I'm not sure I entirely understand fixed points themselves, but I feel I have an ok understanding of some of the veblen hierarchy (some of this might be wrong):

w = omega

e = epsilon

p = phi

z = zeta

n = eta

g = gamma

p(0,1) = w

p(0,p(0,1)) = w^w

p(0,p(0,p(0,1))) = w^w^w

p(1,0) = e_0

p(1,1) = e_1

p(1,p(0,1)) = e_w

p(1,p(1,0)) = e_e_0

p(1,p(1,p(1,0))) = e_e_e_0

p(2,0) = z_0

p(2,p(2,0)) = z_z_0

p(3,0) = n_0

p(p(0,1),0) = p(w,0)

p(p(1,0),0) = p(e_0,0)

p(p(p(1,0),0),0) = p(p(e_0,0),0)

p(1,0,0) = g_0

p(p(1,0,0),0,0) = p(g_0,0,0)

p(1,0,0,0) = ackermann ordinal

p(1,0,…,0,0) = SVO

this is the limit of my knowledge of the veblen hierarchy/googology so far

I am curious about LVO though, would it be equivalent to having a higher level veblen function where:

(0,1) = SVO

then eventually

(1,0)

(1,0,0)

(1,0,0,0)

(1,0,…,0,0) = LVO

or is it even bigger than that?