Signs and multiplicities

Each first-stage partial coefficient has sign and multiplicity $-2$. The complete word has two insertion signs, whose product is $+1$. The middle-slot assignment factor is $2$, not $4$; the partial factor $2$ has already counted the choice of the first middle slot.

The selected order ledger is

Observation differentiation does not change contraction order. It does not introduce independent descendant calibration constants.