Teissier's one-hypersurface conjecture for Arnold exponents

Let $X$ be a smooth complex $n$-dimensional algebraic variety, let $f\in\operatorname{\mathcal O}_X(X)$ be nonzero, and let $P\in X$ be a point in the zero-locus of $f$ such that $f$ has an isolated singularity at $P$. If $H$ is a smooth hypersurface in $X$ containing $P$ and $f\vert_H$ has an isolated singularity at $P$, then Teissier's one-hypersurface conjecture.

$$\sigma_P(f)\geq\sigma_P(f\vert_H)+\frac{1}{1+\theta_P(f)}.$$

This one-hypersurface statement implies the successive-hyperplane formulation above. The paper proves the conjecture in the case of log canonical thresholds, while the general Arnold-exponent formulation is the broader conjectural framework.