What question did this study set out to answer?

The aim is to investigate the Hodge Conjecture using a spectral-fractal framework. It focuses on linking thermodynamic concepts with geometric algebra.

March 25, 2026Open Access

The Hodge Conjecture via Spectral-Fractal Theory A Research Program with Partial Results

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The aim is to investigate the Hodge Conjecture using a spectral-fractal framework. It focuses on linking thermodynamic concepts with geometric algebra.
Developed a spectral-fractal approach combining KMS states with coniveau filtration.
Constructed a non-circular Hodge Boundary Variety using the intersection Gram matrix.
Explored implications of KMS states at critical temperatures for algebraic cycles.
Proved the non-circular Hodge Boundary Variety construction and derived algebraic rank spectrally.
Reformulated the Hodge Conjecture in terms of rank and dimensions of cohomological spaces.
Identified critical gaps in the theoretical framework, including assumptions on algebraicity and reconstruction.

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Implication

Research program develops spectral-fractal theory to reformulate Hodge conjecture, suggesting novel connections in algebraic geometry.

Cite This Study

Thierry Marechal (2026) studied this question.

synapsesocial.com/papers/69c37bc2b34aaaeb1a67e721 https://doi.org/10.5281/zenodo.19195821

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The Hodge Conjecture via Spectral-Fractal Theory A Research Program with Partial Results

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Discussion

Implication

Cite This Study

The Hodge Conjecture via Spectral-Fractal Theory A Research Program with Partial Results

Key Points

Discussion

Implication

Cite This Study

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