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The research aims to explore the fundamental reasons for the unsolvability of the Hodge Conjecture, proposing a new framework.

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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The research aims to explore the fundamental reasons for the unsolvability of the Hodge Conjecture, proposing a new framework.
Introduces Δ-ontology and its primitive element, the right isosceles triangle.
Analyzes the energetic, genetic, and architectural aspects of mathematical constructs.
Examines the interdependencies between discrete and continuous mathematical elements.
Demonstrates that traditional point-based mathematics is inefficient, requiring excessive resources.
Proves the necessity of the triangle in formulating proper mathematical constructs due to historical limitations.
Identifies the unsolvability of fundamental problems as a consequence of misaligned mathematical foundations.

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This article reveals new reasons for the unsolvability of the Hodge Conjecture, indicating the need for a paradigm shift in mathematical reasoning.

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

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This article reveals new reasons for the unsolvability of the Hodge Conjecture, indicating the need for a paradigm shift in mathematical reasoning.