Conditional audit of the inherited switch representative

The switch convention is essential. If the entire intermediate product were compact and the formula were read merely as $P_1{P}_2{P}_3$ applied to a compact distribution, its trisolution would vanish by the annihilation identity. Past-to-future switches avoid that mistaken compact-intermediate reading.

The representative can participate in an admission argument only after the needed wavefront hypotheses are separately established. Preservation of the trisolution does not prove those hypotheses. No such argument is performed for $t_{\mathrm{D}}$ here.