I could be wrong, but I think I remembered reading that in music at least, you have to do something with it (like capture it on paper or recording). I seem to remember reading this came about to prevent people from being able to say something was copyright because they maintained they had written something say 10 years ago but just not gotten around to recording it - and then wanted to sue. But this is vague memories from reading about the bizarre and convoluted world of music publishing....

Correct. The law requires it to be “fixed in any tangible medium.” Such as transcribing onto paper, recording onto record, exposed onto film, etc. Merely thinking, saying, playing, singing, dancing, etc a newly created concept is too ephemeral to be a recognizable act of authorship.

Well, almost any proof that you danced that concept would be fixing it to a tangible medium. That rule mostly just rules out heresay, eyewitness accounts, and other such methods of "proving" that you created something

Putting it on a website is enough.