Research Program
Why do radically different systems — biological organisms, software teams, financial markets, trust networks — exhibit the same mathematical regularities when they scale? This program investigates the hypothesis that capacity constraints on information processing force coordination systems into a small number of universal scaling regimes.
The Core Result
Scaling exponents across diverse systems cluster into two groups: sublinear (β < 1, economies of scale) and superlinear (β > 1, concentration dynamics). We show this bifurcation is forced: when coordination demands exceed processing capacity, the effective dimensionality of the control space collapses, driving systems toward one of two stable configurations.
Systems that route resources through space-filling hierarchies, achieving β = d̂s/(d̂s+1). Unifies Kleiber's Law in biology (β ≈ 0.75) with sublinear scaling in software teams (β ≈ 0.57–0.83).
Systems where agents compete for finite resources through multiplicative reinforcement, producing heavy-tailed distributions and concentration. Trust networks, citation systems, financial markets.
Methods
Established statistical methodology throughout: Clauset-Shalizi-Newman power law analysis, heat kernel trace for spectral dimension, Maslov-Sneppen and Barabási-Albert null models, Granger causality for temporal ordering, bootstrap variance estimation. All primary analyses use publicly available datasets (SNAP, GHTorrent, ISBSG).
Open Questions
Several empirical and theoretical gaps remain: systematic spectral dimension measurement across organization types; the conjectured relationship between eigenmode collapse and the Cheeger constant; whether mean-field Landau-Ginzburg approximation requires corrections for sparse clustered graphs; and whether increasing capacity can reverse bifurcation. Documented transparently in the paper's limitations section.