The whole point of range proofs, and bulletproofs, is the ability to prove a transaction is balanced, without revealing the transaction history.

Ring CT, and key images, prevent double spend and prevents transaction history from being public.

I've given you the reference documents. If you'd like to read those documents and then discuss the details with me I will engage you in a reading group no problem.

But just repeating the same point back at me without reading what I've indicated or even acknowledging what I've said isn't productive for either of us.

I want to thank you, however, I've been meaning to go through all of the paperwork on monero. And this gave me an opportunity to do so.