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I can precisely say what the atomistic treatment of “reality” is:
The atomistic treatment describe matter and interacting fields correctly (for instant at each velocities of particles; no matter how large the velocities are) under the circumstance that neither the positions, nor the velocities are ever exactly known. For the description, only invariants are used (for instant invariant elementary charges, invariant terms in the Lagrange density, invariant action integral, etc.) in order to get covariant equations of motions; that means: equations of motions which are independent from coordinate systems (and are valid for all velocities of particles). That is exactly the dynamics of the universe. The laws of nature are non-deterministic, however causal.
You said “Invariance, covariance, form invariance… these are “buzz-words” to me…..”. I’m unhappy to hear this. You try to use treatments, either such within you don’t use invariants (entropic treatment), or you tries to use exactly known velocities (Lorentz factor with a mass, but which mass?). If you want, there is little connection between our both theoretical settings.