Capacity Constraint Forces a Bifurcation in Coordination Scaling Laws
Abstract
Scaling laws across radically different systems — tumor progression, financial markets, open-source software — cluster into two exponent groups, yet no unified framework explains this bifurcation. We show that capacity saturation forces a bifurcation into Class T (Hierarchical Optimization, β < 1) and Class M (Multiplicative Competition, heavy tails).
We validate across four domains. Trust & Finance: Trust networks exhibit Class M signatures with spectral concentration exceeding both static null models (z > 5) and Barabási-Albert dynamic nulls (z = 43–112), ruling out preferential attachment as explanation. Oncology: Tumor metabolism scales superlinearly (β ≈ 1.25), exceeding geometric bounds on surface-limited growth. Software Teams: Teams operate on a spectrum of coordination manifolds (d̂s ≈ 0.8–3.0). Bootstrap analysis of 16,822 GitHub repositories confirms the Landau-Ginzburg prediction: variance of β peaks 56-fold at N ≈ 100–200, exactly where β crosses unity (p < 10⁻⁸). Within-system analysis of 7,743 repositories confirms the predicted growth-productivity tradeoff (p < 10⁻⁶). Out-of-sample: Citation networks confirm Class M predictions with unanimous classifier votes.