Instance #25 — Stratospheric ozone (Montreal Protocol)
Datasets: NASA Ozone Watch TOMS+OMI+OMPS hole-minimum (1979–2025), TOMS+OMI+OMPS zonal-mean 90S–60S (1979–2025), NASA SBUV V8.7 polar bands (1970–2023). Three shadows of Antarctic stratospheric ozone.
Outcome C (physical-shadow-mismatch): median R² = 0.015 across all (shadow, regime) cells. Per-shadow decline-vs-recovery slope ratios are 22×, 500×, ~10× — Montreal's signature is in rate magnitude, not in β.
Theorem 10 anchor — anti-shadow detection
Pair-difference brake dispersion \(\mathfrak{A} = 22.4 \gg \tau_{T3}\). Hole-minimum and zonal-mean shadow structurally distinct cascades (localised extremum vs spatial average). Theorem 10's verdict is non-admissibility — not poor methodology.
PELT independently rediscovers Montreal Protocol date within 2–3 yr in all three shadows (A→1989, B→1989, C→1984; protocol signed 1987) — clean policy-intervention detection with no imported regime date. EMD-trend brake-p does fit per-shadow once QBO/ENSO oscillations are stripped (R² climbs from 0.001–0.06 to 0.22–0.53).
Instance #26 — Permafrost carbon cascade
Datasets: 6 CMIP6 SSP5-8.5 ESMs with cSoil published (CESM2, CESM2-WACCM, CMCC-CM2-SR5, CMCC-ESM2, IPSL-CM6A-LR, MPI-ESM1-2-LR), 2015–2100, ≥55°N permafrost-relevant land area.
Zero models flip sink → source by 2100; models split 4 source / 2 sink from year one. σ_cross of β = 149–153 across estimators — Theorem 3 forbids Layer-A call. Verdict: theorem_3_bound_inconclusive.
New finding — first-break warming threshold
Cross-model warming-anomaly at first PELT change-point: median = +0.36 ± 0.12 K across 6 models (σ_cross only 0.122 K). Far below the published +1.5–2.0 °C tipping window. Framework identifies an early regime-break warming threshold the literature does not currently emphasise — potentially publishable as a "first-break temperature" framework prediction distinct from the literature's tipping concept. The threshold has already been crossed (~+1.2 K observed).
Instance #27 — Cross-model timing-of-tipping prediction
Strict pre-2050 / post-2050 hold-out split. Rolling 20-yr brake-p; linear extrapolation of rolling-β to predict β=1 crossing year.
- β=1 crossings predicted and actual exist for every model in every element (mismatch_rate 0.00 across 21+19+25 trajectories).
- Systematic early bias of ~20–25 years: sea-ice signed error −24.5 yr, AMOC −20.1 yr, Amazon NPP −22.9 yr.
- Framework beats naive baseline: |framework error| 20–25 yr vs |naive Φ→Φ₀/2 error| 38–41 yr — both biased early, framework closer.
- Cross-shadow median tightens (Law III consensus confirmed).
Calibration-honest predictive result with quantified bias and demonstrated improvement over naive baseline.
Instance #28 — ENSO regime characterisation
Substantive framework finding: brake-p R² < 0.01 across all indices and wavelet scales. ENSO is oscillatory, not brake-cascade — the framework correctly reports that ENSO doesn't have rate-vs-magnitude scaling brake-p was built to detect (pairs with #22 MPT resonance-shift finding: climate has both cascade-class and resonance-class phenomena).
1976–77 Pacific shift partial detection: PELT picks it up independently in 3/6 indices (Niño 1+2, 3, 4 within ±3 yr of literature) but misses Niño 3.4, MEI, SOI at BIC default.
Theorem 10 (S2) sub-region failure
The four Niño sub-region indices (1+2, 3, 4, 3.4) are spatial sub-regions of one SST field with correlated noise. \(\mathfrak{A}\) inflates above \(\tau_{T3}\) because (S2) independence fails, not because they shadow different cascades. SOI alone preserves (S2). Theorem 10 correctly excludes Niño-only candidate sets from joint admissibility.
Instance #30 — Tropical cyclone cross-basin intensity-duration
HURDAT2 Atlantic + East Pacific best-track + IBTrACS WP/NI/SI/SP. ~3000 cyclones across 6 ocean basins.
Cross-basin σ_cross(med β) wind = 0.090, pressure = 0.141; both exceed within-basin half-CI95 noise floor 0.056 — ratios 1.61 and 2.51. Genuine basin grouping: Atlantic+EP vs WP/NI/SI/SP.
Wind and pressure shadows DO NOT measure the same cascade in 5/6 basins: Atlantic |Δβ| = 0.002 (consistent); other basins |Δβ| 0.15–0.36 with pressure-deficit decay systematically slower than wind decay. Third instance (after #16 CMIP6, #25 ozone) of the lesson: cross-shadow consensus requires shadows of the same physical observable.
PELT recovers intensification + decay onsets on 97–98% of storms.