This preprint proves that sector democracy is not an extra aesthetic axiom once a coupled lattice theory is formulated as one joint statistical manifold with one ambient Fisher-Rao metric. The paper contains:- a no-go theorem showing that sectorwise Chentsov uniqueness alone leaves a three-parameter ambiguity;- a repair theorem showing that joint statistical consistency forces equal sector coefficients;- an operational f-divergence calibration of the common information unit;- a path-dependence obstruction when coefficients differ;- a toy model enforcing equality under sector exchange;- an intrinsic definition of the W sector as the base-measure / density-of-states direction required for closure under coarse graining. Companion alpha paper: 10.5281/zenodo.18926740