If there is an error in the moon sighting, and it is proven that we did not fast on one day of Ramadan, do we have to make it up?

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She intended to fast ‘Arafah to make up a missed (obligatory) fast one week before ‘Arafah, then she forgot that intention and fasted it as a voluntary fast; is that acceptable in order to make up the missed (obligatory) fast?
She is not sure whether she formed the intention to make up a missed Ramadan fast before dawn or not, so she changed her intention to observing a voluntary fast

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Related Answers:
Which takes precedence: making up missed Ramadan fasts or fasting in expiation for breaking an oath or fulfilment of a vow?
Is it permissible for her to have a medical exam or test which requires her to break her fast during the day in Ramadan?
She did not fast because she was unaware that fasting was obligatory for her; does she have to make up the fasts?
She intended to fast ‘Arafah to make up a missed (obligatory) fast one week before ‘Arafah, then she forgot that intention and fasted it as a voluntary fast; is that acceptable in order to make up the missed (obligatory) fast?
She is not sure whether she formed the intention to make up a missed Ramadan fast before dawn or not, so she changed her intention to observing a voluntary fast

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