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

Abstract

Version 1.5. 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). v1.5 adds: (a) Ratio Primacy Principle - pi as C/d ratio, alpha as cross-ratio; (b) Completion Lattice - all 5 Ostrowski completions (R, Q_2, Q_3, Q_5, adele ring) with physical correspondences and cross-formula bridges; (c) Tate-compliant adelic extension. 15-page PDF, 21 references, 8 cross-domain bridges.