Counterfactual + recovery scenarios
Three observational shadows: A_TOMS+OMI_min (hole-minimum), B_TOMS+OMI_zonal (zonal-mean 90S–60S), C_SBUV_zonal (polar bands).
Per-shadow rates (used for forward extrapolation):
| Shadow | Decline (DU/yr, 1980–88) | Recovery (DU/yr, 2000–24) |
|---|---|---|
| A_TOMS+OMI_min | −7.81 | +0.33 |
| B_TOMS+OMI_zonal | −3.40 | +0.006 |
| C_SBUV_zonal | −5.39 | −0.58 |
Counterfactual no-Montreal
Counterfactual extrapolation at observed 1980–88 decline rate: Antarctic ozone hole would have hit zero in 2010 (hole-minimum shadow A).
165σ separation — Montreal as the principal lever
Cross-scenario β separation between counterfactual and observed recovery: 165σ. Recovery is slow regardless of additional intervention — even +50% recovery rate doesn't return any shadow to 1979 baseline within +50 yr. The original Montreal Protocol intervention was the principal lever; further strengthening of compliance produces only marginal recovery acceleration.
Theorem 10 anchor
Hole-minimum and zonal-mean shadows: \(\mathfrak{A}\) (pair-difference brake dispersion) = 22.4 ≫ \(\tau_{T3}\). Joint admissibility fails — they shadow structurally distinct cascades. Hole-minimum responds to polar-vortex chlorine chemistry; zonal-mean responds to global photochemical balance. Theorem 10's verdict: non-admissibility, not poor methodology. See instance #25.
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 per shadow).