How do I prove that I don't collect data from my llm app?

Building an incognito llm chat app for hobby and fun. I don't want users to trust me that I don't log prompts. I want them to be able to verify it.

I can't really go the TEE route as that is very hardware leaning and I don't have the resources

I'm not sure if open-sourcing the repo also would be enough to really prove it. maybe open sourcing the model and the repo then it and hashing it to show that it was not changed somehow... i'm not super sure

What would actually convince you that a someone is not your logging prompts, is there some way to prove it ? (For instance why does someone trust proton)