Several second order differential operators are shown to annihilate the YM
and GR tree scattering amplitudes. In particular we prove a conjecture of
Loebbert, Mojaza and Plefka from their investigation of a hidden conformal
symmetry in GR.Comment: 31 pages; v2: edits in various sections to improve clarity; computer
code included in an appendix; v3: acknowledgments adde
