My Lynskey frame is meant to be used with 700x28c tires, with Michelin 700x28c rear tire mounted on my rear wheel.

Chainstays and seat stays have about 3-4mm of clearance on both sides of the rear tire.
Plenty of clearance for the seat stay bridge, over 30mm of space.

I don't use a Lynskey carbon fork, so I can't tell if the front tire would have clearance issues with Lynskey forks.
My $100 Chinese carbon fork has plenty of clearance, even for 700x32c tires.