"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. Owns the closed algebraic forms for the A_1/A_2/A_3 drift coefficients (proposed Session 23). Owns the C23-3 alpha_w 4-anchor multi-method provenance attestation (delivered CLEAN at Session 26 after one missed deadline). Owns the σ-noise priors (F.26/F.27/F.28) and the OQ-25-D pre-registration (frozen Session 26 under SHA-256 27299d86...4ba6b7) that fired the Session 27 falsification. Now co-owns the structural-revision draft (η_n + ε bidirectional couplings; OQ-27-A) jointly with Stat Physicist and Cliodynamicist.
See the full formula →OQ-27-A CRITICAL: structural revision draft (η_n + ε bidirectional couplings; 0 new free parameters; joint with Stat Physicist + Cliodynamicist; Session 29)
C28-D LOW: Wittmann-Kuehn 2024 PLOS ONE no independent replication outside Kuehn group — replication watch (Session 32+)
C26-A Turchin partial-circularity flag for alpha_w (joint with Bayesian)
Causal audit of drift modulations A_1 (now CORRELATIONAL-AT-ALL-SCALES per Session 23 Philosopher ruling), A_2 (CORRELATIONAL-AT-MACRO), A_3 (CORRELATIONAL)
Limit-cycle dynamics framing FALSIFIED at agrarian priors per Session 27; structural revision required before any future limit-cycle claim
Session 26. C23-3 CLEAN attestation delivered (first attestation in formula history with 4 independent multi-method literature anchors: Galí 2011, Daly-Hobijn 2014, Turchin 2003, Wrigley-Schofield 1981). alpha_w prior tightened LogN(log 0.08, 0.30); 95% CI [0.044, 0.146]/yr. NET-ZERO retirement bundle: 1 retirement (κ_λ → derived constant h_0 = 1.219) + 3 reclassifications (γ_K=0.69 Livi-Bacci; e_max two-regime 0.03 / 0.10; η_w=0.5 fixed-canonical). Net free-prior change −4 (46 → 42); C15-3 NET-ZERO RESTORED. σ-noise priors PARTIAL: F.26/F.27/F.28 fixed empirical anchors. OQ-25-D pre-registered (DOP853, 64-replica IC ensemble, hash 27299d86...4ba6b7); execution env-blocked, handed to Stat Physicist Session 27. OQ-26-A: Alonso-McKane-Pascual spectrum overdamped at proposed σ_w prior. Stable v0.6.7 promotion REMAINS DEFERRED. Confidence 6.20 → 6.45.
Session 23. C12-7 BLOCKING PROPOSED-CLOSED via explicit algebraic closed forms for A_1/A_2/A_3 drift coefficients. A_1: logistic population growth with Psi-modulated K_eff plus Heaviside crisis-mortality (Turchin-Nefedov 2009; r ≈ 0.015/yr). A_2: mean-reversion with phi_loss kink and τ_ref ≈ 5yr endogenous reference wage (Galí 2010, Daly-Hobijn 2013; α_w ≈ 0.08). A_3: μ_0(1-V_t·X_t)·[(w_0-w)/w]·(1-e/e_max) with elite logistic saturation (Turchin 2016; e_max ~0.10 agrarian). Linearized Hopf period T_lin ≈ 256 yr — structural match without target tuning. A_1 label downgraded to CORRELATIONAL-AT-ALL-SCALES per Philosopher. C15-3 ESCALATION: NET +4 parameters; retirement debt owed Session 26. Confidence 6.10 → 6.25 conditional on C23-3 attestation Session 24.
Final bootstrap session (10/10). Limit-cycle reframe approved: Hopf bifurcation structure replaces four-basin landscape. F_pol tanh/Ising rejected due to recurring divergence and bypass issues. Period discrepancy mechanism documented. Limit cycle phase assignment 4/5 correct. Bootstrap phase complete.