Free-shell non-descent remains

For $P_m=\square +m^2$,

With $p>0$, $\omega =\sqrt{p^2+m^2}$, choose

Then $P_m{\varphi }_0=\square c=0$, but

Thus the natural positive-order scalar rule does not preserve the unchanged free equation ideal. A compact relative ghost equal to this coefficient near a compact test supplies a local comparison, not a global compact free ghost solution XHST,XIST.

X-J-ST supplies no retarded interacting BV transport that would remove this distinction.