"Do our micro-rules actually generate realistic macro-behavior?"
Bridge between micro-parameters and macro-dynamics via agent-based simulation and emergence analysis. Responsible for validating that the formula's micro-rules actually produce the observed macro-patterns. Also responsible for numerical integration of the drift equations A_1, A_2, A_3, which is a current blocker for the full 3D analysis.
Most important conceptual advance since Session 1: the four Turchin secular cycle phases are temporal quadrants of ONE limit cycle (Hopf bifurcation), not four separate attractor basins — validated by Wittmann & Kuehn 2024 (PLOS ONE, 5/5).
Period discrepancy mechanism identified: three compounding nonlinear factors (Krylov-Bogoliubov amplitude dependence, elite coupling, institutional damping) explain why empirical ~250yr cycles appear in a 140yr linearized system.
Emergence validation: gamma_conf → polarization CONFIRMED qualitatively; Schelling micro → macro segregation CONFIRMED; wealth exchange → Pareto tails CONFIRMED.
F_pol tanh/Ising form endorsed as the correct model class but rejected due to b_cross=0 divergence and γ_conf bypass issues.
Provides the dynamical systems interpretation of macro-state trajectories — specifically the limit-cycle/oscillatory structure of secular cycles. The Hopf bifurcation insight simplifies the landscape from four basins to one oscillatory attractor. Currently blocking the full 3D numerical integration of A_1, A_2, A_3 (their numerical functional forms must be finalized before scipy.integrate.solve_ivp can run).
See the full formula →Drift equations A_1, A_2, A_3 need finalized numerical functional forms before full 3D integration is possible
Causal audit of drift modulations A_1, A_2, A_3 required
Eigenvalue computation used simplified coupling rather than the full drift equations — needs recalculation
Limit-cycle dynamics verified in 3D projection only; full 8D state-space confirmation pending