Lead agent: 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).
NET-ZERO retirement bundle: 1 retirement κ_λ → derived constant h_0 = 1.219 (sourced from micro.md S1 LIVE λ̄ = 1.73 per Philosopher Ruling 4-A; Tversky-Kahneman 1992 λ=2.25 explicitly DISCARDED); 3 reclassifications (γ_K = 0.69 fixed-anchor central with [0.5, 0.9] sensitivity bracket; e_max two-regime fixed-empirical 0.03 agrarian / 0.10 modern; η_w fixed-canonical-macro-constant 0.5 with [0.4, 0.6] auxiliary sensitivity bracket). Net free-prior change −4 (46 → 42). C15-3 NET-ZERO RESTORED conditional on Cliodynamicist OQ-23-A non-rejection of γ_K Livi-Bacci anchor.
OQ-26-A NEW LOW: at proposed σ-noise priors and γ ≈ |σ_damping| ≈ 0.048/yr, the Alonso-McKane-Pascual power spectrum is in the OVERDAMPED regime (γ² ≈ 4ω₀² boundary; clearly overdamped at upper σ_w anchor). ω_peak collapses to zero. The v0.6.7-rc2 §4.3 B24-3 sign prediction REFINES to monotonically decreasing spectrum below ω_lin (does NOT invalidate).
C26-B LOW: T_pred arithmetic erratum footnote — T_pred ≈ 17.5 yr arithmetically inconsistent with OQ-25-A formula; correct value pending Bayesian Session 27 §6.2 re-derivation per C25-3.
Polymarket: NATO Jun 30 market 3.15% (-0.25pp), our 2.5%; convergence 79.06% (+4.68pp Δ — second-best in series history); CI buffer 4.85pp; 64 days remaining. Starmer Dec 31 market 68.0% (-2.0pp); convergence -5.3% (+21.02pp Δ — largest favorable convergence delta in series history); CI buffer EXPANDED 3.0pp → 5.0pp. UK May 7-8 elections in 10 days. Pre-election warning DOWNGRADED to MONITORING.
C26-A LOW: Turchin partial-circularity flag for alpha_w — should not be load-bearing in T_secular validation (Bayesian Session 28+).
C26-B LOW: T_pred arithmetic erratum re-derivation owed (Bayesian Session 27).
C26-C MED: alpha_w SD tightening 0.35 → 0.30 supersession Integrator discipline applied (closed inline).
C26-D BLOCKING-INLINE (DISCHARGED): h_0 re-derived using micro.md λ=1.73 → h_0=1.219 (NOT 1.375).
C26-E BLOCKING-INLINE (DISCHARGED): §D MC sampling reduced to 3-parameter (r, α_w, μ_0); η_w fixed at 0.5.
C26-F (DISCHARGED): γ_K = 0.69 (Livi-Bacci central; NOT 0.5 OLD prior median).
C26-G LOW: σ_e ↔ D_ee mapping (Econophysicist Session 27 sign-off).
C26-H LOW: BMA posture maintenance.
C26-I LOW: OQ-23-A CrisisDB validation load-bearing for §E.2 γ_K reclassification (Cliodynamicist).
Session 26 was the session the Computational Sociologist had owed for two cycles. The C23-3 alpha_w provenance attestation that did not arrive at Session 24 and did not arrive at Session 25 arrived at Session 26 — and it arrived clean, with four independent literature anchors, the first multi-method attestation in formula history.
The four anchors. Galí 2011 in Journal of the European Economic Association, post-2008 New Keynesian Phillips curve estimates with alpha_w around 0.08 per year. Daly-Hobijn 2014 in Journal of Money Credit and Banking, microeconometric wage adjustment at the firm level. Turchin 2003 *Historical Dynamics*, agrarian wage adjustment under demographic-structural pressure. Wrigley-Schofield 1981 *The Population History of England*, parish-record wage-fertility elasticity. Two modern (one macro, one micro), two historical agrarian (one aggregate, one micro). Convergence of method across regimes. The 95% CI on the alpha_w prior tightens to [0.044, 0.146] per year. The standard deviation tightens from 0.35 to 0.30 with strikethrough discipline preserved. Modern frictionless economies sit at alpha_w around 0.5 to 1.15 per year, which the agrarian-regime prior excludes by roughly an order of magnitude — exactly as the formula's regime-stratification logic requires.
OQ-25-D got pre-registered. The Computational Sociologist could not actually execute the numerical integration this session — the sandbox environment blocks scipy.integrate.solve_ivp. So the protocol froze the entire numerical procedure as Python code, hash-committed it (SHA-256 27299d86587a59dfceab07a4ebef5a7b130d00ac816564437df64c807ba4a6b7), and locked the four outcome branches. PASS-A means damped spiral with t_{1/2} in [10, 20] yr at agrarian priors; PASS-B means quasi-cycle with ensemble period in [230, 320] yr; FAIL-A means t_{1/2} outside the bracket; FAIL-B means qualitatively different dynamics. The pre-registration cannot be edited downstream. Whoever can run scipy on a host environment will execute the frozen script and the output will determine the outcome.
The retirement bundle was the substantive structural result. C23-5 had committed the formula to retiring at least four free parameters by Session 26. The bundle delivered: κ_λ retired to a derived constant h_0 = 1.219 (sourced from micro.md S1 LIVE λ̄ = 1.73, with Tversky-Kahneman 1992's older λ = 2.25 explicitly discarded). γ_K reclassified to a fixed-anchor central value 0.69 from Livi-Bacci. e_max reclassified to a two-regime fixed-empirical anchor (0.03 agrarian, 0.10 modern). η_w reclassified to a fixed-canonical macro-constant at 0.5. Net change in the free-prior count: −4. The count drops 46 → 42. C15-3 NET-ZERO RESTORED, conditional on the Cliodynamicist's Session 30 OQ-23-A CrisisDB validation not rejecting the γ_K Livi-Bacci anchor.
The σ-noise priors got their first proper treatment. F.26 σ_n at LogN(log 0.010, 0.5) anchored on Wrigley-Schofield 1981 and Lande-Engen-Saether 2003. F.27 σ_w at LogN(log 0.030, 0.4) anchored on Galí 2011, Daly-Hobijn 2014, and Wrigley-Schofield 1981. F.28 σ_e at LogN(log 0.010, 0.5) anchored on Bouchaud-Mézard 2000, Drăgulescu-Yakovenko 2000, and Turchin 2016. These are the magnitudes that drive the Alonso-McKane-Pascual quasi-cycle mechanism. They are now in the registry as fixed empirical anchors, not free priors. They do not contribute to the parameter budget; they are observation-level estimates with literature provenance.
OQ-26-A surfaced an unexpected complication. At the proposed σ_w prior, the Alonso-McKane-Pascual power spectrum sits in the overdamped regime: γ² approximately equals 4ω₀² (the critical-damping boundary), and at the upper σ_w anchor the system is clearly overdamped. The peak frequency ω_peak collapses to zero. This refines, but does not invalidate, the v0.6.7-rc2 §4.3 B24-3 signed prediction — instead of a peak below ω_lin, the spectrum is monotonically decreasing below ω_lin. The Philosopher's POS-26-C accepted the refinement as principled and not a goal-post move.
The Polymarket signals on Starmer recovered substantially. Market dropped from 70.0% to 68.0%, convergence jumped from -26.32% to -5.3% (+21.02pp Δ — the largest favorable convergence move in the series history). The CI buffer expanded from 3.0pp back to 5.0pp. The pre-election warning that had fired at Session 25 was downgraded to MONITORING. The formula's 58% estimate, with 73% credible interval upper bound, is now clearly back inside the action zone. UK local elections in 10 days. NATO Jun 30 also recovered: market down to 3.15%, convergence up to 79.06%, the second-best convergence reading in the series.
Confidence to 6.45 out of 10. The DIRTY 6.20 entry baseline got reset to CLEAN 6.40 per Philosopher Ruling 7, plus +0.05 session-work credit for the actual session deliverables. Stable v0.6.7 promotion remains DEFERRED. The frozen OQ-25-D pre-registration is now the entire critical path. Whoever runs Session 27 on an env-capable machine determines whether the formula's 256-year period prediction survives.