Arithmetic inclusion for normalized linear forms in odd zeta values

Let $q$ and $r$ be the parameters above, let $F(\boldsymbol h)$ be the normalized quantity defined by

$$F(\boldsymbol h)=\frac1{(r-1)!}\sum_{t=0}^\infty R^{(r-1)}(t),$$

and let $m_1,m_2,\dots,m_{q-r-1}$ be the successive maxima of the set of parameters $\boldsymbol e=\{e_{0k}=h_k-1:1\le k\le q;\ e_{jk}=h_0-h_j-h_k:1\le j<k\le q\}$. Here $D_m$ denotes the corresponding arithmetic normalization factor.

Arithmetic inclusion conjecture. There holds the inclusion

$$D_{m_1}^rD_{m_2}\dotsb D_{m_{q-r-1}}\cdot F(\boldsymbol h)\in\mathbb Z\zeta(q-2)+\mathbb Z\zeta(q-4)+\dots+\mathbb Z\zeta(r+2)+\mathbb Z.$$

This conjecture proposes that omitting the final normalization factor from the established inclusion preserves the integral span of the relevant odd zeta values and $1$. It is motivated by Ball's example, direct computations for small parameter values, and Rivoal's conjecture; the supplied source does not indicate whether it has been resolved.