Originally Posted by
reppans
What's so embarrassing? The same thought has certainly crossed my mind climbing short steeps (although my weight differential is hiking 20 lbs vs biking 50 lbs).
A quick search for 'race up mountain - run vs bike' yields the Race To The Top of Vermont - a 4.3 mile, 2564 ft vertical climb up Mt Mansfield, the highest peak in VT.
Race To The Top Of Vermont
Neither runner nor cyclist are carrying camping gear of course, but considering an ultra-lighter can get to a pretty immaterial weights, let's put that aside for a moment and just consider the time difference between man+machine vs man as a proxy. From the rules, it appears that CX/gravel bikes w/knobbies (due to dirt road) are permissible so my guess is that the 'machine' component gets into <20 lbs range among the cycling leaders.
The 2016 Top 5 Results are closer than you'd think. 
Yup, I'm a bit surprised there, OTOH I've seen pro races where riders get forced to stop on short steep climbs & then they often choose to run up the rest of the hill & don't really lose much time. I'm so out of shape mountain touring is tough even w/o luggage,
. UL guys often start out with big weight advantage of CF bikes, I'd love to see a production CF trad-touring bike--folks say there's no demand but I see lots of mediocre riders on local path twiddling around on $$ CF road Cervelos & Pinarellos. For them the weight saving of CF is psychological; for a tourist it's more real.