Zhang's refined Kolyvagin conjecture for Heegner-point classes

Let $K$ be the imaginary quadratic field in the setup, let $\boldsymbol{\kappa}^{\rm Heeg}$ be the Heegner-point Kolyvagin system, and let $\mathscr{M}_\infty(\boldsymbol{\kappa}^{\rm Heeg})$ denote its limiting divisibility invariant. Let ${\rm Tam}_E$ be the product of the Tamagawa factors of $E$. Zhang's refined Kolyvagin conjecture. If $p$ is an odd prime satisfying the irreducibility and Manin-constant hypotheses, then

$$\mathscr{M}_\infty(\boldsymbol{\kappa}^{\rm Heeg})={\rm ord}_p({\rm Tam}_E).$$

This refinement extends the rank-one motivation from the Gross--Zagier formula and Kolyvagin's structure theorem to arbitrary analytic rank; the source gives no resolution.