Very nice, Physics Monkey, but my point was that angular velocity (w) is predicted to decrease as the inertial observer approaches the rotating disk at increasing relativistic velocities. The angular velocity (w) DOES NOT decrease in the co-rotating observer's frame. If I understand your mathematics correctly, the difference in T2-T1 and t2-t1 still depends on the inertial observer's velocity relative to the rotating frame. If that relative velocity is small, the inertial observer and the co-rotating observer agree on the exact difference in time the two light paths take. However, if the relative velocity between the inertial observer and the rotating frame is great, the inertial observer will calculate a smaller difference in the Sagnac effect than the co-rotating observer will measure. In other words, the angular velocity (w) of the rotating frame will appear to decrease for a relativistically travelling inertial observer, but will not change according to the co-rotating observer. Your solution works for small relative velocities between inertial observer and rotating frame, but increasing that velocity (NOT angular velocity in the rotating frame) to where time dilation supposedly slows the angular velocity of the rotating frame leads to discrepancies in the amount of the Sagnac effect in the two frames. The co-rotating observer would measure a constant Sagnac effect regardless of the relative velocity between the two frames.