F(wo, wi)=g(Dot(wo, wi))=g(Dot(wi, wo))=F(wi,wo)
Ah yes, i'd glossed over the fact that g acts on (wi.wo), not (wi). Thanks!
f(wo, wi)=g(Dot(wo, wi))/cos(wo) which is not reciprocal
But I through that reciprocity was defined for f (not F) ? Even though the 1/cos term is irrelevant - it still appears in f.
I can't remember the details (too tired now!), but I think that I considered that you're dealing with small spheres, rather than a flat surface element dA as a reflector, then you get a 1/(wi.n) term appearing in F which then transfers to f - so it became:
F = g(wo.wi)/(n.wi)
f= g(wo.wi)/(n.wi)/ (n.wo) which is reciprocal and everyone's happy.
In advance I concede that I am likely wrong. Was very tired when I came up with that - but it does look nice and neat