Cursed array notation

Cursed array notation (CAN) is my second array notation. It looks rather like R function; an example array is 10$[[ω,2],1,[0,0,1],[0,3],0,4], which is approximately Nωωωω4+ω3+ωω+ω(10^^1010).
Googologisms are here.

Parts

# Name Example Limit array Limit ord.
0 Linear 10$[0,[0,3],0,ω,2] [0,0,...,1] ε0
1 Dimensional 10$[0([0(1)ω([0(1)1])1])0,1] [0([0(...)1])1] Γ0
2 Expanding 10$[0([[0([ω]1)1],1,2]1)0(1)1] [0([0,0,...,1]1)1] ψ(Ω2)
3 Higher expanding 10$[0([0([ω,2]2)0(1)1]1)0([0]1)1] [0([0([0([0(...)1]3)1]2)1]1)1] ψ(Ωω)
4 Infinixpanding ... [0([0][0]...)1] ψ(ψI(0))
5 Dropping ... [0([0([0,0,0,...,1]1)1])1] ψ((+1)-Π0[0])
6 Multi-dropping ... [0([0([0([0(...)1]3)1]2)1]1)1])1] ψ((λα.ωα+ωCK)-Π0[0])
7 Omega-dropping ... [0([0([0([0(...)1]ω)1]ω)1]ω)1])1] ψ((λα.???)-Π0[0])