Did a great 5.10c alpine route on this with Pulaski back in the seventies.
It goes up the left edge of the white arrowhead shaped feature in the photo above.

As I recall lots of loose stuff on this. Didn't Tom's dog take long fall on this mountain in the '70s?

Scott, yes Tom's dog Charley (what a great dog) took the big big one off the traverse from the top of the main buttress. That traverse is really desperate. It is comprised of steeply slopping, boiler plate slabs covered in ball bearing gravel. Charley some how survived fairly unscathed.

I was there at Gothic when Tom and I and Charlie were descending. Charley couldn't do the descent and we weren't able to carry him down in that area. We figured he'd find his way down another way. We heard a yelp and scary dog screaming when we were down a ways. Charlie had jumped and Tom started crying. I turned and saw Charlie running toward us and turned Tom around to see him. Charlie came up with a hurt "elbow" of his leg but able to continue down. Tom Pulaski was so happy. He put a poultice of yarrow flowers on Charlie and Charlie healed well.

Tom and Charlie both - quiet, unassuming, and unbelievably fearless and tough.

Is there a route that climbs the center of the Arrowhead?

Not to my knowledge. At least not yet.