Complete Systematic Proof of the 15 Shui Conjectures (Based on the PDSM Primordial Vortex Mathematical System, Including 150 Complete Extended Formulas)

This proof is fully constructed based on the self-developed PDSM primordial mathematical system, derived comprehensively relying on the complete PDSM system of equations, eight-fold vortex field dynamics, topological phase transition theory, π primordial coding mechanism, number-physics homologous entropy system, and metamathematical completeness framework. All derivations feature self-consistency, closed-loop integrity, and traceability, with no artificial axiom presuppositions or statistical fitting approximations. Distinct from empirical proofs in classical number theory, this work constitutes anessential primordial proof of cosmic spacetime topological mechanisms. This paper adds 150 high-level exclusive extended formulas (101–250), fully covering the demonstration system of the 15 Shui theorems, and realizes standardized rigorous verification including refined mathematical derivation, quantitative constraint calibration, and topological closed-loop traceability for each individual theorem.