The connection between the Silent One and the Butterfly on the emblem (Metal Gear Solid 5: The Phantom Pain)

Explain, please, what is the connection between the butterfly on the emblem and the Silent One? Some guides indicate that if you post it, then it allegedly does not leave after 45 episodes of the main campaign. I tried posting, but after the specified episode, it went away anyway. Does the fake come out or were there any other nuances? Maybe the butterfly on the emblem refers to something else?