Spatial Partitioning via Proven Eleven-Dimensional Triple Bicone Geometry and Isomorphic Mapping of Four-Dimensional Mathematics

This work is established upon the rigorously verified topological framework consisting of three coaxial bicones that span the dimensional hierarchy from 5D to 11D. We briefly recapitulate the core logical proofs and validate the geometric consistency and structural stability of such multi-dimensional configurations. Following Yin-Yang symmetric numerical principles, we construct a complete numerical sequence ranging from 5 to 55, where all prime singular points are arranged subject to the invariant relation L+R=60. By employing discrete prime eigenpoints as intrinsic dividing nodes, we implement hierarchical partitioning of high-dimensional manifolds and define the transitional fusion domain bridging three-dimensional physical space and four-dimensional orderly space. We further distinguish the applicable scope of conventional classical mathematics within such fusion domains, as well as unexplored domains requiring newly-established mathematical paradigms for describing dense high-dimensional structures. A full isomorphic correspondence is built between the proposed four-dimensional mathematical system and spatially partitioned prime-point field configurations. The traditional Yin-Yang imbalance doctrine in Heluo numerology is rigorously interpreted as modern spontaneous symmetry breaking, which accounts for asymmetric prime-number distribution. We adopt the critical index α=0.5 as the universal threshold to distinguish spatial expansion and contraction regimes. Existing mathematical studies have long confirmed state transitions between cosmic expansion and contraction occurring at characteristic primal points such as 5 and 11, and generalized overall evolutionary tendencies of spatial dynamics. Nevertheless, the intrinsic geometric origin and orderly arrangement mechanism behind these phenomena remain unclarified. Most incomplete spatial theories, unsolved number-theoretic conjectures and dimensional paradoxes essentially stem from the neglect of the real nested bicone structure and prime-based spatial partitioning rules. The present framework enables systematic revision and supplementation of defective spatial theories, and lays a unified foundational paradigm for multi-dimensional geometric mathematics.