x.com/konstiwohlwend/status/2107872422825537599

The available primary sources for the two examples being discussed do not present their headline exponents as arbitrary finite cutoffs.

• In OpenAI's Integer multiplication below n log n source, the main theorem says there is a machine that computes the exact product "for every n >= 1" with worst-case running time O(n (lg n)^(1-κ)), where κ = 2^-182. The same introduction adds: "The bound is asymptotic through all input lengths." It also explains where the power saving comes from: "This strict inequality is the source of the power saving." That is, the tiny exponent is part of the proved asymptotic theorem, not a byproduct of only proving the result above an arbitrary threshold.

• In Alman and Vassilevska Williams' 3SUM/APSP paper, the abstract explicitly states the proven running times as O(n^1.9992) for 3SUM and O(n^2.9995) for APSP, and traces them to a thin-matrix-product result with complexity O(N^2 / D^0.063). Again, the paper presents these as the actual asymptotic bounds it proves, not as placeholders created by an arbitrary safety cutoff.

So while it may be fair to speculate that later work could tighten these exponents, the claim that the published bounds come from "absurd safety bounds like 2^50 that are entirely arbitrary" is contradicted by the papers' own theorem/abstract statements and explanations of where the exponents come from.