Non-smoothability conjecture for Gorenstein Stöhr–Torres monomial curves

Let $C$ be a Gorenstein monomial curve of Stöhr–Torres type. Stöhr–Torres non-smoothability conjecture. The curve $C$ is not smoothable. The conjecture is motivated by the example $L_{26}^{13}$, for which the excerpt reports that $T^1$ is concentrated in degree $0$ and that all perturbations of the equations lie in the square of the maximal ideal; the general assertion remains unproved in the supplied text.