The Poincaréan and De-Poincaréan Operators

This paper presents a novel topological resolution to the classical general three-body problem by introducing a pair of meta-dynamical operators: the Poincarean and De-Poincarean operators. By abandoning fixed physical constants and replacing static inverse-square interactions with an adaptive ternary functional flow embedded in Wave-Point Geometry, we prove that geometric collision singularities are naturally smoothed into non-singular cylinders. Furthermore, we expand the topological winding numbers (charges) from integers to transcendental numbers like pi and e, discovering a new family of non-repeating, stable quasi-crystal orbits. We establish a complete bijective commutative diagram between transcendental arithmetic spectra and asymmetric physical trajectories, completely flattening the deterministic chaos proven by Poincare.