Robert
"The speed of light is not directly observable; it is not an observable phenomenon at all. There is always a "privileged" observer."
"...When a light wave is first created, it is created in the reference frame of this privileged observer. It is created at the frequency observed by that observer, not the Doppler shifted frequency of an observer in a different frame of reference. And the privileged observer is always at rest with respect to itself."
"...Hence, when all other observers transform their actual observables to the privileged observer's frame, they too must infer the same constant speed of light."
These phrases and meanings are precisely common to our essays. But I'm awestruck by your logical analysis of mathematical limits. I abandoned the study of maths from intuition about it's shortcomings modelling reality, for which you now give the precise reasons, beautifully argued and written. I now far better understand WHY the Fourier transform fails, though I even wrote of FM receiver mechanisms some time ago.
My route to this end was logic and ontology, also observational from optics and as an astronomer. I dare to suggest I've also pushed a little further than you, in maverick style, to find curved space-time and even pre big bang conditions. Though I hazard that you too report far from all your findings.
I hope you'll find time to read my essay. Quite different to yours as it simply analyses the mechanistic evolution of real systems without abstraction, avoiding the limitations you so brilliantly identify. I'd like to cite you, but saw no references. Do you have anything on this published?
There are a couple of areas we diverge, and I'd like to scrutinise those, along with a couple of new kinetic considerations I consider, such as the relationship of f and wavelength for different observer frames, and the severe limitation I derive for spatial limits of the emitters frame.
Very Best wishes
Peter