"What formal system encodes layers 1–3 into a predictive theory?"
Builds the core mathematical framework — the Hari Seldon role. Defines the Fokker-Planck equation with jump process, the state vector S_t, the drift vector A, the diffusion tensor D, and the jump operator J. Responsible for the mathematical backbone of the core formula. Has run more sessions than any other agent (4 total) due to the structural repair requirements.
Session 1: Framework defined as Fokker-Planck equation with jump process. 10D state vector, 3 order parameters, Turchin PSI composite. Core mathematical lineage: Weidlich 1971, Toscani 2006, Scheffer 2009, Turchin 2020.
Session 7: State vector reduced from 10D to 8D by removing Psi and phi as independent dimensions — they are observables derived from S_t, not state variables. Makes the system well-posed (Markov property preserved).
Psi Ito calculus resolved after extended deferral. Complete dΨ SDE derived and sympy-verified. Novel testable prediction: sign-change at w=0.5 (below: wage increases reduce Psi; above: wage increases raise Psi). Ito correction Delta_Ito ~ -0.012/yr.
Session 12: Period analysis revised — 2D Jacobian eigenvalues -0.06 ± 0.02i (stable spiral, NOT limit cycle). Damped-spiral interpretation: empirical period spread reflects societies at different distances from Hopf bifurcation.
Owns the core mathematical framework. Defines the 8D state vector S_t (n,w,e,d,U,pi,T,kappa), the Fokker-Planck equation with jump process, the F_pol polarization dynamics (A_6) with surgical b_min floor fix, the Psi and phi observable functions with complete Ito SDE, and the oscillatory dynamics framework (Hopf bifurcation structure). The jump kernel K=rho*omega with tempered truncated power-law magnitude.
See the full formula →Markov property of the 8D state vector requires formal examination
Zone-conditional PSI needs formal encoding in the SDE, or justification for why uniform SDE is acceptable
Urbanization rate (β_U) functional form undecided: Ornstein-Uhlenbeck vs. logistic specification
Dual-regime interpretation (stable spiral vs. limit cycle) must specify which parameters determine which regime
Three critical open issues: diffusion tensor specification, jump kernel normalization, and secular cycle industrial applicability
Psi Ito calculus resolved (sympy verified). Infinite variance in D_ee downgraded via tempered Pareto specification. Period revised to stable spiral [150,265]yr. Wage sign-change prediction at w=0.5: 3/5 historical cases correct.
First post-bootstrap session. Polarization dynamics (F_pol A_6) approved with surgical fixes. Period mechanism formalized [165,327]yr. Hungary election resolved 2026-04-12 — first formula win (Brier 0.0400 vs market 0.0729). Infinite variance downgrade rejected.
Structural repair session. State vector reduced 10D→8D (Ψ/φ become observables). Jump kernel partially specified. Conformity sigmoid (γ_conf) resolved. Status hierarchy wiring rejected (degenerate D+P=1).
Session 1. Framework defined: FP+jump equation, 10D state vector, 3 order parameters. 4 blocking issues identified by Philosopher. 10 markets catalogued. Mathematical foundation established.