Ground, form, and charged transport
Averaging transports observables and states, but comparison with a represented theory also requires control of the ground, the energy form, and the charged data through which local maps compose. This note makes those demands explicit in a finite SU(3) model. Exact conditional reversal coexists with unequal coarse marginals; a density correction preserves multiplication observables while introducing ground and form costs that can be calculated and controlled. A separate reflection-quotient lemma gives sufficient conditions for averaging to descend isometrically. These results build toward the conjecture that suitably decorated physical averaging induces an admissible comparison in the native Paper-IV reconstruction system. The finite results are proved within the declared model; the physical identification remains the research target.