"Which economic patterns exhibit phase transitions and power laws?"
Applies physics methods to economic systems — power laws, phase transitions, critical phenomena, and mean-field approximations. Responsible for the econophysics macro parameters. The key empirical validation of the FP+jump architecture: the inverse cubic law (alpha_tail ~ 3) confirms finite variance for continuous dynamics and infinite variance for crisis events.
Inverse cubic law (alpha_tail ~ 3.0): 40M+ data points, replicated across multiple markets (Gopikrishnan 1999, Gabaix 2003, methodology 5/5). This VALIDATES the FP+jump split: alpha_tail > 2 means finite variance for continuous dynamics, while alpha_war = 1.53 < 2 means infinite variance for crises.
lambda_labor ~ 0.57 from BLS/FRED data — resolves the OPEN blocking item and makes epsilon = (1-w)/(0.57*e) computable, yielding realistic ~44x per-capita income for top 2%.
α_pareto ~ 1.5 for wealth distribution (Vermeulen 2018, Klass 2006) — but creates an infinite variance problem in the diffusion tensor D_ee.
T_debt: short cycle Normal(7,3)yr, long cycle Normal(75,25)yr — Dalio 2018 / Reinhart-Rogoff calibration.
Provides Section A macro parameters: alpha_pareto=1.5, alpha_tail=3.0, m_crash=0.33, T_debt (7yr/75yr cycles), T_ineq~125yr (calibration observation). Provides 5 of 6 drift coefficients: alpha_w=0.1, gamma_f=0.05, lambda_labor=0.57, mu_0=0.1, w_0=1.0. The tempered Pareto proposal for D_ee (using Rosinski 2007 tempering) addresses the infinite variance problem.
See the full formula →Tempered Pareto specification for D_ee diffusion tensor awaits concurrence — η_pareto prior still needed
Urbanization rate (β_U) functional form undecided: Ornstein-Uhlenbeck vs. logistic specification
Causal audit of economic drift equations needed — α_w and γ_f may have endogeneity issues
Linearized oscillation period (140yr) differs from empirical secular cycle period (250yr) by 44% — discrepancy unresolved