Is ablution obligatory when in doubt about purity?

It is recommended to renew ablution for every prayer, even if it has not been invalidated. Doubt regarding ablution has two scenarios:

1. If the doubt was not preceded by a certain state of purity, such as someone who slept, then woke up, and the time for prayer entered, and he does not know if he performed ablution, or he entered the restroom and is not sure if he performed ablution afterwards; in this case, ablution is obligatory because the default state is lack of purity.

2. If there was a certain state of purity and then doubt arose, such as someone who prayed Duha, then the time for Dhuhr prayer entered and he doubted whether his ablution was invalidated; in this case, he is not required to perform ablution, because the default state is the continuation of purity, and certainty is not removed by doubt. Whoever is certain of impurity and doubts purity, he is impure. And whoever is certain of purity and doubts impurity, he is pure.