"What is the theoretical limit of predictability for a social system of N agents?"
Turns theory into actionable probabilistic forecasts with honest confidence intervals. Defines prior distributions for all parameters, designs the likelihood function, sets predictability bounds, and calibrates predictions against Polymarket outcomes. The Bayesian Statistician is also responsible for the Seldon reflexivity correction — accounting for how public knowledge of predictions changes the behavior being predicted.
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.
12 informative priors validated against empirical literature; ~18 placeholder priors for undefined parameters. Prior domination acknowledged: ~30 parameters vs ~8 independent observations.
First Polymarket prediction (Session 4): NATO exit by Jun 30, P=2.5% vs market 10% — correctly below market. NATO subsequently converged to ~4.65% (71.3% convergence toward our estimate).
Inference engine recommended: NUTS (No-U-Turn Sampler) for main parameters; Sequential Monte Carlo for online updating; PSIS-LOO-CV for model comparison.
Provides the complete Bayesian Confidence Architecture (9 sub-sections). Defines prior distributions for all formula parameters, likelihood functions for continuous (Gaussian) and jump (truncated power-law) components, predictability bounds, and calibration targets. Brier score target < 0.25 (superforecaster-level). v0.5.9 session formally diagnosed the overfitting regime (p~42, n_eff~6–14) and enacted a net-zero parameter budget.
See the full formula →C25-3 MED OVERDUE: T_pred ↔ σ_noise hidden dependency cross-reference owed (multi-session OVERDUE)
C26-A LOW: Turchin partial-circularity flag for alpha_w — should not be load-bearing in T_secular validation
C14-1 HIGH: PSIS-LOO logistic-vs-OU adjudication still pending live execution (joint with Econophysicist)
C19-3 CRITICAL: OQ-CLIO-D live SQL execution infrastructure-blocker; orchestrator A/B/C decision pending (8+ sessions OVERDUE)
C19-4 HIGH: BMA text-only (no implementation)
C19-5(a/b) MED: standing
C33-A through C33-F LOW: six Critique 33 caveats (C33-F DISCHARGED at Session 34 §L8 inline correction; others standing)
Circular validation: 7 parameters flagged; T_secular tagged LEAST CIRCULAR per Session 18 CROSS-072 partial closure
Session 33. Procedural discharge — third same-day session of 2026-05-09 (after S31 Neuroscientist REJECT and S32 Stat Physicist APPROVE_WITH_CAVEATS). Hash-committed OQ-32-A piecewise-smooth border-collision Hopf F1–F5 falsification bracket under SHA-256 5c05970f3702dde15cbdfe3a09d0642e5bb876bd108e48468849971d2908e910 over 32,058 bytes (C32-F LOW DISCHARGED). κ_e structural non-identifiability at smooth FP formalized: FIM eigenvalue → 0 because κ_e term inactive at FP; identification requires non-stationary observations. Information-content lower bound I_κe ≈ 6e-3 per trajectory; data-volume requirement N_traj ≥ 12–18 for posterior CV(κ_e) ≤ 0.20 (C32-A LOW formalized). C27-E reproducibility EXECUTED on independent numpy toolchain (seed 0xBEEF); spectrum 1+/3- real, 0 complex confirmed. C26-B LOW-OVERDUE rounding-erratum RESOLVED. 6 new LOW caveats from Critique 33 (including arXiv 2409.19729 Sugasawa misattribution catch). NO formula edit; v0.6.7-rc6 stands; p_free = 42 PRESERVED. Confidence 6.70 → 6.75.
Session 25. Analytical-only PARTIAL closure of OQ-24-A: damped-spiral verdict CONFIRMED via three-way triangulation (Session 12 2D Jacobian + CROSS-054 slow eigenvalue + Wittmann-Kuehn 2024 DWM Hopf-slice). Predicted t_{1/2} ≈ 14.4 yr in pre-registered bracket [10, 20] yr — SUPERSEDES Session 24 [30, 70] yr per Philosopher Ruling 1. Three methodology pre-registrations: C23-4 Monte Carlo + Sobol; OQ-24-F hierarchical-budget cap σ(log T) ≤ 0.25; C14-1 PSIS-LOO BF 0.1/10 thresholds. C19-3 SQL infrastructure-blocker record filed. C23-3 alpha_w attestation NOT delivered by Comp Sociologist Session 25 close — DIRTY-branch confidence default per Philosopher Ruling 7. NO SDE structural change, NO new free parameters. Confidence 6.35 → 6.20 (DIRTY).
Session 21. C19-2 BLOCKING closed via dual-location sub-addendum pattern: full MR1-Turkey dual-coding protocol inlined into archetype_calibration_protocol.md §4.6 + forward-reference at archetype_reference_classes.md §9.10 with §§1-8 byte-invariance attestation. Sub-addendum doctrine codified (four-constraint protocol). Philosopher ruled the §§1-8 slice-hash 59b72533... is the load-bearing lock-commitment. AND-gate firing rule formalized (3 scenarios must each clear ≥15% lift). First operational archetype prediction (Dem 2028, $1.09B) AUTHORIZED for Session 22+. 4 new C21 caveats. Confidence 5.75 → 5.85.
Session 19. C19-BS-1 closure package: 22-cell κ-propagated Beta posteriors over the 160-cell archetype × institution-vector grid; leave-Turchin-out BMA showing POP_RIGHT × LD × crisis-bulge robust at +4.6pp lift with 7.0pp credal lower bound. C17-1 POP_RIGHT P_t/V_t profile boundaries LOCKED on Tsebelis 2002 / V-Dem / KESMA / Linz 1975 anchors. Joint populist_right × I_t prediction non-circular by construction (distinct dataset substrates). Conditional unfreeze granted; Dem 2028 firing deferred to Session 20+. 7 new C19 caveats. Confidence 5.6 → 5.7.
Session 15. Overfitting regime formally diagnosed (p~42, n_eff~6–14; practical R² ceiling 0.05–0.15 at 1yr). Parameter freeze enacted (net-zero budget). 7 new/updated priors (eta_pareto, alpha_pol, w_min, eps_w, b_min, beta_U BMA mixture, k_jump). 3-tier out-of-sample validation protocol (LOOCV / Blocked / CPCV). Circular audit expanded 4→7; all 4 fully circular params in jump process. k_jump non-Turchin MLE ~2.5. Epistemological confidence 5.8→5.5/10.