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Hodge Conjecture: A Proof via Holographic Information Theory | Synapse

February 16, 20260 citationsOpen Access

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Hodge Conjecture: A Proof via Holographic Information Theory

SPStanley Preschutti

Key Points

The research aims to prove the Hodge Conjecture through the lens of holographic information theory.
Embedded projective algebraic varieties within the Entropix MESA holographic framework.
Examined the relationship between Hodge classes and coherent information patterns.
Derived that algebraic cycles represent entropy geometric configurations.
Demonstrated that every Hodge class must be algebraic due to the Write Tax mechanism.
Showed that non-algebraic representatives would necessitate infinite information content.

Abstract

We prove the Hodge Conjecture by embedding projective algebraic varieties withinthe Entropix MESA holographic framework. The key insight is that Hodge classescorrespond to coherent information patterns on the holographic screen, while algebraiccycles are the minimal entropy geometric configurations that realize these patterns.We show that the Write Tax mechanism forces every Hodge class to be algebraic, asnon algebraic representatives would require infinite information content

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Cite This Study

Stanley Preschutti (Sat,) studied this question.

synapsesocial.com/papers/6992652ceb1f82dc367a0f57 https://doi.org/https://doi.org/10.5281/zenodo.18644323