Extended Data Fig. 7: Schematic overview and illustrative repayment terms of RCP 1.9 scenarios.

a, Schematic overview of the CRO-ETS. The physical overshoot of a cumulative emission target, potentially amplified by outgassing of CO₂ from the Earth’s stocks, subsequently necessitates carbon sequestration for returning to the target. For accrued carbon debt, CROs are issued, obliging emitters to compensate for a tonne of CO₂ before a specified maturity—for example, by physically removing atmospheric CO₂ or by acquiring an adequate quantity of allowances in the future. Similar to financial debt, CROs require debtors to pay interest to hedge physical and financial risks associated with carbon debt. Three earmarked financial resources are created under a CRO-ETS. (1) Revenues from auctioning allowances are recycled into the economy to the benefit of society. (2) Revenues from interest on carbon debt are targeted at managing risks—that is, by enabling additional carbon sequestration when Earth system risks (for example, permafrost thaw) and financial risks (for example, default risk of debtors) materialize. (3) Funds for repayment of the carbon debt are individually managed by debtors. b–e, The repayment term function T_R(t) for the scenarios illustrated in Extended Data Fig. 3 (b), Extended Data Fig. 4 (c), Fig. 4 (d) and Extended Data Fig. 5 (e). Interest on carbon debt r_d reflects the mean values of the distributions shown in Fig. 4c and Extended Data Figs. 3c, 4c, 5c. Bold lines indicate geometric median repayment terms derived from the scenarios presented in Fig. 4 and Extended Data Figs. 3–5. T_R(t) maps the timing of carbon debt accrual to the time of its compensation (see Methods). For instance, in c, the carbon debt accrued in 2020 is compensated approximately 40 years later in scenarios with interest (r_d = 0.058, yellow lines) and roughly 50 years later in scenarios for which r_d = 0 (turquoise lines). As r_d is increased, the net-zero year moves closer, indicating that carbon debt in 2020 is compensated earlier, whereas, in general, T_R extends over longer periods. The increasingly flat net-negative emissions profile (when r_d is increased) suggests that T_R increases more rapidly in the beginning than when r_d = 0 because the cumulative carbon debt at t grows faster than the cumulative net-negative emissions at t + T_R(t). The point of inflection indicates where cumulative carbon debt begins to grow more slowly than cumulative net-negative emissions that compensate for that carbon debt. For instance, in d (yellow line), the cumulative carbon debt from 2030 onwards grows at a slower pace than the cumulative net-negative emissions approximately 63 years later.