I don't think you're either wrong or right (in fact my intuition sides with yours I think) because I definitely know way less than you about the subject in general, or probably also less than almost anyone here on HN-- just the trust of swaths of people in the authoritativeness of LLM outputs does generally amuse me. I'm sure we'll get there one day, but we're not there yet. I clearly offended you, and I apologize.

Sure, it's okay to be wrong, but it gets significantly less okay when you just keep doubling down on being wrong and refuse to admit you are wrong.

Unless I've missed something, you still seem to be under the very wrong impression that you've come up with a secure shuffling algorithm. You simply have not come up with a secure shuffling algorithm. The minimum viable evidence of security for an algorithm is mathematical proof and you don't have that, and you don't get to sit a the security table until you do. Put bluntly: mathematical proof or GTFO.

Yes, I'm gatekeeping, and there's a very good reason for that: we know from tens of thousands of bad attempts at secure algorithms that if there isn't a proof of security it very likely is not secure, with disastrous effects. It is not a kindness to let this sort of wrong information spread, and it's not assholish to be clear that it is wrong.

EDIT: Even if you want to add "probably" or some other qualifying word to your claims, "This shuffling algorithm is probably secure" is still wrong. No, that shuffling algorithm is probably not secure. I am sorry to be a hardass here, but the idea that this is an effective approach to security needs to be deleted from your mind.