This is a route description for Hawkins' east summit (7,080+ ft), called "Thimble" by Fred Beckey. It is a large 70-foot-high block exposed to all sides.
One can approach the east summit from the west summit with only minor difficulties. Another approach is from the south-side meadow.
From the west summit you will have the choice of staying high on the traverse where Class 3 scrambling will be necessary to cross a cliff band (some exposure) or you can drop a couple hundred feet on the south flank to avoid the scrambling but immerse yourself in a sea of talus.
At any rate, aim for the gully that leads to the notch immediately southeast of the summit block.
The first route is the only one I tried. The rest look viable but are only conjecture.
1. Southeast Side (Class 3 up; Class 4 down)
From the notch simply work up to the obvious break left of the overhang. There is exposure to the left and right but especially to the left (70-ft drop). On the way up there is one move that is slabby where holds are smaller. But the friction as good and it’s over quickly. Total distance from the notch to past the crux is about 50 feet with only the last 20 being a butt clencher. Pro placements might be dubious (I forgot to look; I was occupied with saving my life). For the descent reversing this slab move and then another move lower down is the crux. It was harder. I rated it Class 4 just because I couldn’t get my body positioned right. Plus, the holds aren’t “right there for you.”
2. Northeast Chimney (Class 5; probably mid-5th)
Downclimb from the notch on slabs then take a short ledge left to the obvious chimney. There is a lower Class 5 step up to an alcove then another step up through large blocks somewhat overhanging. After that I think it is merely scrambling. Total height of climb is 30m or less. Take cams for pro.
3. Northwest Elbow Crack (Class 5; probably low-5th)
Continue around the backside as per Route 2 to a short ledge with blocks leading to the northwest side (the side facing Hawkins’ west summit). Find a 15-ft forearm crack (Class 4 or 5?) leading to an alcove. Exit from the alcove looks to involve another bit of Class 5 through blocks. Total height of climb is 30m or less. A big bro or a large cam would work in the elbow crack but they may not be needed. I have no idea what the rest of the climb would require.
A competent climber can do this without protection or a rope. If you're not competent, take a 30m rope or don't bother with it at all. For pro take some cams. For the harder routes, larger cams may be advisable.
An ice axe will be needed in early season. The final gully approach to the southeast notch is fairly steep.
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