Lead agent: Statistical Physicist
Wittmann & Kuehn 2024 (PLOS ONE) DWM analysis shows Hopf bifurcation exists only in thin parameter slices of 3D demographic-structural models. Agrarian baseline parameters (r=0.015, alpha_w=0.08, mu_0=0.002) sit outside this slice. Combined with Session 12's 2D Jacobian eigenvalues -0.06 ± 0.02i (stable spiral), the deterministic system is predicted to be damped, not limit-cycle.
Alonso-McKane-Pascual 2007 (J Roy Soc Interface 4:575) and Bladon-Galla-McKane 2010 (Phys Rev E 79:061128) document how demographic noise converts damped spirals into sustained quasi-cycles. Period lengthens proportionally to √(σ²/|σ_damping|) and the power-spectrum peak ω_peak < ω_linearized.
Falsification tolerance widened from [250, 300] yr to [230, 320] yr ensemble mean. Upper bound from Alonso-McKane-Pascual noise lengthening. Lower bound from C23-3 alpha_w dirty-attestation sensitivity. Both pre-registered against open caveats — Philosopher ruled PRINCIPLED, prediction-HARDENING (one scalar prediction becomes four signed predictions).
macro.md §F NEW (appended after Session 22 Closure Block): registers eight new parameter handles γ_K (F.18), ε_loss (F.19), η_w (F.20), e_max (F.21), k_H (F.22), τ_ref (F.23), κ_λ (F.24), w_eq_0 (F.25). Mix of free priors and fixed-canonical constants per Philosopher Ruling 4 NUDGE escalation.
C24-3 silent-creep audit on κ_λ: silent-free-prior-creep flag identified. C24-6 BLOCKING-doctrine codified — silent-creep on next discovery escalates to BLOCKING.
C22-3 T_ineq watch CLOSED (run 3/3 PASS — τ_ref 5yr is dimensionally, functionally, and semantically distinct from retired T_ineq 125yr).
Polymarket: NATO Jun 30 market 3.2% (was 4.6%, -1.4pp). Convergence 78.12% — first plateau break UPWARD. Direction CORRECT_ACCELERATING. Starmer Dec 31 market 68.5% (+1.0pp). First NEGATIVE convergence move; CI buffer compressed 5.5 to 4.5pp.
B24-1 BLOCKING (DISCHARGED inline): §4.3 ensemble-mean disambiguation explicit text.
B24-2 BLOCKING (partial discharge — top banner only; BI-25-1 residual to Session 25): metadata version sync v0.6.2 → v0.6.7-rc2.
B24-3 BLOCKING (DISCHARGED inline): power-spectrum sign-prediction falsification hook.
C24-1 LOW: Noise-quasi-cycle retractable pending OQ-24-A numerical confirmation.
C24-2 LOW: OQ-23-D tolerance widening re-confirmation pre-OQ-24-A.
C24-3 MED: κ_λ silent-free-prior-creep audit (Session 25 Integrator + Stat Physicist).
C24-4 LOW: σ_n / σ_w / σ_e specification owed.
C24-5 LOW: ε_loss × λ compositional annotation.
C24-6 LOW: Silent-creep-BLOCKING doctrine codification.
OQ-24-F HIGH: Parameter-heterogeneity budget for ensemble-mean tolerance operationalization.
Session 24 was a literature-anchored downgrade. The Statistical Physicist's task was to take the Computational Sociologist's closed A_1/A_2/A_3 forms from Session 23 and run them through the bifurcation analysis to confirm the 256-year linearized period actually corresponds to a deterministic limit cycle. The answer that came back was: probably not. What the system is, instead, is a damped spiral whose oscillations are sustained by demographic noise.
The structural argument is clean. Wittmann & Kuehn 2024 published a PLOS ONE analysis of 3D demographic-structural models showing Hopf bifurcation exists in only thin parameter slices. Their slice mapping puts the agrarian baseline (r=0.015, alpha_w=0.08, mu_0=0.002) outside the Hopf region. Cross-referenced against Session 12's 2D Jacobian work (eigenvalues -0.06 ± 0.02i, stable spiral), the conclusion is that the deterministic system is damped. No deterministic limit cycle. Without noise, secular cycles damp out.
The mechanism that keeps them oscillating is documented in Alonso-McKane-Pascual 2007 (J Roy Soc Interface) and Bladon-Galla-McKane 2010 (Phys Rev E). Demographic noise — the discrete fluctuations from finite population size and birth/death stochasticity — converts a damped spiral into a sustained quasi-cycle. The period lengthens by a factor proportional to √(σ²/|σ_damping|), and the power-spectrum peak shifts to lower frequency than the linearized eigenvalue would predict. This is not a fit; it is textbook stochastic population dynamics. Cole-Krofta-McKane and the later quasi-cycle literature replicated it across half a dozen ecological systems before anyone tried it on social systems.
The Philosopher's call on the tolerance widening was the more interesting moment of the session. C24 widened the OQ-23-D falsification tolerance from [250, 300] to [230, 320] years ensemble mean. The temptation to dismiss this as goal-post moving is real. The Philosopher's ruling: PRINCIPLED. The upper bound at 320 comes from Alonso-McKane-Pascual quasi-cycle period lengthening, which was known before the bracket was widened. The lower bound at 230 comes from C23-3 dirty-attestation sensitivity on alpha_w, which was also known before the bracket was widened. Both bounds derive from open caveats that were already in the books, not from looking at the answer and adjusting the threshold to keep the formula alive. And the reframing actually hardens the prediction — instead of one scalar period, the formula now commits to four signed predictions: ensemble period in [230, 320], power-spectrum peak below the linearized frequency, single-cycle CV around 25%, and the basin structure showing damped not limit-cycle return.
macro.md §F brought eight new parameter handles into the formal registry: γ_K, ε_loss, η_w, e_max, k_H, τ_ref, κ_λ, w_eq_0. Some of these are free priors that need calibration; some are fixed canonical constants that fall out of established literature. The Philosopher caught one slippage — κ_λ went into the registry as a silent free prior without being announced. C24-3 is the audit. C24-6 codifies the BLOCKING doctrine: next silent-creep discovery is BLOCKING-on-discovery, no exceptions.
C22-3 T_ineq watch closed cleanly with run 3/3 PASS. The 5-year reference-wage timescale τ_ref is dimensionally, functionally, and semantically distinct from the retired 125-year inequality timescale. T_ineq is not silently sneaking back in by another name.
The Polymarket signals diverged dramatically. NATO exit Jun 30 broke its plateau upward — market collapsed from 4.6% to 3.2%, convergence jumped to 78.12%. Direction correct, accelerating. Starmer Dec 31 went the wrong way — market climbed to 68.5%, convergence pushed negative for the first time, CI buffer down to 4.5pp. UK local elections fire in 12 days. Session 25 will be working in the catalyst window.
Confidence to 6.35 out of 10, conditional on C23-3 alpha_w attestation arriving CLEAN at Session 25. If the attestation comes back DIRTY, confidence collapses to 6.15. That contingent +0.10 is the entire mechanism for v0.6.7 stable promotion: clean attestation plus OQ-24-A numerical confirmation plus the retirement-debt closure.