Conjectural classification of near-equality for ribbon Schur functions

Let $r_\alpha$ and $r_\beta$ be ribbon Schur functions indexed by compositions $\alpha$ and $\beta$, and let $s_\nu$ be the Schur function indexed by the partition $\nu$. The notation $1^m$ denotes $m$ consecutive parts equal to $1$, and reversal means reversing the parts of a composition. Suppose that

$$r_\alpha-r_\beta=s_\nu.$$

Near-equality classification conjecture. Up to reversal of $\alpha$ and $\beta$, the compositions $\alpha$, $\beta$ and partition $\nu$ are one of the five cases of Theorem 1.1, one of the five cases of its corollary, or one of the following six cases:

$$\begin{aligned} \alpha&=1^{c+d+1}a(b-1)1^c,&\quad \beta&=1^{c+d+1}(b-1)a1^c,&\quad \nu&=ab2^c1^d,\\ \alpha&=(b-1)1^{c-1}21^{c+d}a,& \beta&=(b-1)1^{c+d}21^{c-1}a,& \nu&=ab2^c1^d,\\ \alpha&=1^ca(b-1)1^{c-1}21^d,& \beta&=1^c(b-1)a1^{c-1}21^d,& \nu&=ab2^c1^d,\\ \alpha&=(a-b+1)(b-1)1^{c-1}21^{c+d}(b-1),& \beta&=(a-b+1)(b-1)1^{c+d}21^{c-1}(b-1),& \nu&=ab2^c1^d,\\ \alpha&=2a121,& \beta&=212a1,& \nu&=a42,\\ \alpha&=231^{d+2}21,& \beta&=21^{d+2}231,& \nu&=33221^d. \end{aligned}$$

In particular, $\nu$ must have the form $\nu=ab2^c1^d$, equivalently $\nu_3\leq 2$. This conjecture seeks a complete classification of when the difference of two ribbon Schur functions is a single Schur function; the five earlier cases are referenced through the paper's main theorem and corollary, while the six displayed cases extend the classification in general.