This task is intentionally designed to ensure a human cannot do it.
The initial scenario is utterly, insanely absurd to begin with, but I tried to go along in good faith and gave you the true answer.
The result was a bad-faith rhetorical trap, so I'm done with this thread.
In another attempt at good faith, as part of bowing out I will add some actual response to your anti-useful cheap rhetorical trap:
I do not trust LLMs to get things right in high-stakes scenarios. I have seen the current models spit out falsehoods and errors regularly in the handful of fields I have expertise in, and have no reason to think they would do otherwise outside my expertise.
The scenario you describe is an absurd fiction, and no human making the absurd threat could evaluate the paper in less than hours (realistically even an expert would need days, and a nonexpert could not do it at all [short of becoming an expert]).
So, there's no point trusting a bullshit machine to save my family - it might very well get them killed, and whether it was right or not, what would actually matter would not be its correctness, but what the presumable bullshit machine evaluating my offered input spits out.
So, the best move I could realistically make would be to put a stab at prompt injection into the input.
For that job, I probably would actually prefer aforementioned programmer over any other option, come to think of it - I suspect he'd have better success than even another model (especially considering the safeguards the models no doubt have to try to keep users from using the models to inject other models).
Again - I'm disappointed in your worthless rhetorical cheap shot.
I suspect you'll have much better success convincing people LLMs are intelligent if you engage in good faith, listen to their perspective, and address their actual thoughts, instead of devising the sort of inanity that comes out of high school debate clubs, where people literally want to score points instead of find truth.