Pythagorean Frustum Closed System Complete Integrated Monograph: Ontology, Paradox Resolution, Physical Unification and Practical Paradigm Revolution

For a long time, the academic community of mathematics and physics has fallen into a long-term cognitive inversion: taking algebra as the ontological foundation and geometry merely as an auxiliary intuitive tool. The essential reason is that traditional topology and geometric systems lack strict determinacy, complete axiomatic qualification, and operable minimal structural units. As a result, their practical application efficiency is far inferior to algebraic methods. Based on the unique 45° coaxial double-cone finite closed topological structure, the Pythagorean Frustum Closed System (PFCS) reconstructs a deterministic axiomatic topological geometry. It clarifies the core logical relationship that geometry acts as the ontological foundation while algebra serves only as a computational symbolic tool. This monograph fundamentally resolves long-standing basic paradoxes in mathematics, realizes the unified geometric description of spacetime, dimensional hierarchy, gravitational effect and quantum behavior in physics, and forms a completely self-consistent theoretical closed loop.