Extended Data Table 1. Key results from individual model runs.

(a) Summary of the main double inversion experiments carried out. The terminology “R07” refers to configurations tying the Site 401 records to the chronostratigraphy of ref. 25, the notation “FE” refers to the ³He-based age model of ref. 57). Annotation “sm” refers to inversion of analytically smoothed δ¹³C and pH data sets, “rw” to usage of original sample data for double inversions. “HI” and “LO” represent potentially extreme configurations taking into account the boron proxy uncertainty at 95% confidence level. “noW” has silicate (and carbonate) weathering feedbacks disabled. “Corg” denote model configurations that allow removal of excess organic carbon from the surface ocean. Grey shading highlights experiments focussed upon in the main text and plotted in Figure 3 (“R07sm” in Fig. 3a-f and “R07sm_Corg” in 3i-n.). Note: (1) peak emissions are binned at 2 kyr resolution, (2) both cumulative emissions and C_org burial are measured from 40 to 190 ka model time, and (3) peak excess weathering reflects carbon removal due to silicate weathering above pre-PETM weathering rates. (b) Summary table presenting the results of sensitivity experiments (shown in Extended Data Fig. 5) to quantify the importance of uncertainties in the age model for the CIE onset. In these experiments, the CIE onset phase is assumed to occur linearly, with a duration of the decline in δ¹³C and pH varying from 100 to 20,000 yr duration. Reported are: (1) diagnosed peak carbon emissions, (2) cumulative carbon emissions occurring over the duration of the onset, and mean (flux weighted) δ¹³C of these emissions, (3) cumulative carbon emissions occurring at the 20 kyr time horizon – comparable to the onset duration in our assumed age model, plus the mean (flux weighted) δ¹³C of these emissions, and (4) the cumulative carbon emissions occurring at the 20 kyr horizon, plus the mean (flux weighted) δ¹³C of these emissions. Note that in all experiments, once the onset is complete, the target pH and δ¹³C values are held constant (and low) until the end of the experiment (50,000 yr).

a
Experiment ID	experimental assumptions					peak emissions	cumulative emissions		cumulative Corg burial		ΔSST	peak excess weathering
	age model	δ11B envelope	smoothed data?	weathering?	Corg burial?	(PgC yr-1)	total (PgC)	mean δ13C ‰	total (PgC)	mean δ13C ‰	(°C)	(PgC yr-1)
R07sm_HI	R07	high	YES	YES	NO	0.41	5,688	-18.9	---	---	2.25	0.030
R07sm	R07	mean	YES	YES	NO	0.58	10,213	-11.1	---	---	3.64	0.053
R07sm_LO	R07	low	YES	YES	NO	1.16	19,964	-6.6	---	---	5.99	0.105
FEsm_HI	FE	high	YES	YES	NO	0.17	6,502	-16.5	---	---	2.10	0.038
FEsm	FE	mean	YES	YES	NO	0.36	12,020	-9.8	---	---	3.09	0.069
FEsm_LO	FE	low	YES	YES	NO	0.64	24,124	-6.0	---	---	4.80	0.132
R07rw	R07	mean	NO	YES	NO	0.61	10,984	-12.1	---	---	4.07	0.061
FErw	FE	mean	NO	YES	NO	0.45	12,749	-10.2	---	---	3.14	0.072
R07sm_noW	R07	mean	YES	NO	NO	0.52	6,407	-16.7	---	---	3.34	---
FEsm_noW	FE	mean	YES	NO	NO	0.30	6,665	-16.4	---	---	2.72	---
R07sm_HI_Corg	R07	high	YES	YES	YES	0.41	7,670	-18.0	2,607	-30.0	2.25	0.030
R07sm_Corg	R07	mean	YES	YES	YES	0.58	12,220	-10.9	2,540	-30.5	3.64	0.053
R07sm_LO_Corg	R07	low	YES	YES	YES	1.16	22,593	-7.1	3,333	-30.9	5.99	0.105

b
Duration of onset (yr)	peak emissions	cumulative emissions over onset		cumulative emissions @ 20,000 yr		cumulative emissions @ 50,000 yr
	(PgC yr-1)	total (PgC)	mean δ13C (‰)	total (PgC)	mean δ13C (‰)	total (PgC)	mean δ13C (‰)
100	20.00	1,897	-19.0	8,695	-17.0	13,256	-13.4
200	15.21	2,355	-18.4	8,688	-17.0	13,252	-13.4
500	6.90	2,588	-21.5	8,664	-17.0	13,239	-13.6
1,000	3.72	2,799	-24.5	8,613	-17.1	13,200	-13.4
2,000	2.08	3,074	-27.6	8,526	-17.2	13,181	-13.4
5,000	1.07	3,751	-29.0	8,202	-17.8	13,007	-13.5
10,000	0.70	4,691	-26.3	7,612	-18.8	12,706	-13.6
20,000	0.48	6,141	-22.0	6,141	-22.0	12,025	-14.0