It's possible that you both hit upon or recalled the same cool phrase, especially if the "proving" part was pre-decided and you were thinking of making an incremental improvement.

I was talking to a friend about an idea I had, to build something, he said, "yes! I'm doing that too", then I said "with this specific tooling because is ideal ... " .. he said .. "me too! same tooling", I said "what a coincidence!! amazing ...wait a minute, have you been talking with Claude about this? " ... of course we both did.

My opinion is that that LLMs are influencing us more that we think, and it makes us reach the same conclusions and making us think it was our idea, or that we were the ones steering the conversation.

Perhaps you feel that Claude stole your phrase but I don't think 2 days is enough for that phrase to make it to a re-training, I think it might be more subtle and worse, perhaps you wrote that phrase influenced by the conversation, and the other person did the same.

Just a theory, I can't prove it. But if you think about it, LLMs conversation are the most plausible choices, so it is logical that we all users of this machine are going to tend to converge on the most plausible way of thinking and talking.

No offense, but perhaps that rhyme that you though it was original, it is actually the most plausible in that context.