From Quarks to Cosmos: Scale-Free Organization Across 15 Domains and 30 Orders of Magnitude

We report the measurement of the power-law exponent γ across 15 independent sci-entific domains spanning 30 orders of magnitude in spatial scale — from subatomicparticles (10⁻¹⁵ m) to cosmological structures (10¹⁶ m). Using two independent estima-tion methods — ordinary least squares (OLS) in log-log space and maximum likelihood(ML, Clauset et al. 2009) — we find that γ estimates depend significantly on the fittingmethod: OLS yields γ_OLS ∈ [1.5, 2.6] while ML yields γ_ML ∈ [2.4, 4.4] on the samedata. This methodological sensitivity means that claims of convergence at a specificvalue (e.g., γ ≈ 2.0) must be interpreted with caution. Nevertheless, all 15 systemsexhibit scale-free organization, and Detrended Fluctuation Analysis (DFA) confirmslong-range temporal correlations (α ≈ 1.0, characteristic of 1/f noise) across domainsfrom an artificial cognitive system (Moldavite, α = 1.18) to solar activity (α = 1.17) andthe Saphire cognitive system (α = 0.97). These convergences suggest self-organizedcriticality as a common organizing principle, while the exact exponents depend ondomain-specific dynamics and measurement methodology.