Is fasting obligatory for one who sights the crescent of Ramadan alone, and what is the evidence for that?

Scholars have differed on the issue of one who sights the crescent moon of Ramadan (definition) or Shawwal alone, and whose testimony is not accepted, holding three opinions:

1. He acts upon his own sighting, so he fasts and breaks his fast individually. This is the madhhab (definition) of Ash-Shafi'i, and he does so secretly.

2. He acts upon his own sighting for fasting only, and breaks his fast with the people. This is the madhhab of the majority of scholars, such as Abu Hanifa, Malik, and Ahmad, and it was chosen by Sheikh Ibn 'Uthaymeen.

3. He does not act upon his own sighting at all, so he fasts and breaks his fast with the people. This is a narration from Imam Ahmad, and it was chosen by Sheikh Al-Islam Ibn Taymiyyah, who used as evidence the hadith (definition): "Your fast is the day you fast, and your breaking of the fast is the day you break your fast, and your Sacrifice is the day you sacrifice." He also argued that the crescent moon (hilal) and the month (shahr) are derived from "istihlal" (proclaiming or announcing) and "shuhrah" (fame or widespread knowledge), so the crescent moon is not considered a "hilal" unless it appears to the people and they proclaim it. This opinion was given as a fatwa (definition) by Sheikh Abdul Aziz bin Baz.