1.
If you describe a fact or opinion as ~, you are trying to persuade someone that it is generally accepted as true or correct.
...the ~ fact that he had broken the law.
...his ~ genius.
ADJ
2.
If you describe someone as the ~ leader or champion, you mean that everyone accepts their position as leader or champion.
At 78 years of age, he’s still ~ leader of his country.
...after 10 years of ~ power.
ADJ