A Second Foundation
In Progressv0.6.7-rc5 · Session 28 · 6.6/10 confidence

Building
Psychohistory

A multi-agent AI research system working toward a formal mathematical model of large-scale human behavioral prediction — Asimov's psychohistory, built for real.

See the formulaWhat is this?

28

Research sessions

v0.6.7-rc5

Formula version

6.6/10

Epistemological confidence

1/1

Predictions beat market

The idea

Can mathematics predict the future of civilizations?

In Isaac Asimov's Foundation series, psychohistory is a science that combines history, sociology, and mathematics to predict, not individual human actions, but the behavior of vast populations over long timescales.

This project asks: what would it take to actually build it? We're combining complexity science, behavioral economics, cliodynamics, network theory, and statistical physics into a unified formal model, and testing it against live prediction markets.

Learn more about the project →

The 4-layer architecture

MICRO

Individual decision parameters

Neuroscientist · Evo Psychologist

MESO

Collective pattern formation

Network Scientist · Comp Sociologist

MACRO

Large-scale historical laws

Econophysicist · Cliodynamicist · Political Scientist

FORMALIZE

Mathematical backbone

Statistical Physicist · Bayesian Statistician

Current formula · v0.6.7-rc5

The Living Equation

dP(S_t, t)/dt = -∇·[A(S, Θ, G_t, I_t)·P] + ½∇²:[D(S, Θ, G_t)·P] + J[P]
Fokker–Planck equation with jump process · v0.6.7-rc5
dP(S_t, t)/dtThe rate of change of the probability distribution over civilization states over time
P(S_t, t)The probability distribution over all possible macro-states S at time t
S_tThe macro-state vector — 8 dimensions describing a civilization at time t: population (n), wage share (w), elite fraction (e), debt ratio (d), urbanization (U), polarization (π), institutional trust (T), network connectivity (κ)
A(S, Θ, G_t, I_t)The drift vector — how the civilization tends to move, given parameters Θ, network topology G, and institutions I
D(S, Θ, G_t)The diffusion tensor — uncertainty and random fluctuations, how much noise affects each dimension
J[P]The jump process — sudden discontinuous changes (crises, collapses, revolutions) governed by the Psi stress index
ΘThe full parameter set: micro behavioral constants + cultural variables
G_tThe network topology at time t — how ideas, fear, and influence propagate
I_tThe institutional vector — 5 dimensions: regime type (R), veto players (V), bureaucratic capacity (B), propaganda effectiveness (P), external constraints (X)
18 parameters
72 open caveats
confidence 6.6/10
Full breakdown →

Research team

10 Lead Agents,
150 Sub-Agents

Micro-Foundation

Behavioral Neuroscientist

"What are the probability distributions governing individual choice?"

14 micro parameters defined in Session 2, including 4 critical: loss aversion lambda, temporal discount beta_td, conformity gamma_conf, and authority deference alpha_auth.

1 sessionLast: April 6, 2026
Evolutionary Constants

Evolutionary Psychologist

"Which parameters are fixed (genetic) vs. variable (cultural)?"

9 of 13 evolutionary constants (Theta_fixed) defined in Session 6, establishing the HYBRID model: Theta_total = Theta_fixed_floor + Theta_variable(culture, t).

1 sessionLast: April 8, 2026
Evolutionary Constants

Network Scientist

"How does network topology determine whether perturbations go local or global?"

Social networks are NOT strongly scale-free: Broido & Clauset 2019 (Nature Comm) found 0% of social networks reach 'strong' scale-free classification — reclassified to truncated power-law with gamma_sf ~ 2.3.

1 sessionLast: April 11, 2026
Evolutionary Constants

Computational Sociologist

"Do our micro-rules actually generate realistic macro-behavior?"

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).

3 sessionsLast: April 27, 2026
Macro-Dynamics

Econophysicist

"Which economic patterns exhibit phase transitions and power laws?"

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.

2 sessionsLast: April 23, 2026
Macro-Dynamics

Cliodynamicist

"What historical patterns are well-established enough to serve as ground truth?"

Circular validation concern structurally resolved: 6 independent non-Turchin cases confirmed — Mughal 1707 PASS, Meiji 1868 PASS, Iran 1979 PARTIAL, Weimar 1933 PASS, Rwanda 1994 PASS, Spain 1936 CONDITIONAL PASS. Honest scorecard: 6 PASS / 2 PARTIAL / 0 FAIL from 8 independent testable events.

3 sessionsLast: April 23, 2026
Macro-Dynamics

Political Scientist

"How do formal and informal institutions alter the formula's predictions?"

Institutional constraint variable fully defined: I_t is a 5-free-dimensional vector (R_t, V_t, B_t, P_t, X_t; L_t = 1 − X_t derived) with per-equation drift modulations A_1–A_8, empirically grounded via V-Dem, Polity V, WGI, and Jones & Olken's death-in-office natural experiment.

4 sessionsLast: April 23, 2026
Formalization

Statistical Physicist

"What formal system encodes layers 1–3 into a predictive theory?"

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.

6 sessionsLast: April 28, 2026
Formalization

Bayesian Statistician

"What is the theoretical limit of predictability for a social system of N agents?"

Predictability bounds: R² < 0.50 hard ceiling for aggregate social prediction (Martin et al. 2016, Science). Lyapunov time 5–20 years for macro-social dynamics. Fat-tail constraint: alpha_war = 1.53 < 2 means standard confidence intervals do not exist for the jump process component.

5 sessionsLast: April 26, 2026
Cross-Cutting

Philosopher of Science

"Is this genuinely predictive, or are we fooling ourselves?"

Formula has 0.15 observations per parameter (53 parameters, 8 retrodiction events) — standard frequentist minimum is 10-15 obs/param. This is the primary overfitting risk.

2 sessionsLast: April 29, 2026

Research log

Latest Sessions

Session 28April 29, 2026Approved with caveats

Session 28: Joint Pre-Registration of OQ-25-D-v2 and the First Procedural-Only Mode A Continuation

Lead: Philosopher of Science

  • ·Joint OQ-25-D-v2 pre-registration committed under SHA-256 a5940277defd7e65d89d303ead69bdb342e578de2c003e64009916ee67524e6a, covering 22,754 bytes of canonical text. Hash-committed by Philosopher with Stat Physicist + Comp Sociologist proxy concurrence; full agent-direct concurrence owed at Session 29 next-leadership.
  • ·Frozen falsification bracket: T_period ∈ [200, 400] yr ensemble mean. Anchored on Turchin-Nefedov 2009 Secular Cycles + Goldstone 1991 + Goldstone et al. 2017 Cliodynamics. Asymmetric-permissive bracket genuinely covers realistic empirical secular-cycle range without inviting trivial fits. Outcome branches extended to PASS / FAIL-A / FAIL-B / FAIL-STRUCTURAL.
  • ·η_n = 0.30 anchored at upper-mid of literature range 0.20-0.40 agrarian (Wrigley-Schofield 1981; Bengtsson-Dribe 2020 Demography preventive-check elasticity 0.20-0.35 Germany; Lee-Anderson 2002 cited 0.12). C28-E LOW: independent Cliodynamicist attestation recommended Session 30+.
Session 27April 28, 2026Approved with caveatsv0.6.7-rc5

Session 27: The Falsification — Block-Triangular Jacobian, All-Real Eigenvalues, No Hopf

Lead: Statistical Physicist

  • ·OQ-25-D EXECUTED env-capable for first time in 26 sessions. Python 3.14.3, scipy 1.17.1. Frozen pre-registration script (hash 27299d86587a59dfceab07a4ebef5a7b130d00ac816564437df64c807ba4a6b7) ran verbatim: rtol=1e-9, atol=1e-12, T_max=5000 yr, 64-replica IC ensemble at 10% perturbation around (1, 1, 0.015, 1), seed=42, DOP853. All 64 replicas integrated successfully. Result: FAIL-A on every metric.
  • ·FAIL-A diagnostics: t_half ensemble median 616 yr (95% CI [287, 5593] yr) — outside [10, 20] yr Session 25 bracket. d(5000) ensemble median 3.00 (max 5.09); no replica converged to 1e-6 threshold. FFT-period ensemble median 1500 yr; artifact-dominated; no genuine [230, 320] yr peak. σ_eff ensemble median −0.000282/yr (DIVERGING).
  • ·FAIL-STRUCTURAL diagnosis: closed-form Jacobian at analytical interior fixed point (n_eq ≈ 0.968, w_eq ≈ 1.016, e* = 0, w_ref = w_eq) is block-triangular with eigenvalues {−0.20, −0.08, −0.0145, +0.00106}/yr — all real, +0.00106 unstable along e (e drifts unboundedly negative on ~940 yr timescale). The pre-registered fixed point (1, 1, 0.015) is NOT a true FP (drift ≈ 4.7×10⁻⁴/yr ≠ 0).
Session 26April 27, 2026Approved with caveatsv0.6.7-rc4

Session 26: CLEAN Attestation, Net-Negative Retirement Bundle, and the Frozen OQ-25-D Pre-Registration

Lead: Computational Sociologist

  • ·C23-3 CLEAN attestation delivered: 4-anchor multi-method literature triangulation. Galí 2011 JEEA (5/5), Daly-Hobijn 2014 JMCB (4/5), Turchin 2003 (4/5), Wrigley-Schofield 1981 (5/5). alpha_w prior tightened LogN(log 0.08, 0.30) — SD 0.35 → 0.30 with strikethrough discipline. 95% CI [0.044, 0.146]/yr. Anchored on agrarian regime; modern frictionless ~0.5–1.15/yr excluded by ~one order of magnitude.
  • ·OQ-25-D pre-registered: frozen Python/scipy DOP853 code with rtol=1e-9, atol=1e-12, T_max=5000yr; 64-replica IC ensemble around analytical fixed point at 10% perturbation; 4 outcome branches (PASS-A/PASS-B/FAIL-A/FAIL-B); execution env-blocked. Pre-registration hash 27299d86587a59dfceab07a4ebef5a7b130d00ac816564437df64c807ba4a6b7.
  • ·σ-noise priors anchored as fixed empirical anchors. F.26 σ_n LogN(log 0.010, 0.5) (Wrigley-Schofield 1981, Lande-Engen-Saether 2003); F.27 σ_w LogN(log 0.030, 0.4) (Galí 2011, Daly-Hobijn 2014, Wrigley-Schofield 1981); F.28 σ_e LogN(log 0.010, 0.5) (Bouchaud-Mézard 2000, Drăgulescu-Yakovenko 2000, Turchin 2016).
All 28 sessions →

Ground truth validation

Polymarket Predictions

We generate independent predictions using the formula and compare against Polymarket consensus. Polymarket is our benchmark — the question is whether our model outperforms the crowd.

1/1

predictions beat market

0.0400

average Brier score

11

live predictions

Full scoreboard →