What question did this study set out to answer?

This research aims to demonstrate a rigorous isomorphism between the PFUS and Calabi–Yau manifold.

May 10, 2026Open Access

Isomorphism Between PFUS and Calabi–Yau Manifold and Unified Proof of High-Dimensional Compactification

Key Points

This research aims to demonstrate a rigorous isomorphism between the PFUS and Calabi–Yau manifold.
Proved structural isomorphism using the 45° coaxial double-cone frustum geometry of PFUS.
Demonstrated compliance with core axioms such as Kähler structure and Ricci-flatness.
Established a complete one-to-one correspondence between PFUS and Calabi–Yau manifolds.
Proved PFUS as the unique primitive realization of Calabi–Yau geometry.

Abstract

Based on the Pythagorean Frustum Unified System (PFUS), this paper rigorously proves that the 45° coaxial double-cone frustum geometry of PFUS admits a rigid, global, and contradiction-free structural isomorphism with the Calabi–Yau manifold, a core framework in modern geometry. Starting from primitive geometry, this paper proves that the double-cone and coupling surface naturally satisfy all core axioms including compactness, Kähler structure, Ricci-flatness, first Chern class zero, and high-dimensional closure. This paper establishes a complete one-to-one correspondence between PFUS and Calabi–Yau manifolds, proving that PFUS is the unique primitive ontological realization of Calabi–Yau geometry in the universe. It provides a unified and closed primordial explanation for string-theoretic compactification, unification of gravity and quantum theory, uniqueness of spacetime geometry, and singularity-free cosmic evolution. No external assumptions, free parameters, or logical gaps are introduced; the system is fully self-consistent, complete, and rigorous.

Isomorphism Between PFUS and Calabi–Yau Manifold and Unified Proof of High-Dimensional Compactification

Key Points

Abstract

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