Pythagorean Frustum Closed System: Prime Dimension Regulation and Finite Geometric Ontology - The Ontological Reconstruction of Mathematics

Traditional mathematics and physics carry a deep ontological inversion: algebra, numerical systems, and formal infinity are taken as fundamental reality, while geometry and topology are regarded as secondary representations. This paper establishes a rigorous, closed, and physically grounded paradigm by demonstrating that cosmic dimensions follow a unique, rigid evolutionary path: 1→5→11, governed by prime stability, topological closure, energy conservation, and dynamic equilibrium. We confirm that finite geometry is primary ontological substance, and algebra is secondary symbolic manifestation. The classical concept of zero as absolute nothingness is replaced by zero as a coupling interface between explicit and implicit states, higher and lower dimensions. The global operator β₁ unifies deterministic frameworks and indeterministic local freedoms, realizing the complementarity of finiteness and infinitude. This work reconstructs mathematics at the foundational level, forming a self-consistent, singularity-free, complete system consistent with the Pythagorean Frustum Closed System. This work provides a complete, closed, and physically consistent foundation for the ontological unification of mathematics and physics.