This entry pitch is not new, done by Topher Donahue and Patience Gribble, Tower Arête, 5.11 (although a direct line looks possible if I remember, another thin seam to the left).
Pitch 2 (5.8) a long pitch approaches the dihedral on left via wandery ledges, blocks, and flowers. Stop beneath a gleaming right-facing corner, unfortunately slammed shut.
Pitch 3 (5.12R) Look slightly right from below the blank corner. Climb over 15 feet reaching an overlap with some flakey holds, you are standing on a pillar. It is a bit spicy but provides the just-good-enough edge or two, finishing with a granite hueco)!
Pitch 4 (5.10) heads up a beautiful left-facing, widening hand crack that parallels the original dihedral system. Good climbing, belay at a descent stance.
Pitch 5 (5.11) a longer pitch climbing the next wide hands and fists splitter, a burly and radical pitch, with a thoughtful finish stepping left to a descent stance back in the dihedral system.
Pitch 6 (5.11-) was mine, and I must admit: I wanted out. I headed up a short ways attempting to complete the direct line but the flaring crack and kitty litter was too intimidating. I veered sharp right, foot-traversing, then climbing up a sketchy layback flake. Mind the ridiculous rope drag, step hard right again and up onto moderate terrain. Gain the ridge and moderate blocks to the summit of Snowpatch.

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West Face of Snowpatch Spire.

Doubles in fingers to #4 cams. Small wires nice for the first pitch.