mystery
Well, since I DID rotate my tires right/left 1200 miles ago, this thread had me scratching my head.
Just went out and looked at the tires, and on my Pilot Sports I did NOT see a directional arrow, but did see the word 'OUTSIDE' molded into the tire wall, which as you know is not the same as a directional arrow, cause moving the tire right to left still leaves the same side out, but the tread rotating in the opposite direction.
I looked at the tire as closely as I could given the less than ideal lighting in my garage, and could not discern any clear cut directional arrow on the sidewall. If it's there, it must be a stylized arrow that's part of another image on the sidewall...or my lighting is that bad.