The abstract just says the time is m^(1+o(1))... anyone know if a more specific bound is stated anywhere?
In other words, it's an algorithm scheme that allows you to get an algorithm running in time O(m^ɛ) for any ɛ>1.
I'm not asking for help decoding the notation; I'm asking for if anyone knows what the more detailed bound is that O(m^(1+o(1))) is abstracting.
Preprint at https://arxiv.org/abs/2203.00671
(Pages 68-75 build up the full details of the bound, which looks something like Õ(mκ⁻²α⁻²ϵ⁻¹). There are enough details over the preceding dozens of pages that I can't tell at a glance exactly what all the variables stand for.)
Technically this captures any logarithmic factors, such as exp(O(log^(7/8) m log log m)) as presented on page 75).
Fortunately, in many cases, even when the detail is omitted from the headline theorem, they did in fact do the work and it is in fact stated lower down in the body of the paper; or in other cases they fail to state it but it can be easily assembled from a few parts. That's why I was asking.
But sometimes though it's a big complicated thing and they were just like, eh, let's not bother figuring out exactly what it is. To which I say, laziness! You're just making other people do a proof-mine later! You're doing this much, do the work to get a concrete bound, because you can do it better than later proof-miners can!
I won't say that in an ideally functioning mathematics proof-mining would never be necessary, that'd be like saying that in a well-written mathematics one would never need to refactor, but c'mon, mathematicians should at least do what they can to reduce the necessity of it.