I’m old and slow, so this is not a humble brag by any means. But, focusing on the uphill, I’d argue that the strict definitions of mountain running that most of you are advocating don’t comport with how the term is used by most people who consider themselves mountain runners, and are strict enough that they include only elite or near elite athletes.
Let’s look at Strava, Bierstadt specifically. Again, uphill only. 2,081 people have “run” Bierstadt, i.e., posted a Bierstadt climb as a run. Let’s look at the top 10%. An hour and eleven minutes, an average pace of 19:38 puts you in the top 10%. How about the top one third?. I’ll go with my best time, roughly 31st percentile. That’s a time of 1:30, or 24.51 per mile. Is that mountain running? Most Strava users who “run” Bierstadt would consider that a fairly decent time, but by most of the definitions here that would fall far short.
A 13er example, Audubon (again, TH to summit):
top 10%: 1:15, 19:37 / mile. Actually, that's just outside the top 10%, and is ... Cordis Hall (I'm sure though far from a max effort for him).
top 25% (my best time): 1:25, 22:03 / mile.
Of course I’m sure I’ll get a number of “LOL Strava users” type comments. Point is, among people who consider themselves trail runners, the standards for a mountain run are much more lax than most of the responses here.
Moving on to Ultra running, if we go by JManner’s definition, most Ultra-runners are not “runners.” Which seems counter intuitive to me. No disrespect to John, who often gives me kudos on Strava, even for my slow-ass “runs.”