What the construction adds

The plan requires a second coefficient, a positive selective total-variation gap, and complete instruments. These are different requirements.

A nonzero number chosen to cancel another number is not an independently defined coefficient. A nonzero classical coefficient need not be visible in every encoding. A positive outcome-law gap does not determine the surviving quantum output. Finally, matching charges along one direction does not establish invariance under an entire gauge algebra.

The construction below addresses these points separately:

1. two compact moments are obtained by finite polarization of the already specified X-I-ST vertex;

2. their values and their charge directions are explicitly constructed rather than assumed;

3. a fixed amplitude readout gives a positive finite-task gap, with all failure probability included;

4. the complete selective maps, references, finite composition, and prescribed transport are proved;

5. the precise failure of whole-algebra charge matching is exhibited.

The scalar moment construction is elementary. The general theory of classical BV and finite-dimensional instruments is not new FRBV,DaviesLewis,Watrous. The contribution is the supported assembly and the exact distinction between its positive result and the stronger reference construction that it does not provide.