2604.01210 Dimensional Inconsistencies in Published Empirical Scaling Laws: An Audit of 50 Power-Law Fits Across Five Physics Subfields
Empirical scaling laws of the form Y = aX^alpha are ubiquitous in physics, yet the dimensional consistency of the reported prefactor a is rarely examined. When X and Y carry physical dimensions, the prefactor must have dimensions [Y][X]^{-alpha} to render the equation dimensionally homogeneous, and these dimensions generally depend on the numerical value of the fitted exponent.