The Layer-A / Layer-B / Layer-C taxonomy
Climate observations have characteristically narrow log-ranges and forced-rate regimes. The framework's brake-p magnitude (Layer-A) often binds against the Theorem-3 precision floor at climate cadences. The arc has identified three layers at which the framework reads climate cascades:
Layer-A — brake-p magnitude
The framework's flagship primitive: \(\beta\) directly extracted by OLS / GLS-AR(1) / Bayesian-AR(1). Applies cleanly to long-timescale cascades with wide log-range — anthropogenic CO₂ (β = 4.04 modern, β = 2.96 EPICA paleo, separated at 5.7σ).
Layer-B — direction-and-rate-sign consensus
Where Theorem 3 binds (annual cadence, narrow log-range), the framework falls back to direction-and-rate-sign consensus across the model ensemble. CMIP6 Arctic sea-ice all 21 models agree on direction (Layer-B robust), but Layer-A binds at \(R^2 \approx 0.028\). Layer-B is the operative primitive at climate cadences.
Layer-C — cross-shadow sign-of-β
Identified through instance #20 (Younger Dryas paleoclimate): even when β magnitude dispersion is precision-floor-bound, the cross-shadow sign of β can carry regime-change information. Two of three Greenland ice cores sign-flip in the YD-onset window before YD-active proper. Layer-C is a third distinct framework primitive.
Pattern-4 — closed-domain conservation-decomposition
The Earth-system energy-budget analysis (instance #18) introduced a new framework pattern: closed-domain conservation \(\sum_i \Phi_i = \Phi_{\text{total}} + \text{boundary}\), with each reservoir an independent component cascade (NOT a shadow of the others). The natural readout is the partition fraction \(f_i(t) = \rho_i(t) / \sum_j \rho_j(t)\); the consistency test is the closure residual.
Applied to ocean / ice / land / atmosphere reservoirs against CERES top-of-atmosphere flux, the framework reproduces Trenberth–Fasullo's "missing energy" finding from first principles (78% closure; the 22% gap matches deep-ocean and deep-cryosphere reservoirs not captured by the four measured shadows). Pattern-4 is now part of the framework's methodology library.
The four-tier verdict vocabulary
- Robust — cross-model σ_cross small, direction unanimous, Layer-A clean (Arctic sea-ice loss).
- Partially-robust — direction unanimous but year-by-year rate-sign volatile (AMOC weakening; only 21% of years show ≥80% rate-sign agreement).
- Inconclusive — genuine model disagreement on direction (Amazon NPP; 5/25 models project decline rather than rise).
- Theorem-3-bound inconclusive — log-range too narrow for Layer-A to discriminate (NSIDC observational sea-ice over 47-yr record).
Plus the named outcomes Outcome A / B / C for paleoclimate regime changes, and model-artefact for instances where σ_cross flags a single outlier model.