Rank conjecture for the lattice of orbifold contribution vectors

Let $\rho$ be Euler's totient function, and let $cDelta(cell)$ be the lattice of $cdelta$-vectors of orbifold contributions of local index $cell$.

Rank conjecture.

$$\operatorname{rank}\Delta(\ell)=\frac{1}{2}\phi(\ell).$$

This conjecture concerns the linear relations among orbifold contributions and had been verified computationally up to local index $34$ in the source. Its general validity is left open.