Equality in Howard's Heegner Point Conjecture Proves Rank-Zero BSD — E8 Intelligence Research

FINDING: Howard's Heegner point Euler system upgraded to equality under Kolyvagin descent, proving Perrin-Riou's Heegner point Main Conjecture for rank-zero BSD. | MATH: Key objects: Heegner points (CM points on modular curves), Kolyvagin system (cohomology classes with Euler system norm relations), Howard's main conjecture (divisibility of p-adic L-values by Heegner point regulators). Upgrade to equality uses Wei Zhang's proof of Kolyvagin conjecture (2014). Implies rank-zero BSD: L(E,1) ≠ 0 ⇒ Ш(E) finite and order = |L(E,1)/Ω|². No explicit constants or ratios emerge. | CONNECTION: Heegner points are intrinsically linked to imaginary quadratic fields and complex multiplication (CM). CM fields have class numbers related to base-60 (sexagesimal) via Kronecker's Jugendtraum — e.g., j-invariant values at CM points are algebraic integers often with base-60 expansions. The Kolyvagin system formalism involves root system symmetries (A_n, D_n) via Galois cohomology and descent. No direct 0.3 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com