The short-partition model conjecture for prime gaps

Let $p_n$ be the $n$th prime, let $\mathcal P$ denote the set of partitions, and let $\widehat{N}$ be the supernorm map. A partition has no $1$'s when none of its parts equals $1$, and its length is its number of parts. Short-partition model conjecture for prime gaps. For $n\geq 1$, the odd numbers in the interval $[p_n,p_{n+1})$ can be modeled by the values of $\widehat{N}$ on partitions of norm $n$ having no part equal to $1$ and length exactly one or two. This is a provisional heuristic based on simplifying postulates: longer partitions are assumed to contribute negligibly to the prime-gap estimate, and the relevant length-one and length-two partitions are expected to account for most odd values in the gap. It is explicitly a model rather than an established theorem, and no resolution is supplied.