Reserved-set classification conjecture for multiple harmonic sums

Let ${\boldsymbol{s}}\in\mathbb N^l$. Let $RJ({\boldsymbol{s}})$ be the reserved divisibility set, and let $RJ_1({\boldsymbol{s}})$ and $RJ_2({\boldsymbol{s}})$ denote the corresponding sets obtained from the first and second index ranges. Reserved-set classification conjecture. If (i) ${\boldsymbol{s}}=1$, (ii) ${\boldsymbol{s}}=(1,2,1)$, (iii) ${\boldsymbol{s}}=(2r-1,1)$ for some $r\geq1$, or (iv) ${\boldsymbol{s}}=1^{2l}$ for some $l\geq1$, then

$$RJ({\boldsymbol{s}})=RJ_2({\boldsymbol{s}}).$$

For all other ${\boldsymbol{s}}$,

$$RJ({\boldsymbol{s}})=RJ_1({\boldsymbol{s}}).$$

The claim organizes which parts of the divisibility set contribute to the reserved set; the paper gives heuristic support but no general proof.