A Hodge Theory-Driven Quantum Mapping Between Calabi-Yau Manifolds and Nuclear Topology: First-Principles Derivation and Experimental Verification

Yang Ou and Wenming Sun
2025-12-29 132 views 4 downloads

 

This study adopts Hodge theory as a rigorous mathematical framework to construct a quantitative mapping system between the high-dimensional topological invariants of Calabi-Yau (CY) manifolds and nuclear physics parameters, thereby establishing a strict logical closure from algebraic geometry to low-energy nuclear physics. First, based on the Hodge decomposition theorem of complex manifolds and the geometric properties of compact Kähler manifolds, the study develops a topological characterization system for 3-dimensional complex CY manifolds, clarifying the algebraic structures of Hodge numbers, Chern classes, and Hodge classes, as well as their corresponding physical interpretations. Second, the proton/neutron distributions of nuclides are abstracted as algebraic cycles in Hodge theory (protons correspond to 1-codimensional cycles Z1Z2cl: Zp-HpP3, and neutrons correspond to 2-codimensional cycles). Using the surjectivity of the cohomology mapping (Lefschetz (1,1) theorem and its high-dimensional generalization), the quantitative relationship between “Hodge numbers and nucleon numbers” is derived.

 

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