What is the evidence for those who take the opinion of unifying the commencement of fasting and just using one horizon as reference?

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Ibn ‘Omar (ra), reported that our Prophet (pbuh) said: “The month of Ramadan may consist of twenty-nine days. So do not fast until you have sighted it (the new moon) and do not break the fast until you have sighted it (the new moon of Shawwal), and if the sky is cloudy for you, then calculate.
Commencement of fasting is associated with the moon sighting; however, the sighting of a few people will suffice.

Majority evidence is extracted from Sunnah and Qiyas (using a precedent event as a reference).
Sunnah: Abu Hurairah (ra) reported, the Prophet (pbuh) said, “Observe saum (fast) on sighting of the crescent and terminate it on sighting it (the new moon), but if the sky is cloudy before you, then complete thirty days.”
Fasting must be commenced for all Muslims with the sighting of the new moon. It can be as sighted by the majority or by one whose testimony is accepted.