Unobstructedness conjecture for ellipsoid embeddings into $H_b$

Let $H_b$ be the parameterized symplectic manifold in the source, let $c_b(z)$ denote its embedding-capacity function for the ellipsoid $E(1,z)$, and let $z_[\infty^b$ be the accumulation point for $H_b$. Let $(H)$ be the set of triples encoding $(p,q)$-perfect classes for $H$.

Unobstructedness conjecture. The function $c_b(z)$ is unobstructed for $z<z_[\infty^b$ if and only if $b=m/d$ for some $(d;m;p,q)\in (H)$.

This conjecture seeks to characterize exactly when all embedding obstructions below the accumulation point disappear. The source notes that rationality of full-filling parameters is known from ECH-capacity asymptotics, while this sharper characterization via perfect classes remains open.