Have you ever considered the square root of three with regard to the root mean square value of a triangular waveform?
Basically without going through all the maths, it's the area under the half wave, in this case a triangle, which is the effective value in terms of transmissive power , expressed as a value of the peak .. (base to height) of the triangle.
R.M.S. value of triangular waveform = Peak value (Base to peak)/ The Square Root of Three.
Which is equal to ... 0.577 of the peak value.
Just google R.M.S of a triangular wave, They can explain better than I can.
I'm not sure yet how the clock determines "C" but if it does, it seems to me that what is being stated may have somethiong to do with the root mean square value of a triangular waveform at light speed.
I've been messing about with sine waves which have an R.M.S. of 0.707, I may have been barking up the wrong tree.