Observation plateaux do not determine past response

The operators in (eq:operators) depend on the switch throughout the contributing causal past. Agreement of two switches only near $\mathrm{supp}f$ does not imply equality of either map.

For a comparison with different switch data, keep the bare coordinate prescription fixed and denote the two formal Euler perturbations by $L_g[q]$ and $L_{\tilde{g}}[q]$. The finite inverse identity gives

Only agreement on the complete contributing causal region forces this difference to vanish. This observation follows from the present test operators. VII-A-ST's analogous switch ledger concerns a different coordinate equation space VIIAST.