Refined Kurihara conjecture for modular-symbol invariants

Let $\boldsymbol{\delta}=\{\delta_n\}_{n\in\mathcal{N}}$, and let $\mathscr{M}_\infty(\boldsymbol{\delta})$ be the limiting divisibility invariant defined from these quantities. Let ${\rm Tam}_E$ be the product of the Tamagawa factors of $E$. Refined Kurihara conjecture. If $p>3$ satisfies the irreducibility and Manin-constant hypotheses, then

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

This is the refinement motivated by exact formulas for the Bloch--Kato Selmer group and the Birch--Swinnerton-Dyer formula; the source gives no resolution.