What is the meaning of the word "fact"?

Definitions:

A concept whose truth can be proved. NOUN
- The fact that the climate is changing due to human activities poses significant challenges and requires urgent action.
A piece of information about circumstances that exist or events that have occurred. NOUN
- Historical facts help us understand the events that shaped our world.
A statement or assertion of verified information about something that is the case or has happened. NOUN
- You supported your argument with an impressive array of facts.
An event known to have happened or something known to have existed. NOUN
- The fact that the Earth revolves around the Sun is a fundamental concept in astronomy.