A single dimensionless rate exponent — applied identically to 8 climate cascades and 5 emissions pathways — gives the first unified picture of which tipping points are inevitable, which respond to mitigation, and where the climate models actually agree. No domain-specific tuning. No imported threshold. One number per cell.
Locked in
Across every CMIP6 scenario the ice-sheet stays in super-rate cascade — including the most aggressive 1.5°C pathway (SSP1-1.9). Aggregate "sea-level rise" projections look reassuring under aggressive mitigation, but the dominant component does not.
Already crossed
The framework identified the regime-break temperature at +0.36 ± 0.12 K by reading 6 CMIP6 models. Earth is at +1.2 K. The first permafrost change-point is no longer in the future tense — it has happened.
Counter-intuitive
Under SSP1-1.9, model disagreement on sea-ice is 7× wider than under SSP5-8.5. The forcing signal disappears beneath internal variability. Standard ensemble means hide this. Aggressive policy assessments need wider uncertainty bands, not narrower.
Eight climate observables, five emissions pathways. One number per cell — the rate exponent β. Green = stoppable. Red = locked in. Same diagnostic, every cell.
Click any cell for the full reading: rate exponent β, cross-model dispersion, theorem anchor, and the source code on GitHub.
Click any cell for the full reading: \(\beta\), cross-model dispersion, theorem anchor, and the source code on GitHub.
SSPs (Shared Socioeconomic Pathways) are the IPCC's standard set of emissions futures. The number after the dash is the radiative forcing in 2100 (W/m²).
Every cell is one number: β, the rate at which a climate observable is changing relative to its own size. β < 1 means the change slows itself down (the system returns to rest in finite time). β > 1 means it accelerates (the system is committed to runaway change).
The same operator produced every cell. No model-specific tuning, no domain-specific threshold. The only universal threshold is β = 1, drawn from the framework's first theorem.
Each is a quantitative reading from cross-model data, not a literature summary.
Under SSP1-1.9 / SSP1-2.6 the framework reads atmospheric CO₂ as deeply sub-rate post-2024. Under SSP5-8.5 it crosses β = 1 in 2038 — supercritical thereafter. Aggressive mitigation does what aggressive mitigation is supposed to do — for the trajectory.
The Antarctic component drives sea-level rise post-tipping (β ≈ 3.5 — fastest acceleration in the decomposition). Aggregate GMSL stays sub-rate under SSP1-1.9 only because slower components dilute the average. Component analysis is the operative diagnostic, not aggregate.
Without the 1987 protocol, the framework's counterfactual analysis says Antarctic ozone would have hit zero by 2010. With it, recovery is slow but real. Further compliance tightening produces only marginal recovery acceleration — the original intervention did the heavy lifting.
Each section answers a different question.
"How does this even work?" The diagnostic in plain terms. How model agreement is measured. What β means.
"What did you actually look at?" Fifteen catalogue instances, each with its data, method, and verdict.
"What does each pathway predict?" Eight observables projected forward across all five SSPs, with full per-SSP data.
"What works?" The cross-observable best-pathway analysis. The locked-in components. The σ_cross paradox.