1. Berner, R. A. Atmospheric carbon dioxide levels over Phanerozoic time. Science 249, 1382–1386 (1990).

2. Berner, R. A. & Canfield, D. E. A new model for atmospheric oxygen over Phanerozoic time. Am. J. Sci. 289, 333–361 (1989).

3. Hayes, J. M. & Waldbauer, J. R. The carbon cycle and associated redox processes through time. Phil. Trans. R. Soc. Lond. B 361, 931–950 (2006).

4. Burdige, D. J. Preservation of organic matter in marine sediments: controls, mechanisms, and an imbalance in sediment organic carbon budgets? Chem. Rev. 107, 467–485 (2007).

5. Hatcher, P. G., Spiker, E. C., Szeverenyi, N. M. & Maciel, G. E. Selective preservation and origin of petroleum-forming aquatic kerogen. Nature 305, 498–501 (1983).

6. Hedges, J. I. & Keil, R. G. Sedimentary organic matter preservation: an assessment and speculative synthesis. Mar. Chem. 49, 81–115 (1995).

7. Mayer, L. M. Relationships between mineral surfaces and organic carbon concentrations in soils and sediments. Chem. Geol. 114, 347–363 (1994).

8. Vogel, C. et al. Submicron structures provide preferential spots for carbon and nitrogen sequestration in soils. Nat. Commun. 5, 2947 (2014).

9. Kellerman, A. M., Kothawala, D. N., Dittmar, T. & Tranvik, L. J. Persistence of dissolved organic matter in lakes related to its molecular characteristics. Nat. Geosci. 8, 454–457 (2015).

10. Hedges, J. I., Cowie, G. L., Ertel, J. R., James Barbour, R. & Hatcher, P. G. Degradation of carbohydrates and lignins in buried woods. Geochim. Cosmochim. Acta 49, 701–711 (1985).

11. Rothman, D. H. & Forney, D. C. Physical model for the decay and preservation of marine organic carbon. Science 316, 1325–1328 (2007).

12. Keil, R. G. & Mayer, L. M. Mineral matrices and organic matter. In Treatise on Geochemistry (eds Holland, H. & Turekian, K.) 337–359 (Elsevier, 2014).

13. Torn, M. S., Trumbore, S. E., Chadwick, O. A., Vitousek, P. M. & Hendricks, D. M. Mineral control of soil organic carbon storage and turnover. Nature 389, 170–173 (1997).

14. Six, J., Conant, R. T., Paul, E. A. & Paustian, K. Stabilization mechanisms of soil organic matter: implications for C-saturation of soils. Plant Soil 241, 155–176 (2002).

15. Hunter, W. R. et al. Metabolism of mineral-sorbed organic matter and microbial lifestyles in fluvial ecosystems. Geophys. Res. Lett. 43, 1582–1588 (2016).

16. Hedges, J. I. et al. Evidence for non-selective preservation of organic matter in sinking marine particles. Nature 409, 801–804 (2001).

17. Barber, A. et al. Preservation of organic matter in marine sediments by inner-sphere interactions with reactive iron. Sci. Rep. 7, 366–377 (2017).

18. Lalonde, K., Mucci, A., Ouellet, A. & Gelinas, Y. Preservation of organic matter in sediments promoted by iron. Nature 483, 198–200 (2012).

19. Wagai, R. & Mayer, L. M. Sorptive stabilization of organic matter in soils by hydrous iron oxides. Geochim. Cosmochim. Acta 71, 25–35 (2007).

20. Leinweber, P. & Schulten, H. R. Advances in analytical pyrolysis of soil organic matter. J. Anal. Appl. Pyrolysis 49, 359–383 (1999).

21. Plante, A. F., Fernández, J. M. & Leifeld, J. Application of thermal analysis techniques in soil science. Geoderma 153, 1–10 (2009).

22. Hemingway, J. D., Rothman, D. H., Rosengard, S. Z. & Galy, V. V. Technical note: an inverse method to relate organic carbon reactivity to isotope composition from serial oxidation. Biogeosciences 14, 5099–5114 (2017).

23. Williams, E. K., Rosenheim, B. E., McNichol, A. P. & Masiello, C. A. Charring and non-additive chemical reactions during ramped pyrolysis: applications to the characterization of sedimentary and soil organic material. Org. Geochem. 77, 106–114 (2014).

24. Boudreau, B. P. & Ruddick, B. R. On a reactive continuum representation of organic matter diagenesis. Am. J. Sci. 291, 507–538 (1991).

25. Lehmann, J. & Kleber, M. The contentious nature of soil organic matter. Nature 113, 143–149 (2015).

26. Arnosti, C., Repeta, D. J. & Blough, N. V. Rapid bacterial degradation of polysaccharides in anoxic marine systems. Geochim. Cosmochim. Acta 58, 2639–2652 (1994).

27. Schmidt, M. W. I. et al. Persistence of soil organic matter as an ecosystem property. Nature 478, 49–56 (2011).

28. Keil, R. G., Montluçon, D. B., Prahl, F. G. & Hedges, J. I. Sorptive preservation of labile organic matter in marine sediments. Nature 370, 549–552 (1994).

29. Kennedy, M., Pevear, D. & Hill, R. J. Mineral surface control of organic carbon in black shale. Science 295, 657–660 (2002).

30. Kennedy, M. J. & Wagner, T. Clay mineral continental amplifier for marine carbon sequestration in a greenhouse ocean. Proc. Natl Acad. Sci. USA 108, 9776–9781 (2011).

31. Rosenheim, B. E. et al. Antarctic sediment chronology by programmed-temperature pyrolysis: methodology and data treatment. Geochem. Geophys. Geosyst. 9, Q04005 (2008).

32. Hemingway, J. D. et al. Assessing the blank carbon contribution, isotope mass balance, and kinetic isotope fractionation of the ramped pyrolysis/oxidation instrument at NOSAMS. Radiocarbon 59, 179–193 (2017).

33. Bao, R., McNichol, A. P., McIntyre, C. P., Xu, L. & Eglinton, T. I. Dimensions of radiocarbon variability within sedimentary organic matter. Radiocarbon 60, 775–790 (2018).

34. Bao, R. et al. Tectonically-triggered sediment and carbon export to the Hadal zone. Nat. Commun. 9, 121 (2018).

35. Bianchi, T. S. et al. Paleoreconstruction of organic carbon inputs to an oxbow lake in the Mississippi River watershed: effects of dam construction and land use change on regional inputs. Geophys. Res. Lett. 42, 7983–7991 (2015).

36. Hemingway, J. D. et al. Microbial oxidation of lithospheric organic carbon in rapidly eroding tropical mountain soils. Science 360, 209–212 (2018).

37. Plante, A. F., Beaupré, S. R., Roberts, M. L. & Baisden, W. T. Distribution of radiocarbon ages in soil organic matter by thermal fractionation. Radiocarbon 55, 1077–1083 (2013).

38. Rosengard, S. Z. Novel Analytical Strategies for tracing the Organic Carbon Cycle in Marine and Riverine Particles. PhD thesis, https://darchive.mblwhoilibrary.org/handle/1912/8658 (MIT/WHOI, Joint Program in Oceanography, 2017).

39. Rosenheim, B. E. & Galy, V. V. Direct measurement of riverine particulate organic carbon age structure. Geophys. Res. Lett. 39, L19703 (2012).

40. Rosenheim, B. E., Domack, E. W., Santoro, J. A. & Gunter, M. Improving Antarctic sediment 14C dating using ramped pyrolysis: an example from the Hugo Island Trough. Radiocarbon 55, 115–126 (2013).

41. Rosenheim, B. E. et al. River discharge influences on particulate organic carbon age structure in the Mississippi/Atchafalaya River system. Glob. Biogeochem. Cycles 27, 154–166 (2013).

42. Schreiner, K. M., Bianchi, T. S. & Rosenheim, B. E. Evidence for permafrost thaw and transport from an Alaskan North Slope watershed. Geophys. Res. Lett. 41, 3117–3126 (2014).

43. Subt, C., Fangman, K. A., Wellner, J. S. & Rosenheim, B. E. Sediment chronology in Antarctic deglacial sediments: reconciling organic carbon 14C ages to carbonate 14C ages using Ramped PyrOx. Holocene 26, 265–273 (2016).

44. Vetter, L., Rosenheim, B. E., Fernandez, A. & Törnqvist, T. E. Short organic carbon turnover time and narrow 14C age spectra in early Holocene wetland paleosols. Geochem. Geophys. Geosyst. 18, 142–155 (2017).

45. Williams, E. K., Rosenheim, B. E., Allison, M., McNichol, A. P. & Xu, L. Quantification of refractory organic material in Amazon mudbanks of the French Guiana Coast. Mar. Geol. 363, 93–101 (2015).

46. Zhang, X. et al. Permafrost organic carbon mobilization from the watershed to the Colville River Delta: evidence from 14C ramped pyrolysis and lignin biomarkers. Geophys. Res. Lett. 91, 11,491–11,500 (2017).

47. Hemingway, J. D., Schafer, C. & Rosenheim, B. E. RPO Compilation Online Database https://github.com/FluvialSeds/RPO_Databasettps://github.com/FluvialSeds/RPO_Database and https://doi.org/10.5281/zenodo.1158742 (2018).

48. Dittmar, T., Koch, B. P., Hertkorn, N. & Kattner, G. A simple and efficient method for the solid-phase extraction of dissolved organic matter (SPE-DOM) from seawater. Limnol. Oceanogr. Methods 6, 230–235 (2008).

49. Galy, V. V., Eglinton, T. I., France-Lanord, C. & Sylva, S. P. The provenance of vegetation and environmental signatures encoded in vascular plant biomarkers carried by the Ganges-Brahmaputra rivers. Earth Planet. Sci. Lett. 304, 1–12 (2011).

50. Averett, R. C., Leenheer, J. A., McKnight, D. M. & Thorn, K. A. Humic substances in the Suwannee River, Georgia: interactions, properties, and proposed structures. Water Supply Paper 2373 https://pubs.er.usgs.gov/publication/wsp2373 (USGS, 1994).

51. Miura, K. & Maki, T. A simple method for estimating f(E) and k 0 (E) in the distributed activation energy model. Energy Fuels 12, 864–869 (1998).

52. Hemingway, J. D. rampedpyrox: open-source tools for thermoanalytical data analysis. http://pypi.python.org/pypi/rampedpyrox and https://doi.org/10.5281/zenodo.839815 (2017).

53. Reimer, P. J., Brown, T. A. & Reimer, R. W. Reporting and calibration of post-bomb 14C data. Radiocarbon 46, 1299–1304 (2004).

54. Soulet, G., Skinner, L. C., Beaupré, S. R. & Galy, V. V. A note on reporting of reservoir 14C disequilibria and age offsets. Radiocarbon 58, 205–211 (2016).

55. Fernandez, A. et al. Blank corrections for ramped pyrolysis radiocarbon dating of sedimentary and soil organic carbon. Anal. Chem. 86, 12085–12092 (2014).

56. Galy, V. V. & Eglinton, T. I. Protracted storage of biospheric carbon in the Ganges-Brahmaputra basin. Nat. Geosci. 4, 843–847 (2011).

57. Rayner, J. Linear relations in biomechanics: the statistics of scaling functions. J. Zool. 206, 415–439 (1985).

58. Forney, D. C. & Rothman, D. H. Inverse method for estimating respiration rates from decay time series. Biogeosciences 9, 3601–3612 (2012).