Ishikawa's classification conjecture for stable proper frontal map germs

Let $f\colon (\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$ be a stable proper frontal map germ of corank $1$, with Legendrian lift $\tilde f$. Define Ishikawa's indices by

$$i=\dim\frac{\tilde f^*\mathscr{O}_{2n+1}}{f^*\mathfrak{m}_{n+1}}\in\{2,\dots,n\},\qquad j+1=\dim\frac{\mathscr{O}_n}{\tilde f^*\mathfrak{m}_{2n+1}}\in\left\{1,\dots,\left\lfloor\frac{n}{2}\right\rfloor\right\}.$$

Here square brackets in the source denote the floor function. Ishikawa's classification conjecture. The stable proper frontal map germs are given by Ishikawa's $A_{i,j}$ singularities with these index ranges, and all stable frontal multigerms are obtained by transverse self-intersections of these mono-germs. The paper presents this statement as a theorem and supplies the classification in the cited theorem, so it is resolved rather than an open conjecture.