Yano's generic b-exponent conjecture for irreducible plane curves

Let $f\in\mathbb{C}\{x,y\}$ define the germ of an irreducible plane curve with semigroup

$$\Gamma=\langle\overline{\beta}_0,\overline{\beta}_1,\dots,\overline{\beta}_g\rangle.$$

Let $\pi:X'\to\mathbb{C}^2$ be a log-resolution, and let $E_1,\dots,E_g$ be the rupture divisors, with multiplicities $N_i$ in the total transform and coefficients $k_i$ in the relative canonical divisor. Set

$$e_{i-1}=\gcd(\overline{\beta}_0,\overline{\beta}_1,\dots,\overline{\beta}_{i-1}).$$

Yano's conjecture. For generic curves in some $\Gamma$-constant deformation of $f$, the $b$-exponents are

$$\bigcup_{i=1}^g\left\{\lambda_{i,\ell}=\frac{k_i+1+\ell}{N_i}\ \middle|\ 0\leq\ell<N_i,\ \overline{\beta}_i\lambda_{i,\ell}\notin\mathbb{Z},\ e_{i-1}\lambda_{i,\ell}\notin\mathbb{Z}\right\}.$$

The conjecture gives a formula for the generic Bernstein–Sato exponents of irreducible plane curves using the semigroup or, equivalently, the numerical data of a log-resolution. Its status is not established by the supplied source context.