Adam may be not the clearest example. I'd say the clearest example is the original GAN paper, where "theorems" where completely unrelated to what they were doi

Adam may be not the clearest example. I'd say the clearest example is the original GAN paper, where "theorems" where completely unrelated to what they were doing and trivial at the same time. >>and even if it risks publishing an accidentally incorrect proof. No. If a researcher has even a slightest doubt about the correctness of their proof, they should either spend the time to verify it or talk to an expert. There is no lack of experts in convex optimization in particular. Or, instead of publishing the proof, one could just say "we believe this is provable by these methods". But one can not try and shift the burden of verification to the readers, while claiming the results. This is not how trust is built.