Recognizability conjecture for canonical constant cycle polarizing divisors on K3 surfaces

Let $F_{2d}$ be the moduli space of polarized K3 surfaces of degree $2d$, and let $R$ be a canonical choice of polarizing divisor for $F_{2d}$. A curve on a K3 surface is a constant cycle curve if all of its points have the same class in the Chow group of zero-cycles $\operatorname{CH}_0(X)$. A divisor is recognizable if it can be recovered intrinsically from the polarized K3 surface.

Recognizability conjecture. If $R$ is a constant cycle curve, then it is recognizable.

The statement is suggested by the flex divisor, which is a constant cycle curve and is constructed canonically over the moduli space. The supplied text gives no evidence that this proposed implication has been proved or disproved.