There is no Bitcoin brand and the software is open source. You are failing to grasp these concepts.

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Prove it.

Github is all the proof you need: https://github.com/bitcoin/bitcoin

You don't understand how open source software works and your arguments are invalid.

Doubt that’s satoshis repository, and then whether satoshis white paper holds true, and valid proof of work a different story.

Prove the validity from something when bitcoin and blockchain was published about a decade and a half ago.