The Ostrowski Dimensionless Reformulation: A Systematic Compilation of Fundamental Physics Equations in Planck Units

Abstract

Version 1.8. Systematic compilation and dimensionless reformulation of 53 fundamental physics equations across ten disciplines, motivated by the Ostrowski Dimensionless Mandate. Dimensional formulations implicitly privilege the Archimedean completion of the rationals per Ostrowski theorem (1916). All quantities expressed as pure-number ratios to Planck-scale counterparts (hbar=c=G=k_B=1). v1.6: p-adic valuation correction (pi transcendental, ratios-only framing). v1.7: Running Couplings section — alpha(Q~^2) is a running ratio, 1/137.036 is the deep-IR Archimedean projection, not a fixed constant. v1.8: Ratio Primacy Principle (§2.3) restored — pi as C/d ratio, alpha as cross-ratio, constants-as-ratios table, ratio extraction, cross-ratios in p-adic physics. 18-page PDF, 21 references, 6 self-checks per formula (dimensionless, rational-system, non-computable-free, ratio-traced, running-aware, completion-agnostic).