Neveu–Schwarz and Ramond sector correspondence conjecture

Let $f$ be a quasi-homogeneous polynomial and let $G_{\max}$ be its maximal symmetry group. For each $g\in G_{\max}$, let $f_g$ be the corresponding fixed-locus restriction, let $Q_{f_g}$ be the associated sector algebra, and distinguish Neveu–Schwarz sectors from Ramond sectors as in the spin-curve construction.

Sector correspondence conjecture. The Neveu–Schwarz sectors are in one-to-one correspondence with the one-dimensional twisted sectors, while the Ramond sectors are in one-to-one correspondence with the sectors of dimension greater than one, namely

$$Q_{f_g}\neq\bf{C}.$$

This conjecture is presented as evidence for the Landau–Ginzburg interpretation of the constructions and is stated to have been checked against preliminary results of Fan, Jarvis, and Ruan. The supplied text gives no complete proof or resolution.