This level of skepticism flies in the face of references to Pythagoras across multiple contemporary authors. Keep in mind that it is damn hard to prove something in the 6th century BC with the same level of evidence as today.
But Heraclitus, for instance, was contemporary and accused him of plagiarism and trickery. Why abuse a person that doesn’t exist? Ion of Chios was contemporary and said that he authored Orphic hymns.
The Orphic hymn to Apollo proclaims “your resonance attunes the whole globe”. Now, we don’t know that Pythagoras wrote that. We can’t prove that sort of thing. But it sure seems Pythagorean.
Did you know that Copernicus, Kepler, Galileo and Newton all claimed to be Pythagorean?
The man is a legend. Embrace the legend. He wrote lots of things down but he either destroyed it to avoid creating a doctrine or it was destroyed during one of the different massacres of Pythagoreans. Because that happened.