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 γOLS ∈ 1. 5, 2. 6 while ML yields γML ∈ 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.
Jan Blanc (Sun,) studied this question.