Similar on the surface, yet different on zooming in
I recently uploaded a working paper on arXiv (P1: 2211.13217), which extends one of the previous papers (P2: 2107.07356).
The core contribution of P1 is the proof of Theorem 3 (and the proof sketch of Theorem 4). On the surface, the reductions seem similar to the proof of Theorem 3 in P2, but on zooming in, they make very different contributions. Specifically, the results in P2 are based on multiple assumptions whereas the results in P1 are based on a singular assumption (which, in principle, makes the reduction itself unconditional). Hence, the proofs in P1 are more intricate. I do not expect a computer to capture such nuances. Hence, this brings me to a line of thought:
At what resolution do we measure similarity, especially in theoretical research? We all know that two totally similar problem statements, with a very minor change even in just one number, may lead us on completely different paths and may be mean different things.