IN RESPONSE TO SOMEONE'S QUERY AS TO SOLOING THE ROUTE:
This climb depends on your skill and/or exposure comfort level. I will speak for myself (I led the whole climb) and the general consensus between me, Sergio, and Eric. Note that we simulclimbed the whole mountain, though we did set anchors for the leader and second until the rope came taut for the third, after which time there was no anchor, only set pro between us.
The first 40% of the ridge to the first steep rise in it is easy class 4 stuff. There is a lot of heather and benches abound. Some trees too. Rap anchors are very easy to find (I practically climbed past or up to most of them; they are often conveniently located at nice platforms).
The first steep rise goes at low fifth. It's a little loose in places and still vegetated. One can find protection that is adequate on this rise. You can see a rap station at its top. The rise is maybe about one 60m pitch high. I could see soloing this rise. It is the part in the fourth picture on Eric's Triumph page.
After the first steep rise is the knife-edge traverse. There are two horns on the traverse but the climbing is not hard. Then there is a shimmy/cheval downclimbing section along the knife blade of about 15 feet. This is way exposed but again not really hard. After that, the real steep part begins. From a distance this steepness looks daunting but the closer you get to it and as you begin climbing it you can see it's easier than it looks (5.6). This is the part I know I certainly wouldn't solo. This section can be seen in the 6th picture on Eric's site linked to above. In this picture you can see Sergio on the crest at the bottom. I'm a little hard to see but I'm on the crest too in the sun just up and left of the centerpoint of the image and right of the prominent black vertical crack just left of the crest; I have blue long underwear on). My size gives you some scale.
You may have heard of the 5.7 off-width. From where I am in the 6th image, I climbed up to a small notch (unseen in Eric's photo) and belayed up the other two. From the notch, I aimed up and right to the base of the off-width on narrow ledges (to mid 5th). The off-width can be seen in the 6th photo on the shady side as a right-slanting crack about halfway between me and the top of the image (it looks thin in the photo but it is about six inches wide; it is farther back than it looks) . It is just right of the sunny crest. I tried to go up this crack and got about halfway before running out of good strong hand holds. I backed off. Steep off-widths with only friction for feet is not my bag. Instead, after much umming and ahhing as to which way to go, I traversed right past a small horn block on the corner and found an easy gully/chimney on the other side that trended back to the crest (woohoo!).
The gully is easy and leads to a big platform. From the platform the climbing is easier though there is a nice little steep friction slab from the belay that has only tiny fingerholds and foot nubs. This slab is only about 8 feet high. Its crest is just out of arm's reach so you've got to do one scratch move to get up it. I stood on Sergio's shoulder but only because he offered it. Sergio apparently found a nub for his left foot (severely exposed on the left side of the crest) and got up easily. Eric went around to the right since he had no shoulder to utilize and he is a little shorter than me or Sergio. Eric's way is more exposed. You could solo the slab. If you fall, you'll probably fall back to the platform so no harm no foul.
Once above the slab, you contour around the right side of a small tower to its flat top. From there, there is a giant notch (Sergio is rappelling into this notch in the last photo; Eric calls it a chimney but it's not really a chimney). A way left (a foot path) beyond the notch goes past some big blocks and onto a ledge that ends about 50 feet further on. From there, you can climb up a 4th class chute for about 30 feet. At the top of the chute, another ledge goes left with a foot path. From here to the top it's all easy heather and rocky class 3 and 4. The best completion goes up and right to the ridge crest immediately northeast of the final summit scramble. No register at the summit, which I thought was odd.
To get down, I'd definitely have yourself a 60m rope in the bag. If you have a shorter rope you will find yourself doing that many more rappels and also find yourself doing them from steep faces since the rap stations are set up for 60m lengths (maybe 50m lengths). Be prepared for lots of rapping. It took us 4.5 hours to get up to the top from the start of the technical climbing (about one pitch below the bivy ledge) but roughly 5.5 hours to get down. We did 7 double 60m raps, 1 single 60m rap on a double rope, and one single rope rap to get back to the major notch at the base of the climb. We also simulclimbed back along the knife-edge part. With three people rapping it took us longer. From the summit, you can save time by downclimbing the steep heather back to the aforementioned giant notch. There is a rap station just below the summit that goes down to the giant notch by way of a near-vertical face but I'm pretty sure you need two ropes for it.
At this time of year doing the climb in three days is most appropriate. Earlier in the summer it might be doable in one day but two days is leisurely. It took us roughly 4 hours to get to the 5,840- ft saddle SE of Thornton. Don't believe sandbagger Beckey and his 3 hours. It's a real grunt going up that final ravine from the lakes. There is a faint footpath on the steep heather bank on the right side of the ravine. On the return to the car it took about an hour less. From the saddle over to the NE Ridge of Triumph took about 1.5 hours including all the defecation breaks, etc. On the return going the other way it took about 45 minutes. The glacier is not an issue, it being so receded that it is above the traverse for the most part. You do have to get on snow and ice at this time of year (crampons are a must), but 80% of the traverse is on easy smooth slabs. The most disconcerting thing about crossing under the glacier--which looks very sickly--is that you can constantly hear thunks and bumps as the various ice blocks (the glacier is not very deep) move. Occassionally, while on the ridge we could hear a rumbling clatter down below the glacier. It always sounded like a big serac or block was calving off but we were surprised to see that the ruckus merely resounded from small ice falls and tumbles down the low-angle slabs.
Regarding water at the notch, there was a small snowpatch at the designated camp site, but, being low on fuel, we located a liquid water supply instead. If you descend the steep snowfield on the north side of the saddle about 300 vertical feet you can find water seeping out of the snow. Bringing a platypus-like jug in which to store camp water is helpful.
It's a great climb. Standard Skagit gneiss choss in places (loose flakes, etc.) but all in all a worthy objective. And the views of the entire Picket Range are tremendous!