User blog comment:B1mb0w/The Quantum Function/@comment-25601061-20190613165543/@comment-10262436-20190614014348

all t_ functions in the Quantum function behave like ordinals do in the FGH function. Therefore your option 2 is definitely illegal. Evaluation must follow the defining rules.

Your option 1 is correct, but it evaluates exactly the same as your option 3. IE

Q(Q(n,t_{0}(0)),n) = Q(Q^{Q(n-1,t_{0}(0))}(n-1,t_{0}(0)_{*}),n) = Q(Q^{Q(t_{0}(0)-1,t_{0}(0))}(t_{0}(0)-1,t_{0}(0)_{*}),n)

Therefore the t_ functions are only evaluated when the defining rules call for a decrement of a specific parameter. In this case the left t_{0}(0) = n.

Ordinals are evaluated in the FGH function in the same way.