Requested feature overview description.
In addition to the other sorting options found on the cheatsheet https://e621.net/help/show/cheatsheet#sorting I think it would be useful if we could sort by "hot", which would be the score over time.

• A post with 10 points and is 1 hour old would be sorted above a post with 20 points and is 3 hours old.

• A post with 10 points and is 2 hours old would be sorted below a post with 20 points and is 3 hours old.

Why would it be useful?
It would allow users to see some of the most highly voted recent submissions easily. The current best ways to do this are to search with "score:>10" or "order:score date:day" or similar, but these aren't as good as a hypothetical "order:hot". Neither can make both of the above conditions true at the same time.

What part(s) of the site page(s) are affected?
Searching

This feature doesn't sound useful, I don't understand the need to see popular images within such a tight time frame

Means you can see 'popular' art that isn't just 'popular' because it happens to be the oldest. Ordering stuff by score skews it towards stuff that's been there longer, by virtue of it being around longer to amass more points / views / etc.
Traditional systems make finding newer things that aren't hot garbage harder to do unless you're scouring on the regular in ways like the first guy said.

Yeah, this is basically about fixing the problem where score ends up being partly a proxy for how long ago something was uploaded (positively scoring posts get more upvotes over time, negatively scoring posts get more downvotes over time)

+1 on this, I definitely consider the stated situation to be a problem, and it seems obvious that your proposal would succeed in addressing it.

But you're kind of making things awkward by simultaneously posting the Wilson confidence interval feature request at the same time. Assuming that theoretically we could do both, it seems like there is an obvious question "Can we combine these two proposals?".