  We give a criterion for extending a generically semisimple (not necessarily
conformal) Frobenius manifold locally near a smooth point of the discriminant
to a cohomological field theory.
  As an application, we show that a large set of tautological relations related
to the Givental--Teleman classification for any generically semisimple
cohomological field theories follow from Pixton's generalized Faber--Zagier
relations.
