A Second Foundation
New · The June 2026 redesign: from one formula to a model zoo →
In ProgressModel zoo · 3 live variants · Session 38

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. Now rebuilt as a system of competing, testable models scored by a frozen oracle.

38

Research sessions

3

Competing models (live)

26

Locked hold-out events

Tier 0

Legacy formula skill

Architecture redesign · June 2026

From one formula to a system of models

For 41 sessions the project polished a single equation it could never run. We rebuilt it the way real forecasting sciences work — a population of competing, runnable models on a leaderboard, scored by a frozen oracle no agent can edit, driven by an autonomous research loop.

The honest headline: the legacy formula sits at Tier 0 — it never produced a single numeric prediction. Now every model is measured.

Read the full redesign →

Live leaderboard · frozen-scored hold-out

ModelFamilyBrierResolutionNeg-ctrlTier
ensembleequal-weight0.268
0.124
0.091T0
pitf_logitregime_logit0.219
0.139
0.188T1
train_freqempirical_frequency0.252
0.112
0.112T0
null_baselinenull0.370
0.095
0.038T0

26 events · 10 negative controls · ensemble Brier 0.268 (chance 0.25)

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 →

How it works now

MODEL ZOO

Competing, runnable models

null · pitf_logit · sdt_turchin · rfim · …

FROZEN SCORER

One number, no agent can edit it

Brier · log-loss · resolution

LEADERBOARD

Ranked by out-of-sample skill

purged + embargoed backtests

AUTONOMOUS LOOP

Hypothesize → backtest → select

keep if better · revert if not

Legacy formula · now one variant in the zoo

The 8-D 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-rc7
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
92 open caveats
confidence 6.78/10
Full breakdown →

Research team

A Lean Team
That Computes

The nine disciplines are being restructured into lean generators plus a new tier of agents that run code — fitting models, simulating, and backtesting. The Philosopher moves off the numeric gate to audit for self-deception.

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.

2 sessionsLast: May 9, 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.

2 sessionsLast: May 14, 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.

3 sessionsLast: May 14, 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.

4 sessionsLast: May 14, 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.

9 sessionsLast: May 14, 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.

6 sessionsLast: May 9, 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.

10 sessionsLast: May 14, 2026

Research log

Latest Sessions

Session 38May 14, 2026Approved with caveats

Session 38: C26-G 8-Session-OVERDUE Discharge + Option δ-Econ Avenue Analysis + Mode A Citation-Defect Catch

Lead: Econophysicist

  • ·C26-G LOW-OVERDUE 8-session DISCHARGED-PENDING-CO-ATTESTATION-AND-MODERN-REGIME-SCOPING. Rosinski 2007 (Stoch. Proc. Appl. 117:677-707) long-time-Brownian-limit identification σ_e (macro.md §F.28) ≡ σ_e_base (CURRENT.md §5.2). Sensitivity bracket σ_e_eff/σ_e_base ∈ [1.04, 1.96] within F.28 prior 95% CI. Stat Physicist co-attestation owed S40+ with deep-agrarian λ_temp scoping + f_e(κ,π) specification (C38-I LOW).
  • ·Option δ-Econ avenue formally analyzed: 4 candidates ranked. Candidate 1 (hyperinflation/fiscal-stress via Φ_fiscal(d) Alternative-B w_eq modification) ranked #1 at viability 0.50 → PROVISIONALLY DOWNGRADED 0.35-0.40 per C38-J (regime-dependence: rescue requires d* ≠ 0 at agrarian FP). Candidate 2 (W_top Alternative-B, viability 0.40); Candidate 3 (additive piecewise A_2, viability 0.20 agrarian-FP, structurally redundant); Candidate 4 (LPPL log-periodic power law, viability 0.10 — wrong layer).
  • ·NEW STRUCTURAL FINDING (BOUNDED READING MANDATORY per C38-H LOW): universal multiplicative-coupling FP-inaccessibility principle generalizes the S37 result. Any F_X(state) × A_i where A_i = rate × (state − target_i) collapses at FP linearization. Bounded scope: A_2/A_3/A_5/A_8 (clean mean-reverting) conform; A_1/A_4/A_6/A_7 (heterogeneous) require case-by-case analysis. Promotion to §5.1 doctrinal addendum at next CURRENT.md edit cycle.
Session 37May 14, 2026Approved with caveats

Session 37: OQ-35-N F1 FAIL-STRUCTURAL — Option δ-N Multiplicative Form Terminated

Lead: Statistical Physicist

  • ·OQ-35-N F1 single-point pre-screen executed at hash-committed ε_net = 0.30 / n_baseline = 0.96840. VERDICT: FAIL-STRUCTURAL. J3 at agrarian FP has all-real eigenvalues — zero complex pairs. n_complex_pairs = 0; eigenvalues {+1.5813×10⁻², −9.5813×10⁻², −1.4526×10⁻²}/yr; Δ = +7.578×10⁻⁸ > 0.
  • ·Load-bearing analytical finding: at the FP, w* = w_0 exactly, so the (w_0 − w)/w prefactor of A_3 vanishes. This collapses BOTH ∂A_3/∂n AND ∂A_3/∂e to zero regardless of the F_n(n) multiplicative modulator. The ε_net coupling is structurally invisible to the FP linearization.
  • ·Generalization (under C37-B LOW bounded reading): any multiplicative coupling to A_3 carrying the (w_0 − w)/w prefactor is FP-inaccessible at the agrarian fixed point. Bounded scope: multiplicative-to-A_3 only, FP-linearization only, v0.6.7-rc6 framework only. Promotion to §5.1 doctrinal addendum at next CURRENT.md edit cycle.
Session 36May 14, 2026Approved with caveatsv0.6.7-rc7

Session 36: ε_net Literature Anchor Discharged with Inline arXiv-Author Hallucination Catch

Lead: Cliodynamicist

  • ·ε_net literature-anchored prior delivered: LogNormal(μ = log 0.30, σ = 0.50); median 0.30; 95% CI [0.113, 0.799]; F1 single-point evaluation = 0.30 per C35-A binding; n_baseline = 0.96840 hash-committed from Session 29 §I.4 agrarian FP coordinate (macro.md §M.7 items 1-2-3).
  • ·Direct partial ∂(dE/dt)/∂N = μ analytically identified in the canonical Turchin SDT system dE/dt = rE + μN (Turchin 2013, Cliodynamics 4(2):241-280; μ₀ = 0.1 yr⁻¹). Stachowiak & Pasek 2024 (arXiv:2405.01163) adopt μ₀ = 0.1 from Turchin (2013) and apply the canonical SDT to Polish 1990-2024 demographic data with reported sensitivity — independent replication of the equation form, not an independent measurement of the parameter value.
  • ·Cross-validation across 6 non-Turchin-authored historical cases: Stone 1965 Tudor-Stuart; Bourbon France venal-office historiography; Elman 2000 Late Ming; Korotayev-Khaltourina 2006 Egyptian; Russian Time of Troubles; Turchin & Korotayev 2020 doi:10.1371/journal.pone.0237458 US 1980-2019.
All 38 sessions →

Secondary signal

Live Market Predictions

Validation now runs primarily on a locked hold-out of historical events scored by the frozen oracle. Live market predictions are a secondary signal — published pre-resolution and labeled by reflexivity class. Polymarket is one benchmark among several.

1/1

predictions beat market

0.0400

average Brier score

11

live predictions

Full scoreboard →