives.
Proposed the right isosceles triangle as the fundamental primitive element.
Analyzed the implications of the balance of symmetry and asymmetry.
The point is shown to be an inefficient primitive, requiring infinite resources for general geometrical representation.
Established that the Infinitum's properties offer optimal solutions to geometric representation.
Demonstrated that all fundamental problems are intricately linked, revealing a common structural underpinning.

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This analysis reveals the misdefinition of the Hodge Conjecture, suggesting a cognitive necessity in mathematical formulation.

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

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