question on the slight different round 1 from paper

[NOOMA-42]

I wonder why do the implementation ignore the Z_H in round1 prove

The protocol on paper is as follows

edit:
In MIT plonkathon recording, speaker said Z_H is intend to be omit for simplicity. Round 2 similarly omits k_1 as, below

My question is how to know which to be omit without impact on correctness?

[mmurrs]

My thinking is $Z_H(X)$ can be omitted as it is the vanishing polynomial, meaning it will evaluate to 0 at all points in the subgroup as multiplying by it would not result in a change of value during the construction of A, B, C