Lol do you understand what you're even saying?

First of all literally the definition of NP is that there's a verifier in P (that doesn't make it a proof of P!=NP).

Second of all, "research that is easy to check" is called confirmation bias. What you're saying is that AI helps you confirm your biases (which is correct but not what I think you intended).

Confirmation bias doesn't really apply to the same extent with law as with other fields.

If the AI says "Fisher v Bell [1961] 1 QB 394 is authority for the principle that an item for display in a shop is an invitation to treat", it's either right or wrong. A lawyer can confirm that it's right by looking up the case in Westlaw (or equivalent database), check that it's still good law (not overridden by a higher court), and then read the case to make sure it's really about invitations to treat.

If the AI says "Smith v Green [2021] EWCA Civ 742 is authority for the principle that consideration is no longer required for a contract in England" it will take you under 1 minute to learn that that case doesn't exist.

Law isn't like, say, diet where there's a whole bunch of contradictory and uncertain information out there (e.g. eggs are good for you vs. eggs are bad for you) and the answer for you is going to be largely opinion based depending on which studies you read/prefer and your biases and personality. It's usually going to be pretty black and white whether the AI was hallucinating. There are rarely going to be a bunch of different contradictory rulings and, in most of the cases where there are, there will be a clear hierarchy where the "wrong" ones have been overridden by the correct ones.

their use of P!=NP is not incongruent with its meaning; I understood it as saying the tasks that LLMs are good for are analogous to NP in the verification being significantly faster than the search. and at least in the things I use LLMs for (arithmetic with special functions and combinatorial arrays, which is often of the form "find a pathway of manipulations bringing the left side to the right" with a well-defined goal) verification is indeed able to be certain, often via computer algebra systems (that weren't themselves able to find the path, but can verify each step); even if the suitability of historical casework for a lawyer is not absolute and can't be definitively decided complete (since one person can't read everything), they can at least check that it adheres to the law

> P != NP

Source?

I asked my 13 year old and she proposed N=4 and (after some prompting) P!=0. I always threatened to rename her "Howitzer Higginbitham IV". You can use her as a source.