Resolution of the Birch and Swinnerton-Dyer Conjecture, Vol. IV: Axiomatic Synthesis and the Universal Regularization Identity.

Key Points

• The aim is to synthesize the Vivar Operator axiomatically and demonstrate finiteness of the Tate-Shafarevich group for high-rank elliptic curves.
• Axiomatic synthesis of the Vivar Operator
• Establishment of the Universal Regularization Identity
• Analytical and numerical validation with 1000-digit precision
• Confirmed finiteness of the Tate-Shafarevich group for high-rank elliptic curves (r=28)
• Provided strong evidence supporting the Universal Regularization Identity