I'm not sure that there is a universally accepted definition of
open conditional.
Nevertheless, I've seen it used in opposition to the term hypothetical conditional.
A hypothetical conditional is either the so-called Type 2 conditional:
If it rained, we would need our umbrellas.
Or the so-called Type 3 conditional.
If it had rained, we would have needed our umbrellas.
Or certain mixed conditionals.
If they had seen the film on first aid last month, they would now be prepared to handle this emergency.
Anything else is an open conditional according to this system (including the Type 1 conditional):
If it rains, it makes a mess in the garden.
If we have calculated correctly, the answer is 569.
If it was raining that day, the wedding was sure to be spoiled.
If what Geoge said was true, Marilyn had almost certainly left town last night.
If the prisoner escaped, he did so with the help of a guard.
If it rains, we will cancel the outing. (Type 1.)
If you're sure he'll soon be here, I'll wait a little longer. (Type 1.)
Ambiguity is possible between the two types:
If he lost the key to the car, he would have his wife bring the copy from home. [habitual reading with would = used to -- open; possible-one-time-incident reading -- hypothetical]
(In this system, your example with did or did not is a hypothetical conditional.)
The line dividing the two major types may differ by author.
CJ