The III comparison

The supplied III records distinguish an unreduced Cauchy isomorphism, a reduced quotient, a past-trivial retarded section after a forced scalar correction, and a free-product obstruction CheungIII,CheungXA. These answer different equation-space questions.

In the present comparison:

• the smooth coordinate Cauchy map is defined before a solution-jet quotient is imposed;

• Proposition prop:jet-domain tests membership in VI's solution-jet domain;

• the scalar-switch identity tests a different switched assignment;

• no free-product or quantum-product obstruction is used to decide the coordinate forcing.

III's retarded section is not substituted for either $w[h_{\lambda }]$ or $X_{\mathrm{cand}}$. Likewise, V's fixed-time scalar response is a negative control, not a coordinate jet CheungV.