The relative difference is so absurdly small to be irrelevant at any realisable input size. At least that's my read; e.g. even at n=10^80 (~number atoms in universe), the relative difference is ~0. That's still probably underselling how similar this is to n log n.
this is how all the proofs today are looking, they seems so minimal even when compared to minor improvements in these fields from that last 10 years im wondering why even publish these and not just make research notes public
I'm not sure this is true e.g. you can specify schema `pl.Datetime("ns")`. That survives roundtrip to/from parquet in my experience. True though that the default is `us` whereas pandas defaults to `ns`.
The cost of the standard `actions_linux` is $0.006/minute, so spending $500 to save 6m per invocation, break-even is at ~14k invocations. But, if they're using larger machines and/or parallel jobs the $$$ saving accrues faster. IMO the wall-time saving shortening feedback loop may be a bigger win, but harder to value.
It's used all the time in mathematical optimization, referring to the best feasible solution found so far and therefore the "answer" until/unless something better appears. If you work with people in that space, it leaks out to mean anything "current" you're trying to improve upon.
I saw a breakdown (don't have on hand sorry) where server depreciation was by far the majority. Power was the largest cash opex, probably matching your intuition.
Re Signal, I've taken a few flights lately where there's messenger-only wifi, and it's been handy to have OpenClaw on a box accessible through telegram to do web_searches for me.
That's certainly not justification for setting it up in the first place, but is a mildly useful benefit of having done so.