ESFL reduction conjecture for one-dimensional symmetry groups

Let a contact sub-connection have a control admissible symmetry group $G$ with $\dim G=1$. One-dimensional symmetry reduction conjecture. If the contact sub-connection is EDFL by partial prolongation, then it must admit an ESFL codimension $1$ partial contact curve reduction. The source presents this as a recent insight and gives no proof or resolution; it is intended as a necessary-condition conjecture relating EDFL partial prolongations to ESFL reductions.