Structure conjecture for maximally foldable stamp assignments

Consider mountain-valley assignments for a $1\times n$ strip of stamps, and call an assignment maximally foldable when it has the greatest number of foldings among assignments for that strip. Maximal-assignment structure conjecture. For $n\geq 8$, a maximally foldable MV assignment consists only of blocks of sizes $1$, $2$, and $3$, and no two consecutive blocks have size $3$. The claim is based on computational data; the source does not provide a proof or resolution.