Lead agent: Statistical Physicist
Framework chosen: Fokker-Planck equation with jump process — proven in Weidlich (1971), Toscani (2006), Scheffer et al. (2009). Sociophysics is phenomenological modeling, not a category error.
State vector S_t defined as 10-dimensional: 5 directly measurable (n,w,e,d,U), 3 indirectly measurable (pi,T,kappa), 2 derived (Psi,phi).
Jump process tied to Turchin PSI composite: MMP × EMP × SFD. Base rate lambda_0 undefined; threshold Psi_threshold undefined — all retrodiction untestable.
4 blocking CRITICAL issues: Tier 3 overdetermination (Psi/phi both state vars and derived), jump kernel K unspecified, 2 symbol collisions (kappa, alpha) across files.
CRIT-01: Tier 3 overdetermination — Psi/phi cannot be both state dimensions and derived quantities
CRIT-02: Jump kernel K(S,S') unspecified — probability non-conserving
CRIT-03/04: Symbol collisions (kappa, alpha) across parameter files
HIGH-01: I_t institutional vector in formula signature but absent from all drift equations
Session 1 launched the Psychohistory Research System from zero. No formula existed. The Statistical Physicist dispatched 15 sub-agents in parallel to research the mathematical foundations: partition functions, master equations, Fokker-Planck dynamics, renormalization group methods, bifurcation theory, and Monte Carlo approaches — all applied to social systems.
The core mathematical choice was decisive: a Fokker-Planck equation with jump process. This framework, grounded in Weidlich (1971), Toscani (2006), and Scheffer et al. (2009), treats societal macro-states as a probability distribution that evolves through deterministic drift (long-run economic and demographic forces), stochastic diffusion (random shocks), and discrete jumps (revolutions, crises, regime collapses). The state vector S_t was defined with 10 dimensions: 5 directly measurable variables (population density n, relative wage w, elite fraction e, fiscal stress d, urbanization U), 3 indirectly measurable (polarization pi, institutional trust T, network connectivity kappa), and 2 derived (PSI political stress composite, polarization order parameter phi).
The Philosopher of Science approved the update but identified 4 CRITICAL blocking issues. The most serious: Psi and phi were listed simultaneously as independent state dimensions AND as derived quantities — a mathematical contradiction creating an overdetermined differential-algebraic system. The jump kernel K(S,S') was proposed but left unspecified, making the jump operator probability non-conserving. Two symbol collisions across parameter files added confusion.
Ten Polymarket markets were catalogued for future predictions — the formula was judged not ready for any numerical output. All 5 retrodiction events tested were UNTESTABLE (no calibrated parameters). But the mathematical skeleton was in place: the research system had a structure to build upon.