The C-series largest-entry conjecture

At $q=e^{2i\pi/3}$ and in the homogeneous limit, let

be the normalized ground-state eigenvector for the $C_r$ model, and let the \sum of entries for $C_{r-1}$ refer to the corresponding normalized ground-state vector of the smaller model. **C-series largest-entry conjecture.** The largest entry of

for $C_r$ is the sum of entries for $C_{r-1}$. The assertion is presented after empirical sum and pairing formulas, and the supplied text gives no proof or resolution.