Dear Armin,
tank you very much for your comment, but I was not particularly surprised about this comment.
Actually, I've already read that paper (i.e. topic 329). It caught my attention because you have explicitly made a reference to Epstein's book: Relativity Visualized, Insight Press, 1997.
As you know Epstein described the Postulate of the Constancy of Light in a specific geometrical way - as a (quarter) circle being parametrized by c = 1.
If you interprete this (quarter) circle concsciously as the geometrical blueprint of the wave-like face of c, as I called it, then the question naturally arises: How does the geometrical blueprint of the particle-like face of c look like?
My answer: It looks like a SQUARE, which is also parametrized by c = 1.
That's the formal or principal content of the Dual Parametrization of c.
When Epstein discussed the Galilean Principle of Relativity in terms of his visual approach he should already touch this blueprint of the square, but he did not recognize it as physically meaningful blueprint. (see: pp. 64, 65 ) Instead of that, he excluded it, because it contradicted special relativity, especially the Lorentz-Transformation.
But there is no contradiction: If we assume, that both blueprints the (quarter ) circle and the square are closely entangled, then their relationship to each other can be read in a lorentzinvariant way.
Interestingly the lorentzinvariant design of this entangled geometrical structure is sligthly different from the relativistic type of Lorentzinvariance. Just this subtle difference allows to test this hypothesis experimentally.
This structure is - as conceiced by me - the geometrical core of a more extended space-time-picture. Hence, the Dual Parametrization of c is not implemented in special relativity in an as yet unrecognized way as you have supposed in your comment. It is just the other way around: the relativistic space-time is somehow implemented in t-h-i-s structure. It is more complex and more extended than the relativistic space-time-picture.
My 5-pages NPA-paper "The Hidden Face of c or: The True Meaning of the Kennedy-Thorndike experiment" gives you an impression of all the stuff which I have sketched here in a few lines.
You can easily google this by: hidden face of c
Kind Regards
Helmut
P.S. I will, of course, look at your present paper.