PFUSRC-WEST-001 From the Pythagorean Theorem to the Bicone: A Visible Path of Ontological Reduction — Geometric Origin, Topological Necessity, and Falsifiable Predictions of the PFUSRC System

When Pythagoras discovered his theorem, humanity first grasped the mathematical framework of the universe. For more than two thousand years, the 3-4-5 Pythagorean triple has only been interpreted as a static geometric formula. This paper constructs a complete ontological reduction chain: right triangle → circle → sphere → breathing sphere → symmetry breaking → 45° bicone → 11-dimensional triple nested bicone, and reconstructs the topological essence hidden behind the Pythagorean theorem layer by layer. Its core conclusion holds that the 3-4-5 triple is not merely a mathematical relation, but a projective snapshot of a dynamic 4-dimensional topological structure captured at the moment of steady-state equilibrium, recording the trace of universal cosmic breathing rather than simple spatial relationships. This paper strictly demonstrates that the 45° half-cone angle is a necessary topological condition for the stable existence of bicones; any other angle will trigger structural collapse or tearing. The 11-dimensional framework is not an artificial hypothesis, but the sole dimensional configuration enabling topological closure of triple coaxial bicones. The total of 55 steady-state datum points (19+17+19) is the minimal integer solution for global closed topology, with fewer points causing structural fracture and extra points breaking symmetric balance. This study puts forward seven falsifiable experimental predictions covering dark matter distribution, cosmic large-scale fractal characteristics, CMB signals, dark energy evolution, B meson lifetime ratio, quantum measurement residual entropy, and entanglement propagation speed, which can be verified or refuted by astronomical and particle physics experiments in the future, satisfying Popper’s criterion of scientific falsifiability. Finally, the paper completes the full deduction from the Pythagorean theorem to the bicone topological model, converting the static geometric relation into a dynamic description of cosmic self-evolution.