First visibility of the moon I am new here, and hope to state the question well. 

In Islam, it's known that the Lunar Month starts if the Moon is sighted after the sunset of the 29th day of that month.

If someone claimed that he sighted the moon before the conjunction or if the moon sets before the sun, then this claim is certainly false.

My question is, what is the least conditions on the possible visibility of the moon? 

There are many criteria that confirm the impossibility of sighting the Moon, but many people still claim the sighting. Which one is wrong?
Here is 13 hours 48 minutes.
That's a mighty early sighying:
https://www.universetoday.com/107700/ultra-thin-young-crescent-moon-sighted-from-u-s-southwest/
11 hours 40 minutes was the world record as of 2014.