The Fukaya-category elliptic-curve summand conjecture for the blowup examples

Let $X$ be as in Examples 4.1 and 4.2, and let $C\subset \mathbb{P}^3$ be the intersection of quadrics defined by

$$x_0^2+x_1^2+x_2x_3=0,\qquad x_0x_1+x_2^2+x_3^2=0.$$

Fukaya-category elliptic-curve summand conjecture. The Fukaya category of $X$ should contain a direct summand equivalent to the derived category of sheaves on a genus-one curve whose Jacobian is isogenous to that of $C$. This predicts a mirror-symmetric categorical manifestation of the elliptic curve associated with the quantum-cohomological formal group of the blowup examples; establishing such a summand and its precise geometric realization remains open.