December 5, 2025Open Access

Hodge Theoretic Phase Transitions via Rough Operator Algebra: The Existence of Algebraic Cycles in Rough Cohomology

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Quantization effect stabilizes geometry under roughness fluctuations, showing a unique phase transition.
Hodge Conjecture provides a novel algebraic structure through Rough Current Space, enhancing current mathematical understanding.
This approach integrates geometry and information, presenting a consolidated view of the Roughness Spectrum.
The work proposes that different phases of existence in the universe are interconnected through the concept of roughness.

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This paper reveals the role of quantum stochasticity in defining algebraic cycles in complex manifolds, indicating new geometrical insights.

Lee Sung-gil (2025) studied this question.

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This paper reveals the role of quantum stochasticity in defining algebraic cycles in complex manifolds, indicating new geometrical insights.