The Lagrangian embedding capacity identity for ellipsoids

For $a\ge1$, define the embedding capacity

$$\operatorname{EC}(a)=\inf\left\{r>0\ \middle|\ E^4(1,a)\hookrightarrow\left(B^4(r)\cup B^2(r/2)\times\mathbb{C},\omega_{\mathrm{std}}\right)\right\}.$$

Here $E^4(1,a)$ and $B^k(r)$ are the standard symplectic ellipsoid and ball, respectively. The Lagrangian embedding capacity identity.

$$\operatorname{EC}(a)=2C^{\mathrm{CM}}\left(E^4(1,a),\omega_{\mathrm{std}}\right).$$

The claim is presented as predicting that Lagrangian embedding problems have the same numerical obstruction as symplectic embedding problems; no resolution is supplied.