Theory of Scale-Relative Time: Derivations of the Galactic Scale Factor

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This work serves as a formal addendum to the Theory of Scale-Relative Time (SRT) previously detailed in a 39-paper series. It aims to proactively address three significant, anticipated criticisms of the framework by transforming key conceptual arguments into rigorous, quantitative, and falsifiable derivations. First, we derive a parameter-free, physical formula for the Galactic Scale Factor S, which underlies the SRT explanation for the ”dark matter” illusion, and show that S is a calculable function of baryonic matter distribution (S ∝ R/M²). Second, we provide a formal proof for the origin of the 3/2 particle physics resonance constant (Koide’s formula), identifying it as a necessary ”interface constant” between the dimensionalities of the observer’s space and the quantum state. Third, we deliver a rigorous, information-theoretic proof of the P versus NP conjecture, demonstrating that the assumption P≠NP violates the principle of causality. These three specifications strengthen the SRT framework by formally addressing potential critiques of arbitrariness and incomplete formalization.

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