Axiomatic Physics: Distinction as Irreducible Primitive

By C. Rich

DOI 10.17605/OSF.IO/Q63C5

In Cosmological Pangaea I set out to prove that the complexity of our universe doesn’t require a complex foundation. I propose that distinction, the simple, binary capacity for state A to differ from state B, is the only irreducible primitive of reality. By stripping away the assumptions of pre-existing fields, particles, or smooth manifolds, I treat distinguishability itself as the ontological ground floor. From this single axiom, I am able to derive the 3+1 dimensional signature of our spacetime as the unique stable arena for propagating these distinctions. Using Huygens’ Principle and Bertrand’s Theorem, I show that 3+1 dimensions is the only environment where a distinction can travel as a sharp wave and maintain stable orbital motion, making our four-dimensional reality a logical necessity rather than a cosmic accident.

To address the mystery of why matter comes in three repeating “families,” I developed the Self-Reference Closure (SRC) Theorem. My research suggests that for any system of distinctions to reach a state of physical closure, where it can distinguish its own internal structure from the external world, it requires a minimum of exactly three generators. This combinatorial requirement directly predicts the three fermion generations we observe in the Standard Model, such as the electron, muon, and tau. Furthermore, I argue that the fundamental split between the “stage” of spacetime geometry and the “actors” of matter and energy isn’t an arbitrary design, but a mandatory partition within the distinction algebra itself. I even see the fine-structure constant not as a random number, but as a counting invariant inherent to this structural logic.

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