On one hand, the Rambam says (in 2:10)
Once the court sanctifies the new month, it remains sanctified regardless of whether they erred unwittingly, they were led astray [by false witnesses], or they were forced [to sanctify it]. We are required to calculate [the dates of] the festivals based on the day that they sanctified [as the beginning of the new month].
Even if [a person] knows that [the court] erred, he is obligated to rely on them, for the matter is entrusted to them alone. The One who commanded us to observe the festivals is the One who commanded [us] to rely on them, as [implied by Leviticus 23:2]: "Which you will pronounce as days of holy convocation."
The Rambam seems to say that the "making of the new moon" of the court makes the new month (from the fact that even if they made a mistake, the new moon is sanctified).
Yet, on the other hand, the Rambam in (3:16) writes regarding witnesses who came many days after the new moon:
If the witnesses remain steadfast in their testimony, if it is compatible [according to the calculations of the court], if the witnesses are men whose character is well known, they are men of understanding, and if their testimony was scrutinized in a proper way - the moon is sanctified [retroactively]. We recalculate the dates of the month beginning from the thirtieth day [after the previous Rosh Chodesh], since the moon was sighted [on the appropriate] night.
If their sanctification is a "reason" for the Rosh Chodesh, why do they have to retract it if they realized they made a mistake?
