James,
"The fundamental equation modeling patterns in changes of velocity is f=ma. The empirical evidence is represented by a."
No it isn't. The evidence is the differential measure between mass at relative rest, and mass in relative motion. I'm seeing your problem now -- you think that the variability of the acceleration curve determines states of mass at rest relative to the value of the variation -- that isn't true. States of rest mass are determined relative to states of accelerated mass, not to the acceleration curve, which is not a physically real quantity. As I said before, the *meaning* of f = ma does not change when we truncate the statement to f = m.
You're confusing the physical concepts of "speed" and "velocity." We can speak of an instantaneous measure of speed, which is always a positive value; velocity, which averages speeds over a given interval, can consist of both positive and negative acceleration. So there's no sense in which one can say that acceleration is a physically real phenomenon -- it is not independent of the instantaneous energy content (the speed) of the body (the mass).
A universal constant for speed, OTOH, symbolized by c, IS independent of the properties of velocity.
"The variations of patterns in that evidence tells us that there is a cause and there is a resistance to that cause."
No, it doesn't. I consider it a travesty of the essay contest that Vesselin Petkov's entry did not get near the attention it deserves -- it is brilliant -- and if one understands what it means that bodies do not resist their motion, one understands the true depth of relativity theory's contribution to physics. Gravity is primary.
"The cause is called force and the resistance to cause is called mass."
No. We don't know what causes mass (the standard model favors the Higgs field), and we don't know that mass and inertia are related, though the equivalence principle does identify that inertial and gravitational mass are equivalent.
"No one knows what cause is and no one knows what mass is. We only know the roles they play in forming patterns of changes of velocity of objects."
I hope I have convinced you that the patterns of changes in velocity are not physically real. They are abstract representations of physically real phenomena.
"Everything that is to be learned about the roles they play must be discerned from patterns in changes of velocity. Everything that is said to be true about either cause or resistance to cause must be communicated by use of terms of empirical evidence only. Anything else added into that communication is imagined."
What we know about speed, velocity and inertia IS empirical. What you call "imagined" -- i..e, the theoretical explanation -- is how we communicate the evidence, not something we made up in a knowledge vacuum.
Cheers,
Tom