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The research aims to establish a complete integrable system of geometric objects within the moduli space of Calabi-Yau manifolds.

April 13, 2026Open Access

The Conformity Gradient on Calabi--Yau Moduli: From Statistical Rigidity to an Integrable System on the Fermat Quintic

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The research aims to establish a complete integrable system of geometric objects within the moduli space of Calabi-Yau manifolds.
Proof of the integrable system using five geometric objects.
Establishing rigidity theorems for the Sasaki-Dombrowski lift.
Verifying identities symbolically and numerically on the Fermat quintic.
The conformity cubic is universally of type I_1 with central charge c = 1.
Proven identities related to the Amari tensor and its dynamics.
Establishment of new theorems related to the Amari-Hodge identity and Amari-Schwarzian cubic.

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Proves a complete integrable system in Calabi-Yau manifolds, highlighting geometric invariance and identities.

Nicholas Daniel Maino (2026) studied this question.

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