The Rigorous Breakthrough System of CY3-π for Core Problems in Three-Dimensional Calabi-Yau Manifolds (Complete Closed Final Version)

As core research carriers in complex geometry, arithmetic topology, and string theory, three-dimensional Calabi-Yau (CY3) manifolds have long confronted numerous publicly acknowledged pending challenges, including ambiguous topological finiteness, non-analytic metric bottlenecks on compact manifolds, topological phase transition instability of moduli spaces, string vacuum landscape degeneracy, and scale inconsistency between number theory and geometry. Traditional frameworks of complex geometry, string theory, and classical arithmetic geometry can only handle these problems via approximate computation, qualitative analysis, and artificial truncation, failing to construct a self-consistent, closed, and rigorously provable unified system. Based on the self-established CY3-π arithmetic topological dynamic framework, this paper proposes original π-phase topological conservation axiom and conformal compatibility axiom. By supplementing the core deficiencies of classical theories with high-order topological phase constraints, a cross-disciplinary unified theoretical system with mathematical self-consistency, logical closure, strict provability, and quantitative computability is constructed. This work systematically solves multiple decades-long open problems in interdisciplinary fields and provides a novel research paradigm for the in-depth integration of high-dimensional topological geometry, string theory, and arithmetic topology.