Conjecture on four-term irredundant generating sequences of PSL(2,p)

Let $G=\mathrm{PSL}(2,p)$), and let $\iota_n(G)$ denote the set of divisors occurring as the relevant invariant for irredundant generating sequences of length $n$ in the paper. Four-term generating-sequence conjecture. For $G=\mathrm{PSL}(2,p)$, $\iota_4(G)=\emptyset$ unless $p=7,11,19,$ or $31$. In these exceptional cases, $\iota_4(G)=\{2\}$ unless $p=11$, in which case $\iota_4(G)=\{2,3\}$. The preceding theorem determines most of the sets $\iota_n(G)$, while the question asks for the remaining cases; the conjecture gives a proposed complete description of $\iota_4(G)$, but its general status is not established in the supplied text.