PFUSRC 30: Global Topological Unification of Ancient Chinese Mathematics: From Double-Cone Ontology to Inverted Pythagorean Frustum

This paper establishes a rigorous scientific framework for the unification of core ancient Chinese mathematical prototypes—Hetu, Luoshu, Earlier Heaven Bagua, Later Heaven Bagua, and the Nine Palaces—based on the axiomatic system defined in PFUSRC 00 1. By strictly distinguishing the ontological origin from observable projections, this work proves that Hetu and Luoshu correspond respectively to the discrete skeleton and steady-state projection of the 45° triple coaxial double-cone ontology. The Earlier Heaven Bagua represents the radial symmetry of this structure, while the Later Heaven Bagua and the Nine Palaces are shown to be not part of the primary double-cone structure, but rather a closed, inverted Pythagorean frustum, a four-dimensional observable steady-state model derived by reverse truncation. This paper constructs a complete projective chain from high-dimensional ontology to low-dimensional manifestation, demonstrating that ancient Chinese mathematics forms a self-consistent, closed-loop sequence of cosmic models isomorphic to the fundamental topology of the universe. The inverted frustum configuration possesses inherent properties of helical anchoring and dynamic flow, allowing social structures to synchronize with the rhythm of cosmic growth, thereby providing a rigid topological foundation for the unity of cosmic laws and social order. This work redefines the scientific status of Chinese civilization by proving that its ancient sages mastered the geometric principles of anchoring and steady-state construction millennia ago.