The formal scalelessness conjecture for monomials in Feynman integral families

Let $I(z_1,\ldots,z_n)$ be an $L$-loop integral with nonnegative indices, and let $D_1,\ldots,D_n$ be the propagator generators in the associated noncommutative rational double-shift algebra. For a sector with $n-u$ active propagators, a monomial $D_1^{i_1}\cdots D_{n-u}^{i_{n-u}}$ is formally scaleless with respect to $I(\underbrace{1,\ldots,1}_{n-u},\underbrace{0,\ldots,0}_u)$ when its normal form under the Gröbner basis $G$ vanishes after setting $z_1=\cdots=z_{n-u}=1$ and $z_{n-u+1}=\cdots=z_n=0$. Formal scalelessness conjecture. A monomial $D_1^{i_1}\cdots D_n^{i_n}$ is formally scaleless if and only if

$$I(1-i_1,\ldots,1-i_{n-u},-i_{n-u+1},\ldots,-i_n)$$

is scaleless. Scaleless integrals vanish in dimensional regularization, so this would identify formally scaleless monomials algebraically with integrals that vanish because the corresponding sector has no mass scale. The source presents this as a conjecture motivated by computations in the noncommutative rational double-shift algebra; no resolution is supplied.