What gives you basis to believe and accept that all of the above is exhaustive, complete and devoid of fakes? That "finding" finds ALL what exists and NONE of what does not exist? Ditto for categorising, summarising and labeling?
There is no fundamental guarantees provided by LLM architecture, so to assert anything of sorts would require manually executing the operation and comparing the results. And why not asserting the correctness is not negligence or fraud?
I am not saying it is impossible, but so far I have not found any explanations that would close this huge gap in logic for me. LLMs themselves "admit" the gap cannot be explained rationaly.