B A Killingsworth
email: bkillingsworth@usgs.gov

P Cartigny

J A Hayles

C Thomazo

P Sansjofre

V Pasquier

S V Lalonde

P Philippot

Towards a holistic sulfate-water-O2 triple oxygen isotope systematics

Keywords: sulfate, oxygen isotopes, atmospheric oxygen, sulfide oxidation, paleoclimate

Triple oxygen isotope (∆ 17 O with δ 18 O) signals of H 2 O and O 2 found in sulfate of oxidative weathering origin offer promising constraints on modern and ancient weathering, hydrology, atmospheric gas concentrations, and bioproductivity. However, interpretations of the sulfate-water-O 2 system rely on assuming fixed oxygen-isotope fractionations between sulfate and water, which, contrastingly, are shown to vary widely in sign and amplitude. Instead, here we anchor sulfate-water-O 2 triple oxygen isotope systematics on the homogeneous composition of atmospheric O 2 with empirical constraints and modeling. Our resulting framework does not require a priori assumptions of the O 2 -versus H 2 O-oxygen ratio in sulfate and accounts for the signals of massdependent and mass-independent fractionation in the ∆ 17 O and δ 18 O of sulfate's O 2oxygen source. Within this framework, new ∆ 17 O measurements of sulfate constrain ~2.3 Ga Paleoproterozoic gross primary productivity to between 6 and 160 times present-day levels, with important implications for the biological carbon cycle response to high CO 2 concentrations prevalent on the early Earth.

INTRODUCTION

As a product of sulfide oxidation, sulfate results from sulfuric acid chemical weathering that increases acidity, alkalinity, and concentration of metals in mining environments [START_REF] Raymond | Long term changes of chemical weathering products in rivers heavily impacted from acid mine drainage: Insights on the impact of coal mining on regional and global carbon and sulfur budgets[END_REF], while asserting controls on atmospheric O 2 and CO 2 over millions of years [START_REF] Berner | GEOCARBSULF: A combined model for Phanerozoic atmospheric O2 and CO2[END_REF]. Oxygen isotopes of sedimentary sulfates in rocks are ideal for understanding Earth's O 2 history, environmental conditions of sulfide oxidation, and the biological imprints of local and/or global (i.e., ocean) sulfur cycling [START_REF] Bao | Sulfate: A time capsule for Earth's O2[END_REF].

Our understanding of the oxygen sources of sulfide-derived sulfate relies on decades of chemical and isotopic studies (e.g., [START_REF] Lloyd | Oxygen isotope behavior in the sulfate-water system[END_REF][START_REF] Taylor | Stable isotope geochemistry of acid mine drainage: Experimental oxidation of pyrite[END_REF][START_REF] Van Everdingen | Interpretation of isotopic compositions of dissolved sulfates in acid mine drainage: U.S. Bureau of Mines Circular[END_REF][START_REF] Balci | Oxygen and sulfur isotope systematics of sulfate produced by bacterial and abiotic oxidation of pyrite[END_REF][START_REF] Tichomirowa | Oxygen isotope evidence for sorption of molecular oxygen to pyrite surface sites and incorporation into sulfate in oxidation experiments[END_REF][START_REF] Heidel | The isotopic composition of sulfate from anaerobic and low oxygen pyrite oxidation experiments with ferric iron-New insights into oxidation mechanisms[END_REF][START_REF] Kanzaki | Rates and stoichiometry of pyrite dissolution at pH 3 under low O2 conditions[END_REF], reviews of pyrite oxidation mechanisms [START_REF] Williamson | The kinetics and electrochemical ratedetermining step of aqueous pyrite oxidation[END_REF][START_REF] Rimstidt | Pyrite oxidation: a state-of-the-art assessment of the reaction mechanism[END_REF], and isotope systematics (e.g., [START_REF] Van Everdingen | Interpretation of isotopic compositions of dissolved sulfates in acid mine drainage: U.S. Bureau of Mines Circular[END_REF][START_REF] Van Stempvoort | Controls of δ18O in sulfate: a review of experimental data and application to specific environments[END_REF][START_REF] Taylor | Sulfur-and Oxygen-Isotope Geochemistry of Acid Mine Drainage in the Western United States[END_REF][START_REF] Seal | Stable-isotope geochemistry of mine waters and related solids: Environmental aspects of mine wastes[END_REF][START_REF] Gomes | Oxygen and sulfur isotopes in sulfate in modern euxinic systems with implications for evaluating the extent of euxinia in ancient oceans[END_REF]. Such substantial research efforts emphasize the complexity of sulfide oxidation in which seven electrons are transferred in total, one or two at a time, proceeding through intermediate sulfur species from an S(-I) to S(VI) oxidation state [START_REF] Rimstidt | Pyrite oxidation: a state-of-the-art assessment of the reaction mechanism[END_REF]. Sulfidederived sulfate gains oxygen from sources such as ambient water and O 2 , as in the pyrite oxidation reactions given by [START_REF] Taylor | Sulfur-and Oxygen-Isotope Geochemistry of Acid Mine Drainage in the Western United States[END_REF],

FeS 2 + 7/2O 2 + H 2 O  Fe 2+ + 2SO 4 2-+ 2H + (1)
FeS 2 + 14Fe 3+ + 8H 2 O  15Fe 2+ + 2SO 4 2-+ 16H + (2).

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These reactions imply that the product sulfate incorporates 87.5 % O 2 -oxygen during reaction (1) and 100 % water-oxygen via oxidation with Fe 3+ in reaction (2). In turn, the rate of reaction ( 2) is limited by the oxidation of Fe 2+ to Fe 3+ by O 2 , Fe 2+ + 1/4O 2 + H +  Fe 3+ + 1/2H 2 O (3).

This suggests that O 2 is required to sustain pyrite oxidation, with the cumulative sulfate product containing oxygen atoms from both water and O 2 in proportion to the contributions of reactions ( 1) and ( 2). Despite their utility, the mass balance of these reactions does not match the sulfate oxygen isotope end members inferred from field and experimental data (Fig. 1), which should include oxygen isotope fractionation as well.

Although the direct incorporation of O 2 -oxygen into pyrite-derived sulfate has recently been challenged [START_REF] Hemingway | Triple oxygen isotope insight into terrestrial pyrite oxidation[END_REF], pyrite oxidation experiments at low O 2 concentrations [START_REF] Johnson | Experimental determination of pyrite and molybdenite oxidation kinetics at nanomolar oxygen concentrations[END_REF][START_REF] Kanzaki | Rates and stoichiometry of pyrite dissolution at pH 3 under low O2 conditions[END_REF] and analyses of weathered shales [START_REF] Gu | Deep abiotic weathering of pyrite[END_REF] have consistently shown the O 2 -dependence of pyrite oxidation. Experiments and fieldwork have also highlighted the role of O 2 for setting sulfate triple oxygen isotope (∆ 17 O and δ 18 O) compositions [START_REF] Farquhar | Sulfur and oxygen isotope study of sulfate reduction in experiments with natural populations from Faellestrand, Denmark[END_REF][START_REF] Kohl | Triple-oxygen-isotope determination of molecular oxygen incorporation in sulfate produced during abiotic pyrite oxidation (pH=2-11)[END_REF][START_REF] Killingsworth | Assessing Pyrite-Derived Sulfate in the Mississippi River with Four Years of Sulfur and Triple-Oxygen Isotope Data[END_REF][START_REF] Waldeck | Deciphering the atmospheric signal in marine sulfate oxygen isotope composition[END_REF]. Sulfate ∆ 17 O, adding a dimension beyond δ 18 O, is a powerful tracer of isotopic signatures of atmospheric O 2 through time (e.g., [START_REF] Bao | Sulfate: A time capsule for Earth's O2[END_REF][START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF]. We also suggest that sulfates in rocks could allow characterization of potentially long-term variations, on the order of 100s of millions of years, of the oxygen isotope difference between seawater and atmospheric O 2 , which is known as the Dole Effect [START_REF] Dole | The relative atomic weight of oxygen in water and in air[END_REF][START_REF] Morita | Oxygen isotope fractionation of dissolved oxygen during abiological reduction by aqueous sulfide[END_REF]. However, to fully assess ∆ 17 O and δ 18 O of sulfate, outstanding issues must be addressed. Three key assumptions have been that 1) all of sulfate's negative ∆ 17 O signal is inherited from J o u r n a l P r e -p r o o f oxidation with atmospheric O 2 that, in turn, ultimately reflects mass-independent photochemistry, 2) the proportion of O 2 -oxygen in a given sulfate can be estimated, a priori, as being less than 25 %, and 3) oxygen-isotope systematics of sulfates are effectively constrained by consistent sulfate-water oxygen-isotope differences. The first assumption has been a useful approximation for examining relatively large negative ∆ 17 O (please see methods for isotope notation and the capital delta definition used here)

anomalies in sulfate that extend as low as ∆ 17 O 0.528 = -1.84 ‰ [START_REF] Bao | Stretching the Envelope of Past Surface Environments: Neoproterozoic Glacial Lakes from Svalbard[END_REF].

However, for considerations of smaller ∆ 17 O variations (e.g., between -0.3 ‰ to +0.3 ‰), mass-dependent triple oxygen isotope effects must be included in sulfate ∆ 17 O-based models [START_REF] Cao | Small Triple Oxygen Isotope Variations in Sulfate: Mechanisms and Applications[END_REF]. For example, the 17 O-deficit in sulfate's atmospheric O 2 oxygen source is not solely due to mass independence, as it is largely attributable to mass-dependent reactions such as kinetic isotope effects during respiration that contribute to the Dole Effect [START_REF] Luz | 5.14 -The Stable Isotopic Composition of Atmospheric O2[END_REF][START_REF] Young | On the Δ17O budget of atmospheric O2[END_REF]. The second assumption that places a maximum limit of 25 % for the fraction of O 2 -oxygen in sulfates (e.g., [START_REF] Balci | Oxygen and sulfur isotope systematics of sulfate produced by bacterial and abiotic oxidation of pyrite[END_REF][START_REF] Bao | Triple oxygen isotope evidence for elevated CO2 levels after a Neoproterozoic glaciation[END_REF][START_REF] Kohl | Triple-oxygen-isotope determination of molecular oxygen incorporation in sulfate produced during abiotic pyrite oxidation (pH=2-11)[END_REF][START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF], may result in overestimations of the negative ∆ 17 O of O 2 that in turn affects constraints on ancient CO 2 and bioproductivity. Lastly, the third assumption anchors the oxygen isotope systematics of sulfate on fractionations between sulfate and water that are shown to be highly variable in sign and amplitude (see review in [START_REF] Gomes | Oxygen and sulfur isotopes in sulfate in modern euxinic systems with implications for evaluating the extent of euxinia in ancient oceans[END_REF]. The isotopic relationships, and the isotopic constraints on the proportion of atmospheric O 2 -oxygen in sulfate, are unconstrained because oxygen-isotope differences between sulfate and water are effectively moving targets. Oxygen of sulfate is predicted to carry a mix of equilibrium and non-equilibrium isotopic signatures that have been summarized, using

J o u r n a l P r e -p r o o f available constraints, by [START_REF] Cao | Small Triple Oxygen Isotope Variations in Sulfate: Mechanisms and Applications[END_REF]. However, despite the leverage of isotopic techniques, fixed magnitudes and signs for oxygen-isotope fractionations between sulfate and water (e.g., equations 13 and 15-18 in [START_REF] Cao | Small Triple Oxygen Isotope Variations in Sulfate: Mechanisms and Applications[END_REF] do not match sulfate results, either (Fig. 1). This mismatch between isotopic predictions and data is clearly observed with δ 18 O even before introducing the added dimension of ∆ 17 O. Considering these issues, outstanding assumptions need to be eliminated by updating sulfate-oxygen isotope systematics alongside an atmospheric O 2 triple oxygen isotope model that can handle both large and small δ 18 O and ∆ 17 O variations.

Figure 1.

Paired sulfate and water oxygen isotope data with predicted curves for the sulfate-water-O 2 system from mass balance and isotopic approaches. The data are from original and compiled sources in Van Everdingen and [START_REF] Van Everdingen | Interpretation of isotopic compositions of dissolved sulfates in acid mine drainage: U.S. Bureau of Mines Circular[END_REF][START_REF] Seal | Stable-isotope geochemistry of mine waters and related solids: Environmental aspects of mine wastes[END_REF][START_REF] Balci | Oxygen and sulfur isotope systematics of sulfate produced by bacterial and abiotic oxidation of pyrite[END_REF][START_REF] Kohl | Triple-oxygen-isotope determination of molecular oxygen incorporation in sulfate produced during abiotic pyrite oxidation (pH=2-11)[END_REF][START_REF] Hendry | Interpretation of oxygen and sulfur isotopes from dissolved sulfates in tills of southern Alberta[END_REF][START_REF] Sun | Lost cold Antarctic deserts inferred from unusual sulfate formation and isotope signatures[END_REF][START_REF] Pierre | Supratidal evaporitic dolomite at Ojo de Liebre Lagoon; mineralogical and isotopic arguments for primary crystallization[END_REF] J o u r n a l P r e -p r o o f [START_REF] Balci | Tetrathionate and elemental sulfur shape the isotope composition of sulfate in acid mine drainage[END_REF][START_REF] Krouse | 18O incorporation into sulphate during the bacterial oxidation of sulphide minerals and the potential for oxygen isotope exchange between O2, H2O and oxidized sulphur intermediates[END_REF] [START_REF] Taylor | Sulfur-and Oxygen-Isotope Geochemistry of Acid Mine Drainage in the Western United States[END_REF], as described in the main text for pyrite oxidation by O 2 (equation 1) and Fe 3+ (equation 2), and the dashed-dotted line is for oxidation with water and O 2 described in Van Stempvoort and [START_REF] Van Stempvoort | Controls of δ18O in sulfate: a review of experimental data and application to specific environments[END_REF]. The dashed lines show oxygen isotope fractionations for sulfate in the sulfate-water-O 2 system that are summarized and calculated in [START_REF] Cao | Small Triple Oxygen Isotope Variations in Sulfate: Mechanisms and Applications[END_REF].

METHODS

METHODS: TRIPLE OXYGEN ISOTOPE NOTATION

Oxygen isotope data are reported in delta notation in units × 1000 ‰ as deviations from the international isotope standard Vienna Standard Mean Ocean Water (VSMOW), as

δ ≡ R sample /R standard -1 (4),
with R being the 18 O/ 16 O or 17 O/ 16 O isotope atomic ratio. We report oxygen-17 in linear capital delta notation, also in ‰, as

Δ 17 O ≡ δ 17 O -C × δ 18 O (5),
where C is a reference slope of 0.528 useful for comparisons against meteoric waters and within low-temperature systems (e.g., [START_REF] Luz | Variations of 17O/16O and 18O/16O in meteoric waters[END_REF] Mass-dependent processes, such as within the hydrosphere, yield roughly predictable isotopic fractionations that have small but measurable variations that can be diagnostic.

Starting with seawater at the origin, meteoric waters follow ∆ 17 O-δ 18 O trends that are indicated by a best-fit polynomial line, the Global Meteoric Water Line, in Figure 2.

Given that meteoric water isotope compositions relate to both equilibrium and kinetic isotope effects whose mechanisms are dependent on temperature and relative humidity (e.g., [START_REF] Luz | Variations of 17O/16O and 18O/16O in meteoric waters[END_REF], respectively, the isotopic relationships of waters are unlikely to have changed much over time. A different oxygen-isotope composition of seawater in the past would, however, require a shift in the anchor point for the oxygen isotope system of water, away from its current seawater origin defined by modern ocean water (VSMOW). Despite this possibility, the extant chert oxygen isotope record through the Proterozoic to the present does not require secular changes in ocean oxygen isotope composition (e.g., [START_REF] Sengupta | Triple oxygen isotopes of cherts through time[END_REF].

The terrestrial Dole Effect (DE) was originally defined as the δ 18 O difference (or ∆δ 18 O) between tropospheric O 2 and seawater [START_REF] Dole | The relative atomic weight of oxygen in water and in air[END_REF][START_REF] Morita | Oxygen isotope fractionation of dissolved oxygen during abiological reduction by aqueous sulfide[END_REF], which was further J o u r n a l P r e -p r o o f extended to ∆ 17 O (or ∆∆ 17 O tropO2-seawater ) [START_REF] Bender | The Dole effect and its variations during the last 130,000 years as measured in the Vostok ice core[END_REF][START_REF] Luz | Tripleisotope composition of atmospheric oxygen as a tracer of biosphere productivity[END_REF].

Parameterizations by [START_REF] Luz | 5.14 -The Stable Isotopic Composition of Atmospheric O2[END_REF] and [START_REF] Young | On the Δ17O budget of atmospheric O2[END_REF] J o u r n a l P r e -p r o o f additional constraints imposed from literature sources. After [START_REF] Crockford | Triple oxygen isotope evidence for limited mid-Proterozoic primary productivity[END_REF], the flux of oxygen production is considered stoichiometrically related to photosynthetic oxygen flux, which, in turn, is proportional to gross primary productivity (GPP). Because of the assumption that the ratio of GPP to respiration is fixed, GPP could also be a standin for net primary production that is equal to GPP minus respiration. This is built into the model due to the assumption that the biological contribution has a fixed O-isotope composition with a majority of the isotopic signature being due to respiration. We will further test the assumption that the ratio of GPP/respiration is fixed within the model.

Although our model is a refinement, it is still only a rough approximation due to the many uncertainties about the past biosphere, pCO 2 , and pO 2 . As such, we will test the The photochemical effect that we term strateff is the diminution of the tropospheric O 2 triple oxygen isotope composition, i.e., the lowering of its 17 O and 18 O versus 16 O, by mixing with O 2 that has been isotopically fractionated in the stratosphere. Separate calculation of the strateff must be done to distinguish the mass independent effect from the mass dependent effects (from the biosphere) on the composition of atmospheric O 2 .

Note that the strateff is due to the nearly equal enrichment of 17 O and 18 O (versus 16 O) in photochemically reacted ozone (O 3 ) from which electronically excited atomic oxygen goes on to react and enrich CO 2 in 17 O and 18 O [START_REF] Yung | Isotopic exchange between carbon dioxide and ozone via O (1D) in the stratosphere[END_REF]. This is balanced by the depletion of 17 O and 18 O in the O 2 that is the ultimate source of ozone [START_REF] Wen | Multi-isotope study of the O (1 D)+ CO2 exchange and stratospheric consequences[END_REF]. By isotopic mass balance, the large tropospheric O 2 reservoir has a small depletion of 17 O and 18 O compared to the larger enrichments of the 17 O and 18 O in the much smaller O 3 and CO 2 reservoirs. The stratospheric effect on tropospheric O 2 was calculated by [START_REF] Bender | The Dole effect and its variations during the last 130,000 years as measured in the Vostok ice core[END_REF] as a -0.4 ‰ decrease in both δ 17 O O2 and δ 18 O O2 . Later, the stratospheric effect on atmospheric O 2 was measured and calculated to be δ 17 O = δ 18 O = -0.3 ±0.1 ‰ [START_REF] Luz | Tripleisotope composition of atmospheric oxygen as a tracer of biosphere productivity[END_REF][START_REF] Luz | 5.14 -The Stable Isotopic Composition of Atmospheric O2[END_REF]. We update the isotopic mass balance calculation [START_REF] Bender | The Dole effect and its variations during the last 130,000 years as measured in the Vostok ice core[END_REF] for incorporation into our model, as follows,

δ 1x O strateff = str-trp CO2 × (pCO 2 /pO 2 ) × (τ trpO2 /τ trp-strO2 ) × -1 (8).

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Descriptions of equation ( 8) parameters are found in Table 1, whereas δ 1x O strateff is for both 17 O and 18 O. We calculate the strateff to be δ 17 O strateff = δ 18 O strateff = -0.3648 ‰, identical, within uncertainty, to the estimation by [START_REF] Luz | Tripleisotope composition of atmospheric oxygen as a tracer of biosphere productivity[END_REF][START_REF] Luz | 5.14 -The Stable Isotopic Composition of Atmospheric O2[END_REF].

δ 1x O strateffmod = (-δ 1x O CO2-O2 × γ × θ × τ trpO2 ) ÷ (1+ ρ + γ × θ × τ trpO2 ) (9).
The strateffmod returns δ 18 O strateffmod = -0.3648 ‰ and δ 17 O strateffmod = -0.3611 ‰, and therefore ∆∆ 17 O tropO2-respiredphotoO2,0.528 = -0.1685 ‰ for the stratospheric effect on modern tropospheric O 2 . Our initial strateffmod state at modern conditions compares to the previous model [START_REF] Cao | Dynamic model constraints on oxygen-17 depletion in atmospheric O2 after a snowball Earth[END_REF] with a biosphere flux of O 2 that is more than doubled due to the inclusion of land production alongside marine production and a value of θ that is half of the previously used value. Note that θ is used here to be consistent with the Cao and Bao model but it is not to be confused with isotopic θ (see

δ 1x O tropO2 = δ 1x O strateffmod + δ 1x O bioO2mod (12).
In the simplified model, the fixed δ 17 O bioO2 and δ 18 O bioO2 calculated from equation ( 10 Non-quantitative sample yields during triple oxygen isotope measurements of sulfates add another challenge to the normalization of ∆ 17 O data. Data treatment is therefore required for normalization of ∆ 17 O against VSMOW [START_REF] Miller | Standardizing the reporting of Δʹ17O data from high precision oxygen triple-isotope ratio measurements of silicate rocks and minerals[END_REF] and to compensate for associated mass dependent fractionation [START_REF] Cowie | High-precision measurement and standard calibration of triple oxygen isotopic compositions (δ18O, Δ′17O) of sulfate by F2 laser fluorination[END_REF].

The analytical oxygen-isotope fractionation slope was determined from a linear versus VSMOW previously obtained via quantitative EA-coupled mass spectrometry [START_REF] Killingsworth | Constraining the rise of oxygen with oxygen isotopes[END_REF]. This slope, C = 0.5158 (standard error ±0.0069), is likely the result of multiple fundamental processes. In contrast, a slope close to the hightemperature limit θ = 0.5305 may be determined from the CO 2 -laser fluorination of barite using F 2 instead of BrF 5 [START_REF] Cowie | High-precision measurement and standard calibration of triple oxygen isotopic compositions (δ18O, Δ′17O) of sulfate by F2 laser fluorination[END_REF]. The target for NBS-127 of δ 18 O VSMOW = 9.3 ±0.3 ‰ [START_REF] Gonfiantini | Standards and intercomparison materials distributed by the International Atomic Energy Agency for stable isotope J o u r n a l P r e -p r o o f Journal Pre-proof measurements: Reference and intercomparison materials for stable isotopes of light elements[END_REF] was used for ease of comparison As a test of our correction, we applied ( 13) and ( 14) to the long-term IPGP NBS-127 data returning a mean of ∆' 17 O 0.528,VSMOW = -0.03 ‰, comparing well with the ∆' 17 O 0.528,VSMOW = -0.04 ‰ resulting from quantitative graphite reduction + CO 2 fluorination of NBS-127 [START_REF] Bao | Generation of O2 from BaSO4 using a CO2-laser fluorination system for simultaneous analysis of δ18O and δ17[END_REF]. A comparison between the measured and corrected triple oxygen isotope data is shown in the supplementary information (Fig. S1).

RESULTS AND DISCUSSION

REASSESSING SULFATE-WATER δ 18 O SIGNALS IN SULFATE

Our compilation of paired sulfate-water data from the oxidation of different sulfur species (Fig. 3) shows the δ 18 O difference between sulfate and ambient water (∆δ 18 O sulfate-water )

varies from -77.3 ‰ [START_REF] Krouse | 18O incorporation into sulphate during the bacterial oxidation of sulphide minerals and the potential for oxygen isotope exchange between O2, H2O and oxidized sulphur intermediates[END_REF] -oxygen, while there is no a priori reason to exclude even higher contributions from O 2 in some circumstances. For example, initially produced sulfates suggest incorporation of >75 % molecular oxygen in oxidation J o u r n a l P r e -p r o o f experiments with pyrites of grain sizes < 63 μm [START_REF] Tichomirowa | Oxygen isotope evidence for sorption of molecular oxygen to pyrite surface sites and incorporation into sulfate in oxidation experiments[END_REF][START_REF] Heidel | The role of dissolved molecular oxygen in abiotic pyrite oxidation under acid pH conditions -Experiments with 18O-enriched molecular oxygen[END_REF]. At the very least, it is apparent that sulfates exceed the 8 to 15 % O 2 -oxygen contribution [START_REF] Balci | Oxygen and sulfur isotope systematics of sulfate produced by bacterial and abiotic oxidation of pyrite[END_REF] that was previously assumed in models (e.g., [START_REF] Bao | Triple oxygen isotope evidence for elevated CO2 levels after a Neoproterozoic glaciation[END_REF][START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF]. Therefore, in our assessment here, such limits on sulfate's proportion of O 2 -oxygen cannot be assumed in advance. * end member indicate its reported ranges, while the solid horizontal line is its average.

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TESTING THE MODEL AGAINST EXTANT RECORDS OF PROTEROZOIC EXTREME OXYGEN-17 DEPLETIONS

Extreme negative ∆ 17 O sulfate data are associated with the ~635 Ma Neoproterozoic Marinoan Snowball Earth meltdown and from earlier Proterozoic sulfates (Fig. 4). Such data are unambiguous in requiring an O 2 -oxygen end member because atmospheric O 2 is the only suitable oxidant of sulfide that has a mass-independent 17 O-deficit. The upper bounds of the anomalous ∆ 17 O-δ 18 O data of Proterozoic sulfate generally conform to the Global Meteoric Water line, consistent with 100 % water-oxygen end members.

Meanwhile, the minimum pCO 2 for the meltdown of a Snowball Earth event has been estimated to be 100 mbar of CO 2 [START_REF] Hoffman | Snowball Earth climate dynamics and Cryogenian geologygeobiology[END_REF]. We use this pCO 2 in our model [START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF] with additional data [START_REF] Sun | Lost cold Antarctic deserts inferred from unusual sulfate formation and isotope signatures[END_REF][START_REF] Kim | Multiple oxygen (16O, 17O and 18O) and sulfur (32S, 33S, 34S and 36S) isotope signatures of the dissolved sulfate from Deception Island, Antarctic Peninsula: Implications on sulfate formation, transportation and deposition in the Antarctic region[END_REF][START_REF] Killingsworth | Constraining the rise of oxygen with oxygen isotopes[END_REF][START_REF] Zhang | Assessing the oxidative weathering of pyrite and its role in controlling atmospheric CO2 release in the eastern Qinghai-Tibet Plateau[END_REF][START_REF] Peng | Oxygen isotope composition of meltwater from a Neoproterozoic glaciation in South China[END_REF][START_REF] Waldeck | Deciphering the atmospheric signal in marine sulfate oxygen isotope composition[END_REF][START_REF] Hemingway | Triple oxygen isotope insight into terrestrial pyrite oxidation[END_REF]. The sulfate data are presented together with the caution that they are not all corrected for mass-dependent fractionation during partial fluorination yields, and that they are not universally normalized to the same accepted values for reference standards. As such, discrepancies may exist on the order of ~0.1 ‰ for ∆ 17 O. Error bars are shown for ∆ 17 O and are smaller than the symbols for δ 18 O. The Global Meteoric Water Line (GMWL) [START_REF] Sengupta | Triple oxygen isotopes of cherts through time[END_REF] represents the distillation (lighter δ 18 O) and evaporation (heavier δ 18 O) of meteoric waters as compared to their seawater source at the origin (represented by the isotope standard VSMOW at ∆ 17 O = δ 18 O = 0 ‰). The composition of modern O 2 is also shown [START_REF] Pack | Tracing the oxygen isotope composition of the upper Earth's atmosphere using cosmic spherules[END_REF]. Highly 17 O-anomalous sulfates, with isotopic arrays that extend in a more vertical orientation, are noted for the Paleoproterozoic, Mesoproterozoic, and Neoproterozoic. These anomalous arrays display the negative correlation between 17 O and 18 O that is predicted by the modeled curves for the variation in the triple oxygen isotope composition of O 2 as it tracks increasing pCO 2 and/or decreasing strength of biological O 2 fluxes. The model is

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Journal Pre-proof also mirrored in the curve for the fractionated O 2 * that is incorporated into sulfate. Fractionation curves for surface oxidation and sulfate in equilibrium with water (equilibrium) are calculated according to [START_REF] Cao | Small Triple Oxygen Isotope Variations in Sulfate: Mechanisms and Applications[END_REF] [START_REF] Sun | Lost cold Antarctic deserts inferred from unusual sulfate formation and isotope signatures[END_REF] that fall below the typical range of glacial sulfate, but this does not appear to be the case. Instead, the anomalous Neoproterozoic sulfates show a near-vertical ∆ 17 O-δ 18 O relationship within the lower right quadrant, indicative of mixing between evaporated water-oxygen (potentially seawater) and O 2oxygen sources. Furthermore, the Neoproterozoic sulfate array contrasts sharply with the most δ 18 O-negative sulfates found in rocks, which are from Neoproterozoic diamictites (upper left-most data plotted on Fig. 4; [START_REF] Peng | Oxygen isotope composition of meltwater from a Neoproterozoic glaciation in South China[END_REF]; whereas mixing between the Neoproterozoic glacial and anomalous (vertical array) sulfates is not apparent.

In a back-of-the-envelope calculation we estimate ∆ 17 O O2,0.528 using the average Marinoan sulfate (∆ 17 O = -0.66 ‰), the average O 2 * -oxygen ratio of sulfate (0.315) from our compilation (Fig. 4), and an evaporated water source (∆ 17 O = -0.2 ‰). The post-Marinoan Snowball O 2 is thus estimated at ∆ 17 O = -1.7 ‰, close to the minimum sulfate data at ∆ 17 O = -1.84 ‰ [START_REF] Bao | Stretching the Envelope of Past Surface Environments: Neoproterozoic Glacial Lakes from Svalbard[END_REF]. This scenario suggests two important features.

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First, our findings from paired sulfate and water δ 18 O show that sulfate can contain as much as 100 % O 2 *oxygen (Fig. 3), which implies that the Neoproterozoic ∆ 17 O minimum of sulfate may be notable not only for its extremity, but also for recording the composition of O 2 itself. Second, according to our model assessment, the Neoproterozoic sulfate ∆ 17 O-δ 18 O record may only require pCO 2 ≈ 3.2 mbar, far short of the 100 mbar needed to deglaciate a Neoproterozoic Snowball Earth [START_REF] Hoffman | Snowball Earth climate dynamics and Cryogenian geologygeobiology[END_REF]. As an aside, if we fix pCO 2 at 1 times present atmospheric levels (PAL), a fraction of 0.12 of present levels of pO 2 and photosynthetic O 2 flux (here, they are linked together, keeping O 2 residence time fixed at 1271 years) would be required for ∆ 17 O O2 = -1.7 ‰. We reconcile these pCO 2 estimates, for now, by suggesting that the full ∆ 17 O-δ 18 O signal of O 2 responding to short-lived ultra-high CO 2 has not yet been observed in sulfates. If such extreme ∆ 17 O compositions of sulfate do exist, perhaps it will one day be feasible to observe this with in situ triple oxygen isotope measurements at the micro-scale.

Our model gives insight on earlier Proterozoic published ∆ 17 O data from sulfates as well.

The Mesoproterozoic 1.4 Ga sulfates from the Sibley Group are interpreted as coming from a lacustrine setting [START_REF] Crockford | Triple oxygen isotope evidence for limited mid-Proterozoic primary productivity[END_REF], displaying a loosely defined array (filled green triangles in Fig. 4) that is consistent with a stronger strateff on O 2 as compared to today and consistent with a lower-δ 18 O water-oxygen source than the Marinoan case. The Mesoproterozoic Sibley Group sulfates occur below the evaporite field in Figure 4, reaching as low as ∆ 17 O sulfate,0.528 = -1.02 ‰. The 17 O-anomalous 1.7 to 1.89 Ga Paleoproterozoic gypsum data [START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF] show a very similar pattern to the Sibley Group sulfates, falling within the same ∆ 17 O-δ 18 O region (open J o u r n a l P r e -p r o o f black triangles in Fig. 4), in sub-vertical arrays reaching as low as ∆ 17 O sulfate = -0.75 ‰.

Similar to the Neoproterozoic case, we identify potential end members. Starting with a less-evaporated water end member at ∆ 17 O = -0.1 ‰, we use the averages of the 1.4 Ga (∆ 17 O ≈ -0.67 ‰) and 1.7 to 1.89 Ga (∆ 17 O ≈ -0.53 ‰) sulfates to estimate their corresponding ∆ 17 O O2 values at -2 ‰ to -1.6 ‰. The respective intervals' ∆ 17 O O2 could correspond to a pCO 2 of 4 to 2.9 mbar, which is on the order of these time intervals' minimum estimated pCO 2 whose regulation of the climate, in turn, may have been boosted by methane [START_REF] Catling | The Archean atmosphere[END_REF]. Indeed, work on Proterozoic analogs has suggested CH 4 may have had a significant control on early climate [START_REF] Cadeau | Carbon isotope evidence for large methane emissions to the Proterozoic atmosphere[END_REF].

A more prominent role for atmospheric methane eases the need to invoke high ranges for the pCO 2 estimated for the Proterozoic, likewise being amenable with our rough approximation that the extant triple oxygen isotope record of sulfate may not require pCO 2 higher than 4 mbar (≈ 10 PAL) since 1.89 Ga.

ANOTHER LOOK AT EVAPORITE O-ISOTOPE RECORDS

Records of evaporite gypsum and anhydrite S-and O-isotope signals are invaluable for insight on coupled ocean-atmosphere redox changes through the Proterozoic and Phanerozoic [START_REF] Claypool | The age curves of sulfur and oxygen isotopes in marine sulfate and their mutual interpretation[END_REF][START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF]. The shaded field within (light blue curves). The upper range of sulfate-water equilibrium is very similar to the Global Meteoric Water Line. Given our findings that calculated fractionations for the sulfate system do not closely describe measured data (Fig. 1), we suggest the upper bounds of sulfate data may indeed match the GMWL itself instead of a sulfate-water equilibrium curve offset from the GMWL. That most evaporite data fall into the shaded field in Fig. 5 suggests that oxygen isotope compositions of seawater, and perhaps O 2 , have been largely stable since the Proterozoic. Such agreement implies strong feedbacks that maintain stable isotope compositions of O 2 despite drastic differences in pO 2 and pCO 2 between the Proterozoic and the Phanerozoic. Crucially, such stability could occur if the flux of photosynthetic O 2 has been maintained within the same order of magnitude as modern fluxes (the flux of bioO2 in the model).

J o u r n a l P r e -p r o o f [START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF] are shown here alongside the GMWL [START_REF] Sengupta | Triple oxygen isotopes of cherts through time[END_REF], sulfate-water equilibrium curve [START_REF] Cao | Small Triple Oxygen Isotope Variations in Sulfate: Mechanisms and Applications[END_REF], and the composition of modern atmospheric O 2 [START_REF] Pack | Tracing the oxygen isotope composition of the upper Earth's atmosphere using cosmic spherules[END_REF]. The shaded region is where sulfates formed from initial oxidation of sulfides in seawater or re-oxidation after microbial sulfate reduction may occur. Such sulfate would have oxygen sources from seawater (filled green square) and O 2 * (black multi-pointed star) with variable effects from the fractionation of residual sulfate caused by microbial sulfate reduction that pushes sulfate composition towards sulfate-seawater equilibrium (filled blue circle symbol). Biologically produced O 2 (yellow x symbol) and its respective O 2 * (yellow star) are discussed in the text.

Another aspect to be explored in the record of evaporites (and sulfates, generally) is possible incorporation of O 2 -oxygen that is only from biologically produced O 2 (bioO2 in the model) with no mixing of stratospheric O 2 (strateff in the model). Such O 2 would be J o u r n a l P r e -p r o o f produced and consumed in situ, thus retaining no mass-independent signal while only registering the isotopic effects of photosynthetic O 2 production and biological respiration (see also Fig. 2). This O 2 , and its corresponding O 2 * , are shown as the yellow X and star symbols, respectively, in Figure 5. We hypothesize that such oxygen signals might be possible under atmospheric pO 2 low enough for photosynthetic O 2 to be consumed in situ or diffuse into the atmosphere without diffusion of O 2 back into water from the atmosphere. Some Proterozoic evaporites are consistent with this possibility, spanning between bioO2 and its corresponding O 2 * , while very few evaporite data plot in the area below the bioO2-bioO 2 * boundary and between the model curves for O 2 * and O 2 .

Meanwhile, the potential distillation of atmospheric O 2 , which would follow a Rayleigh fractionation curve characterized by increasing δ 18 O (Fig. 4), is not clearly observed in the triple oxygen isotope record of sulfate. We therefore suggest that atmospheric O 2 drawdown could be indicated in ∆ 17 O-δ 18 O space by sulfates that span across O 2 * and O 2 instead of tracking a Rayleigh distillation curve, possible, for example, in the case of the anomalous Neoproterozoic sulfates (Fig. 4).

IMPLICATIONS FOR THE EARLY PALEOPROTEROZOIC FROM KAZPUT BARITE ∆ 17 O

The study section of the W. Australia lower Kazput Formation of the Turee Creek Group consists of an interval, ~60 meters thick, of drill core of finely laminated mud-and siltstones bracketing a carbonate-rich interval [START_REF] Killingsworth | Constraining the rise of oxygen with oxygen isotopes[END_REF]. Absolute age constraints place the Kazput Formation between 2.31 to 2.2 Ga [START_REF] Philippot | Globally asynchronous sulphur isotope signals require redefinition of the Great Oxidation Event[END_REF][START_REF] Caquineau | U-Pb detrital zircon geochronology of the Turee Creek Group, Hamersley Basin, Western Australia: timing and correlation of the Paleoproterozoic glaciations[END_REF], while detailed sedimentary context is available elsewhere (e.g.,

J o u r n a l P r e -p r o o f

Van [START_REF] Van Kranendonk | A conformable record of the transition from early to modern Earth[END_REF][START_REF] Barlow | Lithostratigraphic analysis of a new stromatolite-thrombolite reef from across the rise of atmospheric oxygen in the Paleoproterozoic Turee Creek Group[END_REF]. Prior quadruple sulfur and oxygen-18 isotope results from the Kazput barite, which features unusually low δ 18 O, were interpreted in favor of sulfate derived from continental sulfide oxidation being precipitated as barium sulfate (barite) within a possibly restricted basin between 2.31 to 2.2 billion years ago [START_REF] Killingsworth | Constraining the rise of oxygen with oxygen isotopes[END_REF]. Trace element and in situ microanalysis of sulfur isotopes [START_REF] Philippot | Globally asynchronous sulphur isotope signals require redefinition of the Great Oxidation Event[END_REF] and additional petrologic evidence [START_REF] Killingsworth | Constraining the rise of oxygen with oxygen isotopes[END_REF] have ruled out post-depositional oxidation of pyrite as the source of sulfate for Kazput barites.

Our ∆ 17 O data (n = 32) of Kazput barite range from -0.30 ‰ to -0.14 ‰ with a mean of -0.22 ‰ (Table 4). A regression of the ∆ 17 O of Kazput barite with its prior δ 18 O data intersects the Global Meteoric Water Line at δ 18 O = -35.5 +3.5/-5 ‰ (2σ) and ∆ 17 O = -0.13 +0.03/-0.05 ‰ (2σ) (Fig. 6). These values constrain the sulfate's water end member, which previously was not possible with the δ 18 O sulfate data alone. This wateroxygen source is within range of the Paleoproterozoic Snowball Earth meltwater source estimated at δ 18 O = -43 ±3 ‰ (1σ) that was invoked for hydrothermal alteration of ca.

2.3-2.4 Ga silicate rocks [START_REF] Herwartz | Revealing the climate of snowball Earth from Δ17O systematics of hydrothermal rocks[END_REF]. Although it is uncertain if these Paleoproterozoic records of 18 O-depleted waters are from the same time period or not, at the least they both indicate sources of glacial meltwaters from within the ca. 2.4-2.2 Ga interval of extensive global glaciations [START_REF] Gumsley | Timing and tempo of the Great Oxidation Event[END_REF]. In the case of the Kazput barite, such a record of meltwater is consistent with recent suggestions of an additional younger glacial unit within the Turee Creek Group succession [START_REF] Martin | Geology of the Hardey Synclinethe key to understanding the northern margin of the Capricorn Orogen[END_REF][START_REF] Philippot | Comment on "Correlation of the stratigraphic cover of the Pilbara and Kaapvaal cratons recording the lead up to Paleoproterozoic Icehouse and the GOE[END_REF].

J o u r n a l P r e -p r o o f Compared to its meltwater source, the Kazput sulfate isotopic array also requires a more 17 O-depleted and 18 O-enriched oxygen isotope end member. Existing sulfates from ~2.3

Ga could represent an 18 O-enriched end member for the Kazput barite, but their occurrence, as evaporite gypsum, and their mass-dependent ∆ 33 S data being less than 0.07 ‰ [START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF] are both inconsistent with the Kazput sulfate meltwater oxygen source and its ∆ 33 S range between 0.6 ‰ to 1.6 ‰ [START_REF] Killingsworth | Constraining the rise of oxygen with oxygen isotopes[END_REF]).

An influence from microbial sulfate reduction (MSR) would push residual sulfate closer to sulfate-water oxygen isotope equilibrium with either the Kazput water end member or seawater, but this is not observed in the Kazput barite data array (Fig. 5). Neither was the influence of MSR on Kazput barite sulfur-oxygen isotope correlations observed previously [START_REF] Killingsworth | Constraining the rise of oxygen with oxygen isotopes[END_REF]. Meanwhile, the minimum ∆ (Fig. 6).

J o u r n a l P r e -p r o o f

The ∆ 33 S signals from Kazput barite that are larger than +0.3‰ [START_REF] Killingsworth | Constraining the rise of oxygen with oxygen isotopes[END_REF] imply an anoxic atmosphere (O 2 <10 -5 PAL; [START_REF] Pavlov | Mass-independent fractionation of sulfur isotopes in Archean sediments: strong evidence for an anoxic Archean atmosphere[END_REF], while in an apparent paradox, the oxygen end member for Kazput barite with ∆ seawater sulfate and the GMWL (Fig. 4; [START_REF] Bao | The five stable isotope compositions of Fig Tree barites: Implications on sulfur cycle in ca. 3.2 Ga oceans[END_REF]. For the waning ∆ 33 S signals of anoxia that occur after 2.45 Ga, [START_REF] Farquhar | Multiple sulfur isotopes and the evolution of the atmosphere[END_REF] first gave two hypotheses: 1) sulfide-derived sulfate may retain the sulfur isotope signatures of their weathering sources even though the atmosphere was sufficiently oxygenated to shut down contemporaneous generation and preservation of ∆ 33 S > ±0.3 ‰, or 2) after 2.45 Ga the atmosphere was oscillating between anoxic and oxic states (above and below the 10 -5

PAL threshold) that allowed episodic generation and preservation of primary atmospheric sulfur with ∆ 33 S > ±0.3 ‰. The first hypothesis was expanded further to show such low-T sedimentary recycling of sulfur anomalies could prolong their specifically positive-sign (+∆ 33 S) signals under an oxygenated atmosphere to a maximum ∆ 33 S around +2 ‰, with this memory effect disappearing below +0.3 ‰ by ~200-250 Myrs [START_REF] Reinhard | Long-term sedimentary recycling of rare sulphur isotope anomalies[END_REF][START_REF] Philippot | Globally asynchronous sulphur isotope signals require redefinition of the Great Oxidation Event[END_REF]. The second hypothesis has recently been supported by the interpretation of the reappearance ∆ 33 S signals of pyrite reaching up to +2.7 ‰, indicating a return of atmospheric anoxia before ~2.2 Ga [START_REF] Poulton | A 200-million-year delay in permanent atmospheric oxygenation[END_REF].

Meanwhile, two persistent features stand out in this 2.45 Ga to 2.2 Ga interval of the Great Oxidation and beyond: 1) since 2.42 Ga, there are only positive, and no negative, J o u r n a l P r e -p r o o f ∆ 33 S anomalies preserved in rocks [START_REF] Killingsworth | Constraining the rise of oxygen with oxygen isotopes[END_REF] ‰ (1σ) (Fig. 6). We use the same starting point as [START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF] for the early Paleoproterozoic, based on estimates of atmospheric gas concentrations of pO 2 = 0.001 to 2 (10 -4 to 10 0.3 ) and pCO 2 = 10 to 80 at ~2.3 Ga, both with respect to their present atmospheric levels (PAL). We further test this pO 2 range in our model to down below the threshold of the disappearance of sulfur isotope mass-independent fractionation, 10 -5

PAL, going all the way down to 0 PAL. The relative importance of land versus marine O 2 production in the early Earth is unclear as evidence implies life was already on land in the J o u r n a l P r e -p r o o f

Archean (e.g., [START_REF] Thomazo | Possible nitrogen fertilization of the early Earth Ocean by microbial continental ecosystems[END_REF][START_REF] Homann | Microbial life and biogeochemical cycling on land 3,220 million years ago[END_REF]. Thus, we do not change relative contributions, running our model with total land and marine O 2 production inclusive as a ratio of present bioO2 flux, which is proportionally equivalent to GPP versus present levels. Furthermore, we estimate the isotopic difference between terrestrial and marine contributions to O 2 to be small, within ∆δ 18 O ≤ 0.3 ‰, a difference that can be neglected in the model considering the much greater uncertainties surrounding pCO 2 , pO 2 , and total O 2 flux. We do not assume limits on the specific proportion of O 2 signal that can be registered in sulfate, though this is the approach used in previous works (e.g., [START_REF] Cao | Dynamic model constraints on oxygen-17 depletion in atmospheric O2 after a snowball Earth[END_REF][START_REF] Planavsky | Large Mass-Independent Oxygen Isotope Fractionations in Mid-Proterozoic Sediments: Evidence for a Low-Oxygen Atmosphere?[END_REF]. In contrast, our triple oxygen isotope approach may attribute a less-negative ∆ 17 O O2 value from sulfate constraints. For our approach to be most effective, sulfate records with meteoric, instead of oceanic, water end members are needed. The effectiveness can be seen in Figure 5, where the ∆ 17 O-δ 18 O array of the Kazput barite is compared to published evaporite sulfate records from around the same time (~2.3 Ga; [START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF]. The low δ 18 O value of its water end member makes the ∆ 17 O-δ 18 O array of the Kazput barite intersect its O 2 end member at a lower angle as compared to the near-vertical approach of the evaporite data. In effect, these sulfate data from ~2.3 Ga are consistent with one another, though their interpretation differs with the minimum ∆ 17 O data of evaporites previously assumed to contain a maximum of 15 % O 2 -oxygen [START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF]. Here we observe that, instead, the same evaporite with minimum ∆ 17 O might contain much closer to a maximum 100 % O 2 -oxygen, or, more accurately, nearly 100 % O 2 * -oxygen. In another departure from prior approaches, we do not assume that the biosphere imparts O 2 with a ∆ 17 O value of 0, because, in fact, the biological production and respiration of O 2 do J o u r n a l P r e -p r o o f impart a significant mass-dependent triple oxygen isotope fractionation to O 2 on the order of ∆ 17 O ≈ -0.3 ‰ to -0.4 ‰ [START_REF] Luz | 5.14 -The Stable Isotopic Composition of Atmospheric O2[END_REF][START_REF] Young | On the Δ17O budget of atmospheric O2[END_REF]Fig. 2), that we calculate as ∆ 17 O = -0.32 ‰ (see discussion on the bioO2mod in section 2.3). In sum, compared to prior approaches, here the net result is that we determine a less-negative ∆ 17 O O2 value from ∆ 17 O records of sulfate but a higher biological O 2 flux (i.e., GPP)

because we account for the negative signal of ∆ 17 O bioO2 .

Our model results with triple oxygen isotope constraints from Kazput barite suggest gross primary production was between 6 to 160 times (or 10 0.8 to 10 2.2 ) present levels at ~2.3

Ga with large fluxes of photosynthetic O 2 being required to balance 10 -2 to 10 -0.4 PAL pO 2 and pCO 2 of 10 to 80 times PAL (Fig. 7). These GPP results are higher than those found previously for ~2.3 Ga, which were 27.3 times present levels at maximum [START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF]. The GPP results that are below 10 -2 PAL pO 2 fall outside of the 99.5 percentile, an independent confirmation that an oxygenated atmosphere may be unstable below this pO 2 horizon [START_REF] Gregory | Photochemical modelling of atmospheric oxygen levels confirms two stable states[END_REF]. At higher pO 2 , GPP becomes more sensitive to the range of pCO 2 . Maximum pO 2 is limited here to 40 % (10 -0.4 ) PAL after constraints from Proterozoic ocean anoxia [START_REF] Kump | The rise of atmospheric oxygen[END_REF]. Analysis of the burial of organic carbon through time indicates ~2.3 Ga may have had a comparably productive biosphere as the present [START_REF] Krissansen-Totton | A statistical analysis of the carbon isotope record from the Archean to Phanerozoic and implications for the rise of oxygen[END_REF], an implication that is in contrast to the demands from high pCO 2 of 10 to 80 PAL and potentially elevated GPP in the early Paleoproterozoic [START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF]. Enhanced efficiency of total carbon burial has also been invoked to balance such higher carbon inputs in the past [START_REF] Kipp | High Organic Burial Efficiency Is Required to Explain Mass Balance in Earth's Early Carbon Cycle[END_REF]. However, recent reinterpretation of the Paleoproterozoic Lomagundi-Jatuli carbon J o u r n a l P r e -p r o o f isotope excursion, which has previously been interpreted as a global-scale episode of enhanced carbon burial, suggests that surficial influxes and outfluxes of carbon have been in balance throughout Earth history [START_REF] Prave | The grandest of them all: the Lomagundi-Jatuli Event and Earth's oxygenation[END_REF]. Meanwhile, our estimate of GPP between 6 to 160 present levels at ~2.3 Ga offers further support that the constraints imposed by records of carbon burial, indicators of high pCO 2 , and sulfate triple oxygen isotopes may all be satisfied by a highly productive early Paleoproterozoic biosphere. constraints (e.g., [START_REF] Planavsky | Large Mass-Independent Oxygen Isotope Fractionations in Mid-Proterozoic Sediments: Evidence for a Low-Oxygen Atmosphere?[END_REF]. From an oxygen-isotope perspective, however, we can use the full version of our tropO2 model to further examine the effect of the biosphere on O 2 and its implications for GPP. For example, the need for more constraint on the oxygen isotope composition of photosynthetic O 2 is highlighted by the uncertainties surrounding global average leaf water [START_REF] West | A Simplified GIS Approach to Modeling Global Leaf Water Isoscapes[END_REF][START_REF] Young | On the Δ17O budget of atmospheric O2[END_REF]). Here we focus on respiration because this process is the most important isotopic control on biologically affected O 2 . A lower efficiency of respiration for the Paleoproterozoic may have served as an additional source of O 2 by way of permitting more organic carbon burial. We test the implication of lowered respiration efficiency on triple oxygen isotope-constrained GPP to see if it would still require high GPP for the Paleoproterozoic, ca. 2.3 Ga. This is done with the caveat that the triple oxygen isotope slope of global respiration is still being refined (e.g., [START_REF] Ash | What Fractionates Oxygen Isotopes during Respiration? Insights from Multiple Isotopologue Measurements and Theory[END_REF]. Decreasing efficiency of respiration will cause the upper bound of O 2 (biological O 2 without the stratospheric effect) to track along the triple oxygen isotope respiration slope towards photosynthetic O 2 production (Fig. 5). With the model set for maximum pO 2 at 10 0.3 (2 PAL) and minimum pCO 2 at 10 PAL for ~2.3 Ga we can observe the minimum GPP required by the isotope composition of O 2 that is constrained by Kazput barite using the J o u r n a l P r e -p r o o f

Figure 2 .

 2 Figure 2. Simplified versions of two models of the oxygen isotopic differences between seawater and atmospheric O 2 , or the Dole Effect, are shown alongside the triple oxygen isotope fractionation among meteoric waters, the Global Meteoric Water Line (a

  model's applicability by comparing with existing O-isotope records of sulfate. Then, specifically in the case of ca. ~2.3 Ga Kazput barite analyzed for its ∆ 17 O as part of this study, we will leverage ∆ 17 O barite and δ 18 O barite measurements to estimate the triple oxygen isotope composition of O 2 , then, ranges of pCO 2 and pO 2 at ~2.3 Ga will be taken from published geochemical proxy or model constraints to invert the model and solve for GPP.In sum, here the improvements with respect to the[START_REF] Cao | Dynamic model constraints on oxygen-17 depletion in atmospheric O2 after a snowball Earth[END_REF] model are that we can solve for δ 18 O O2 , and the stratospheric mass-independent and biological massdependent contributions are separated. The updated model is accordingly retuned to solve for the isotopic composition of modern O 2 . This retuning is crucial to ensure the model works under known constraints before applying it to ancient records where pO 2 and pCO 2 are poorly constrained. Three aspects are first examined separately and then integrated into the final model as follows, 1) the stratospheric photochemical effect (strateff) on J o u r n a l P r e -p r o o f tropospheric O 2 is isolated and calculated, 2) the stratospheric effect module (strateffmod) is retuned for the final model, 3) the module for the effect of the biosphere on atmospheric O 2 (bioO2mod) is constructed, and 4) the final model (tropO2) returns the triple oxygen isotope composition (δ 18 O and ∆ 17 O) of tropospheric O 2 as a function of pO 2 , pCO 2 , and marine and terrestrial biological O 2 production.

  ) are used within equation (12) instead of δ 17 O bioO2mod and δ 18 O bioO2mod . If constraints on the isotope composition of tropospheric O 2 , pO 2 , and pCO 2 are available then the model can be inverted to solve for GPP (as equivalent to the sum of oxygen production in the ocean and on land). The interpretation ∆ 17 O and δ 18 O measurements of sulfate within our updated sulfate-water-O 2 framework will allow for estimation of the ∆ 17 O and δ 18 O of tropospheric O 2 . To do this requires calculating between the triple oxygen isotope compositions of sulfate, O 2 * for the fractionated O 2 -oxygen incorporated into sulfate, and O 2 . This conversion is done by adopting our estimation of O 2 * -O 2 fractionation as ∆δ 18 O = -8.8 ‰ (see discussion in section 3.1) and adopting the triple oxygen isotope exponent C = 0.52 in order to calculate ∆ 17 O O2 . Our choice of this C value is admittedly arbitrary, representing a generic mass-dependent triple oxygen isotope slope, whereas an arbitrary value of 0.5110 was similarly chosen for the kinetic isotope effect between sulfate and O 2 found in Cao and Bao (2021). The use of a 0.5110 slope, instead of 0.52, would shift the O 2 * -based ∆ 17 O O2 estimate lower by -0.08 ‰, and as such, we consider 0.52 as conservative. J o u r n a l P r e -p r o o f 2.4. METHODS: SULFATE TRIPLE OXYGEN ISOTOPE MEASUREMENTS AND DATA TREATMENT For this study we measured the triple oxygen isotope composition of aliquots of the same purified barium sulfate (BaSO 4 ) sample extracts that were measured for δ 34 S, ∆ 33 S, ∆ 36 S, and δ 18 O by Killingsworth et al. (2019), with details of the sample extraction in that prior study. Sulfate was extracted from powdered sedimentary rock samples from drill core 3 from the Turee Creek Drilling project (~2.3 Ga, see Philippot et al., 2018). The ∆ 17 O values of sulfate and a silicate reference standard were measured from evolved O 2 using a CO 2 -laser fluorination (using BrF 5 ) technique (Bao and Thiemens, 2000) on a Thermo Finnigan Delta V Plus mass spectrometer in dual inlet mode using an in-house O 2 reference gas at the Institut de Physique du Globe de Paris (IPGP). The analytical uncertainty for the prior barite δ 18 O measurements is ±0.4‰ (2σ) (Killingsworth et al., 2019), while barite measurements at IPGP are ±0.04‰ (2σ) for ∆ 17 O (Legendre et al., 2016), with both uncertainties based on replicate analysis of the NBS-127 BaSO 4 standard. Here, single samples of 3 to 6 mg of Kazput barite were measured for their ∆ 17 O. During the same sample measurement sessions, replicates of the silicate standard UWG-2 (n=9) yielded an analytical uncertainty of ±0.04‰ (2σ) for ∆ 17 O.

J

  o u r n a l P r e -p r o o f regression of the δ' 17 O versus δ' 18 O of long-term measurements (n=66) of barite standard NBS-127, removing outliers beyond ±1σ of the mean. Using the determined slope, measured sample δ' 17 O data were recalculated to the anchor point of the accurate δ' 18 O

Figure 3 .

 3 Figure 3. A compilation of experimental and field dissolved sulfate oxygen isotope data in cross-plot against paired ambient water oxygen isotope data. The data references are the same as in Figure 1. Here it is illustrated how sulfate-water oxygen-isotope fractionation ranges both positive and negative, depending on the relationship between ambient water and fractionated O 2 during oxidation of reduced sulfur species to sulfate. Curves for sulfate end member cases, as described in the main text, are labeled and shown as H 2 O = 100 % water-oxygen and O 2 * = 100 % fractionated O 2 -oxygen. The numbered lines show the fractional incorporation of O 2 * -oxygen. Dashed lines for the horizontal O 2* end member indicate its reported ranges, while the solid horizontal line is its average.

  photosynthetic O 2 flux, is set at modern levels for these estimates. Lowering pCO 2 and/or photosynthetic O 2 flux would further decrease ∆ 17 O sulfate and δ 18 O sulfate values, as these

Figure 4 .

 4 Figure 4. Kazput barite ∆ 17 O data and model O 2 results are shown from this study alongside published sulfate triple oxygen isotope data (∆ 17 O and δ 18 O) from compiled and original sources[START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF] with additional data[START_REF] Sun | Lost cold Antarctic deserts inferred from unusual sulfate formation and isotope signatures[END_REF][START_REF] Kim | Multiple oxygen (16O, 17O and 18O) and sulfur (32S, 33S, 34S and 36S) isotope signatures of the dissolved sulfate from Deception Island, Antarctic Peninsula: Implications on sulfate formation, transportation and deposition in the Antarctic region[END_REF][START_REF] Killingsworth | Constraining the rise of oxygen with oxygen isotopes[END_REF][START_REF] Zhang | Assessing the oxidative weathering of pyrite and its role in controlling atmospheric CO2 release in the eastern Qinghai-Tibet Plateau[END_REF][START_REF] Peng | Oxygen isotope composition of meltwater from a Neoproterozoic glaciation in South China[END_REF][START_REF] Waldeck | Deciphering the atmospheric signal in marine sulfate oxygen isotope composition[END_REF][START_REF] Hemingway | Triple oxygen isotope insight into terrestrial pyrite oxidation[END_REF]. The sulfate data are presented together with the caution that they are not all corrected for mass-dependent fractionation during partial fluorination yields, and that they are not universally normalized to the same accepted values for reference standards. As such, discrepancies may exist on the order of ~0.1 ‰ for ∆ 17 O. Error bars are shown for ∆ 17 O and are smaller than the symbols for δ 18 O. The Global Meteoric Water Line (GMWL)[START_REF] Sengupta | Triple oxygen isotopes of cherts through time[END_REF] represents the distillation (lighter δ 18 O) and evaporation (heavier δ 18 O) of meteoric waters as compared to their seawater source at the origin (represented by the isotope standard VSMOW at ∆ 17 O = δ 18 O = 0 ‰). The composition of modern O 2 is also shown[START_REF] Pack | Tracing the oxygen isotope composition of the upper Earth's atmosphere using cosmic spherules[END_REF]. Highly 17 O-anomalous sulfates, with isotopic arrays that extend in a more vertical orientation, are noted for the Paleoproterozoic, Mesoproterozoic, and Neoproterozoic. These anomalous arrays display the negative correlation between 17 O and 18 O that is predicted by the modeled curves for the variation in the triple oxygen isotope composition of O 2 as it tracks increasing pCO 2 and/or decreasing strength of biological O 2 fluxes. The model is

  , with the curves shown as the labeled dotted lines with tie lines to meteoric water compositions. The possible trajectory of Rayleigh fractionation of atmospheric O 2 during distillation by respiration is labeled. A potential oxygen-isotope mixing trajectory for Neoproterozoic post-Marinoan Snowball sulfates is shown with the large shaded arrow. If negative ∆ 17 O O2 and δ 18 O O2 signals were incorporated into sulfate during continental sulfide oxidation in the glacial aftermath, then the sulfate triple oxygen isotope data should show mixing between high-low ∆ 17 O-δ 18 O of continental meteoric waters and low-high ∆ 17 O-δ 18 O atmospheric O 2 . Such mixing would fall within the trajectory of the large shaded arrow in Fig. 4 like the few samples of Antarctic mirabilite near δ 18 O = -20 ‰ and ∆ 17 O = -0.5 ‰

Figure 5

 5 Figure 5 indicates O-isotope compositions that we expect for sulfates incorporating oxygen from modern seawater (δ 18 O = 0 and ∆ 17 O = 0) and modern O 2 (large pink X, at δ 18 O = 24.15 ‰, ∆ 17 O = -0.49 ‰ (Pack et al., 2017)), with O 2 * being the O 2 -oxygen end

Figure 5 .

 5 Figure 5. Compiled Phanerozoic and Proterozoic evaporite gypsum triple oxygen isotope data[START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF] are shown here alongside the GMWL[START_REF] Sengupta | Triple oxygen isotopes of cherts through time[END_REF], sulfate-water equilibrium curve[START_REF] Cao | Small Triple Oxygen Isotope Variations in Sulfate: Mechanisms and Applications[END_REF], and the composition of modern atmospheric O 2[START_REF] Pack | Tracing the oxygen isotope composition of the upper Earth's atmosphere using cosmic spherules[END_REF]. The shaded region is where sulfates formed from initial oxidation of sulfides in seawater or re-oxidation after microbial sulfate reduction may occur. Such sulfate would have oxygen sources from seawater (filled green square) and O 2 * (black multi-pointed star) with variable effects from the fractionation of residual sulfate caused by microbial sulfate reduction that pushes sulfate composition towards sulfate-seawater equilibrium (filled blue circle symbol). Biologically produced O 2 (yellow x symbol) and its respective O 2 * (yellow star) are discussed in the text.

Figure 6 .

 6 Figure 6. Results of Kazput barite triple oxygen isotope measurements (open circles) from this study are shown in ∆ 17 O-δ 18 O space. The Global Meteoric Water Line (GMWL) is a curve fit after Sengupta et al. (2020). In the O 2 system, the constraints used for biological O 2 production and respiration in our model are shown by the respective labeled curves, while the modeling of the stratospheric effect on O 2 that is attributed to pCO 2 concentrations is shown as the O 2 model. The O 2 * model denotes our estimation of the fractionated O 2 that is incorporated into sulfate, which is tied to the O 2 model. A linear regression of the mixing between Kazput barite oxygen isotope end members is shown along with ±1σ and ±2σ of the mean, with the intersection of the regression with the GMWL and the O 2 model curves allowing estimation of the respective water-and O 2oxygen end members for the Kazput sulfate oxygen sources. The compositions of sulfatewater equilibrium with respect to the Kazput sulfate water end member and seawater are shown as the large open and filled circle symbols, respectively. Evaporite (gypsum) data from 2.3 Ga from Crockford et al. (2019) are shown for comparison. Table 4 Triple oxygen isotope measurements of Kazput barite. The δ 18 O data are from J o u r n a l P r e -p r o o f

Figure 7 .

 7 Figure 7. ∆ 17 O-constrained model results of Paleoproterozoic gross primary production (GPP) from this study are shown in comparison with prior results from Crockford et al. (2019), all for ~2.3 Ga and shown as a function of pO 2 (x-axis) and different pCO 2 estimates (labeled curved fields). The Proterozoic pO 2 minimum is from Gregory et al. (2021), while the Proterozoic pO 2 maximum is taken from Kump (2008). Monte Carlo treatment of our inverted model constrains GPP results to within the percentiles labeled in the figure.

J

  o u r n a l P r e -p r o o f Journal Pre-proof The simplifications being made here, and in prior studies, leave room for further exploration of controls on O 2 sources and sinks. For example, equating GPP with biological O 2 flux does not account for other O 2 fluxes such as permitted by pyrite formation. Ferrous iron or sulfide sinks of O 2 are not examined here either, whose inclusion in triple oxygen isotope-constrained GPP estimates would require an even higher GPP. Accounting for such other O 2 sources and sinks requires additional model

  . The data are from field samples (crosses), sulfide oxidation experiments (open diamonds), sulfite oxidation experiments (open triangles), tetrathionate oxidation experiments (open squares), and elemental sulfur oxidation (filled circles). The solid lines represent the mass balance of reactions given by

2. METHODS: THE ORIGIN OF THE TRIPLE OXYGEN ISOTOPE TRACERS FROM ATMOSPHERIC O 2 AND H 2 O THAT ARE FOUND IN SULFATE Most

  with 1x O referring to the isotope18 O or 17 O. The Δ 17 O and Δ' 17 O data are reported with respect to VSMOW when possible. For consistency and ease of comparison, we most frequently use the notation Δ 17 O. Between two given substances, two-isotope fractionation, such as between16 O and 18 O, is commonly represented as α A-B ≡ R A /R B and ln(α A-B ) ≡ δ' xx O A -δ' xx O B , with R X representing the isotopic ratio, and δ' xx O X representing the isotopic delta of a sample A or B. However, given the contributions of multiple reservoirs of oxygen, each with specific fractionation factors between them (α),

	Journal Pre-proof
	2006; Figure 2 inset) indicates stratospheric ozone has the largest mass-independent 17 O
	enrichment (∆ 17 O 0.528 ≈ +37 ‰) while stratospheric CO 2 has a smaller 17 O enrichment
	(∆ 17 O 0.528 ≈ +5 ‰) ultimately derived from ozone. Meanwhile, tropospheric O 2
	measurements (∆ 17 O 0.528 = -0.49 ‰; Pack et al., 2017) indicate the 17 O-depleted balance
	is hosted by O 2 within the stratospheric network with relative reservoir sizes O 2 > CO 2 >
	O 3 .
	(Bao et al., 2016 and references therein) is
	Δ' 17 O ≡ δ' 17 O -C × δ' 18 O	(6),

. Our use of linear delta definitions helps characterize source-mixing because such mixing follows straight-line paths in multiple-isotope space. In contrast, under linear delta definitions, isotopic fractionation processes follow curved arrays. Model calculations use the logarithmic δ' 1x O and Δ' 17 O delta definitions where appropriate. The Δ' 17 O capital delta definition with δ' being a logarithmic definition of delta that is δ' 1x O = ln(δ 1x O + 1) = ln(R sample /R standard ) (7), J o u r n a l P r e -p r o o f we instead use ΔΔ 17 O A-B and Δδ 18 O A-B (Bao et al., 2016) to generically describe Δ 17 O or δ 18 O isotopic differences between two substances A and B. This convention also avoids the potential confusion when a single big delta is being used to describe isotopic differences (e.g., a two-isotope Δ 18 O A/B or Δ 17 O A/B , after Coplen, 2011) at the same time as the three-isotope capital delta (Δ 17 O) is in use to describe triple oxygen isotope deviations from a reference slope C. 2.terrestrial processes fractionate oxygen isotopes according to differences in isotopic masses. These mass-dependent processes are largely predictable, within ±0.3 ‰ (e.g., for equilibrium processes, Hayles et al., 2017), of the terrestrial fractionation line at ∆ 17 O ≈ δ 17 O -1/2 × δ 18 O (Thiemens, 2006; Figure 2 inset). In contrast, mass-independent signals in the terrestrial oxygen isotope system result from photochemical fractionations in the stratosphere that are characterized by the relationship δ 17 O ≈ δ 18 O (Thiemens and Heidenreich, 1983). A synthesis of isotope results from atmospheric species (Thiemens, J o u r n a l P r e -p r o o f

  ). The mass independently fractioned contribution from stratospheric reactions to the ∆ 17 O of O 2 is denoted with the arrow labeled MIF. Model 1 and its respective O 2 composition (O 2 1) are from[START_REF] Luz | 5.14 -The Stable Isotopic Composition of Atmospheric O2[END_REF], and model 2 and its respective O 2 (O 2 2) are from[START_REF] Young | On the Δ17O budget of atmospheric O2[END_REF].

	The net
	fractionating processes contributing to final composition of atmospheric O 2 are lettered in
	sequence: the composition of seawater (represented by the isotope standard VSMOW) is
	found at the origin, which is the starting source of oxygen for meteoric waters, with both
	water sources contributing to (a) the photosynthetic production of O 2 , followed by (b)
	effects of respiration on O 2 , and (c) the stratospheric photochemical effect on O 2 . The
	figure inset gives an expanded view of atmospheric oxygen-bearing species after the
	δ 17 O-δ 18 O figure 6 in Thiemens (2006) that is redrawn here in ∆ 17 O-δ 18 O. The
	abbreviations used for the figure inset labels are for tropospheric (trop.), stratospheric
	(strat.), atmospheric (atm.), and surficial (surf.).

Table 1 strateff

 1

	Parameter description	value	term unit or	reference
	str-trpCO2	average δ 18 O difference of stratospheric CO2 versus tropospheric CO2	8.0167	‰	Thiemens et al., 1995; Thiemens et al., 1991
	pCO2	partial pressure of CO2 by volume	375	ppm	Cao and Bao, 2013
	pO2	partial pressure of O2 by volume	209500	ppm	Cao and Bao, 2013
	τtrpO2	trop O2 residence time in years	1271	yr	calculated in strateffmod
	τtrp-strO2	trop O2 turnover time in stratosphere in years	50	yr	Andrews et al., 2001
		sign change for O2	-1		Bender et al., 1994

Next, we use the calculated strateff as constraint on the inverse module strateffmod, which will then match the triple oxygen isotope contributions to O 2 from the biosphere and stratosphere, today, and interface this constraint with the final model. Compared with the

[START_REF] Cao | Dynamic model constraints on oxygen-17 depletion in atmospheric O2 after a snowball Earth[END_REF]

model, the strateffmod now includes the biological flux of terrestrial photosynthetic O 2 , not only marine photosynthetic O 2 , and retunes the θ parameter, which is the fraction of steady state O 2 within the O 2 -CO 2 -O 3 reaction network versus total stratospheric O 2 . As before, the θ parameter is tuned so that the model returns the isotopic composition of modern atmospheric O 2 . However, now the biosphere's contribution to the 17 O depletion in tropospheric O 2 is separately accounted for. The strateffmod is calculated as follows, where δ 1x O refers to separate calculations for both δ 17 O and δ 18 O, with parameters described in Table

2:

Table 2 strateffmod

 2

	Parameter	description	value	term unit or	reference
	Fop	flux of ocean oxygen production	1.09 × 10 16	mol/yr	Blunier et al., 2002
	Flp	flux of land oxygen production	1.90 × 10 16	mol/yr	Blunier et al., 2002
	γ	ratio of stratospheric O2 flux involved in stratosphere-troposphere gas exchange / total O2	0.1321		Cao and Bao, 2013
	θ	ratio of steady state O2 within O2-CO2-O3 reaction network / stratospheric O2 (tuned)	0.00836		this study
	ρ		pCO2/pO2		Shaheen et al., 2007
	δ 18 OCO2-O2	steady-state δ 18 OCO2 normalized against δ 18 OO2, within the O2-CO2-O3 reaction network	(64 + 146 × ρ/1.23)/(1 + ρ/1.23)	‰	Shaheen et al., 2007; Cao and Bao, 2013
	δ 17 OCO2-O2	as above, but for δ 17 OCO2 versus δ 17 OO2	1.039 × δ 18 OCO2-O2 -7.1738	‰	Cao and Bao, 2013
	pCO2	partial pressure of CO2 by volume	375	ppm	Cao and Bao, 2013
	pO2	partial pressure of O2 by volume	209500	ppm	Cao and Bao, 2013
	O2trp	tropospheric O2 in moles	3.8 × 10 19	mol	Young et al., 2014
	τtrpO2	trop O2 residence time in years	O2trp / (Fop + Flp)	yr

J o u r n a l P r e -p r o o f

Table 2

 2 . Biological O 2 is combined from separate calculations of the Dole Effect coming from the marine and terrestrial biosphere, where their respective O 2 fluxes are F op (ocean production) and F lp (land production)[START_REF] Blunier | Biological oxygen productivity during the last 60,000 years from triple oxygen isotope measurements[END_REF], and the triple oxygen isotope calculations are done separately for their respective δ 17 O and δ 18 O values[START_REF] Luz | 5.14 -The Stable Isotopic Composition of Atmospheric O2[END_REF] using known constraints summarized in Table3. What emerges in our calculation is that the δ 17 O and δ 18 O of the present-day marine and terrestrial Dole Effect are within 0.3 ‰ of each other, a small range consistent with both prior work[START_REF] Luz | 5.14 -The Stable Isotopic Composition of Atmospheric O2[END_REF], and

	The next step after isolating the mass independent stratospheric effect is to characterize
	the triple oxygen isotope composition of biologically produced and respired O 2 in the
	bioO2mod model component, which accounts for the mass dependent effects on the triple
	oxygen isotope composition of O 2 . Biologically affected O 2 is already constrained by the
	isotopic composition of modern atmospheric O 2 minus that of the stratospheric effect;

). The immediate implication is that, here, the contribution of stratospheric photochemistry to the negative ∆ 17 O of tropospheric O 2 is half of what it was in the Cao and Bao model, at least for the initial tuning to modern conditions. The important feature of the strateffmod for the final model is that it responds to variations in atmospheric pO 2 and pCO 2 , after

[START_REF] Cao | Dynamic model constraints on oxygen-17 depletion in atmospheric O2 after a snowball Earth[END_REF]

and as based on the experimental results of

[START_REF] Shaheen | Investigations of the photochemical isotope equilibrium between O2, CO2 and O3[END_REF]

. therefore, the bioO2mod component is not used in the simplified version of the final J o u r n a l P r e -p r o o f modelthe relatively restricted long-term variations of the DE in ice core records

[START_REF] Yan | Two-million-year-old snapshots of atmospheric gases from Antarctic ice[END_REF]

. Another important aspect is that the large uncertainty for the global average oxygen isotope composition of global leaf water, for example δ 18 O = 6.5 ±2.1 ‰

[START_REF] West | A Simplified GIS Approach to Modeling Global Leaf Water Isoscapes[END_REF]

, makes it necessary to adjust the δ 17 O and δ 18 O of leaf water in our model, similarly as

[START_REF] Young | On the Δ17O budget of atmospheric O2[END_REF]

, to match the biological O 2 to its final composition that is constrained by the strateff. Accordingly, our leaf water is δ 18 O lw = 7.69 ‰ and δ 17 O lw = 4.03 ‰. Because respiration effects are the most significant biological controls on the isotope composition of biological O 2 , more refined triple oxygen isotope slopes (e.g.

[START_REF] Ash | What Fractionates Oxygen Isotopes during Respiration? Insights from Multiple Isotopologue Measurements and Theory[END_REF]

will be needed to examine smaller ∆ 17 O-δ 18 O variations of O 2 such as found in ice cores. The summed marine and terrestrial biological O

  Our final simplified model, tropO2, gives the full triple oxygen isotope composition of tropospheric O 2 , separately for δ 17 O tropO2 and δ 18 O tropO2 from which ∆ 17 O can be calculated, as a function of the fluxes of photosynthetic O 2 from the land and ocean biospheres, and the partial pressures of O 2 and CO 2 , as integrated in the previously described modules:

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	δ 18 OO2moder n		24.15	‰	Pack et al., 2017
	Table 3
	bioO2m
	od
				uni
	Parameter	description	value	t or ter	reference
				m
	xm	fraction of marine production	Fop/(Fop + Flp)
	xt	fraction of terrestrial production	Flp/(Fop + Flp)
	δ 17 Ompo	δ 17 O of marine photosynthetic oxygen	(e^(δ' 17 Ompo/1000)-1) × 1000	‰
	δ 18 Ompo	δ 18 O of marine photosynthetic oxygen	5.00	‰	Luz et al., 2014
	δ' 17 Ompo		0.521 × δ' 18 Ompo	‰	Luz et al., 2014 for beta = 0.521
	δ' 18 Ompo δ 17 Omresp δ 18 Omresp δ' 17 Omresp δ' 18 Omresp δ 17 OmDE δ 18 OmDE δ' 17 OmDE δ' 18 OmDE δ 17 Olw δ 18 Olw δ' 17 Olw δ' 18 Olw δ 17 Oeqdo δ 18 Oeqdo δ' 17 Oeqdo	ln(δ 18 Ompo/1000 + 1) × 1000 (e^(δ' 17 Omresp/1000) -1) × 1000 24.3 -δ 18 Ompo 0.516 × δ' 18 Oresp ln(δ 18 Omresp/1000 + 1) × 1000 δ 17 Ompo + δ 17 Omresp δ 18 Ompo + δ 18 Omresp ln(δ 17 OmDE/1000 + 1) × 1000 ln(δ 18 OmDE/1000 + 1) × 1000 4.0280 7.6878 ln(δ 17 Olw/1000+1) × 1000 ln(δ 18 Olw/1000+1) × 1000 (e^(δ' 17 Oeqdo/1000)-1) × 1000 0.75 0.5284 × δ' 18 Oeqdo J o u r n a l P r e -p r o o f ‰ δ 17 O of marine respiration ‰ δ 18 O of marine respiration ‰ ‰ ‰ δ 17 O of marine Dole Effect ‰ δ 18 O of marine Dole Effect ‰ ‰ ‰ leaf water δ 17 O tuned so that δ 17 OO2modern -δ 17 Ostrateffmod = δ 17 ObioO2 ‰ leaf water δ 18 O tuned so that δ 18 OO2modern -δ 18 Ostrateffmod = δ 18 ObioO2 ‰ ‰ ‰ δ 17 O of equilibrium isotope fractionation of dissolved O2 with respect to atmospheric O2 ‰ δ 18 O of equilibrium isotope fractionation of dissolved O2 with respect to atmospheric O2 ‰ ‰	calculated from Luz et al., 2014 Luz et al., 2014 beta 0.516 this study this study Luz et al., 2014 Blunier et al., 2002 for beta = 0.5284
	δ' 18 Oeqdo		ln(δ 18 Oeqdo/1000+1) × 1000	‰
	δ 17 Otresp	δ 17 O of terrestrial respiration	(e^(δ' 17 Otresp/1000)-1) × 1000	‰
	δ 18 Otresp	δ 18 O of terrestrial respiration	17.7	‰	Landais et al., 2007
	δ' 17 Otresp		0.514 × δ' 18 Otresp	‰	Luz et al., 2014 for beta = 0.514
	δ' 18 Otresp		ln(δ 18 Otresp/1000+1) × 1000	‰
	δ 17 OtDE	δ 17 O of the terrestrial DE	δ 17 Olw+δ 17 Otresp-δ 17 Oeqdo	‰	calculation after Luz et al., 2014
	δ 18 OtDE	δ 18 O of the terrestrial DE	δ 18 Olw+δ 18 Otresp-δ 18 Oeqdo	‰	calculation after Luz et al., 2014
	δ' 17 OtDE		ln(δ 17 OtDE/1000+1) × 1000	‰
	δ 17 OO2moder n		12.26	‰	Pack et al., 2017

  [START_REF] Killingsworth | Constraining the rise of oxygen with oxygen isotopes[END_REF], ∆ 17 O data are from this study.

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	CAS 36	-7.0	-0.24
	Sample name CAS 38	δ 18 O VSMOW (‰) -8.8	∆ 17 O VSMOW,0.528 (‰) -0.29
	CAS 39	-13.7	-0.25
		(Killingsworth et al.,	(this study)
	CAS 40	2019) -3.3	-0.23
	CAS 1	-6.0	-0.25
	CAS 41	-2.1	-0.26
	CAS 3	-15.0	-0.20
	Analytical uncertainty based on replicates of the NBS-127	±0.4‰ (2σ)	±0.04‰ (2σ)
	CAS 4 BaSO 4 standard	-2.7	-0.20
	CAS 5	-9.4	-0.19
	CAS 6	-12.7	-0.22
	CAS 8 CAS 9 CAS 10 CAS 11 CAS 13 CAS 14 CAS 15 CAS 16 CAS 18 CAS 19 CAS 20 CAS 21 CAS 23 CAS 24 J o u r n a l P r e -p r o o f -12.7 -16.8 -13.8 -16.1 -18.0 -11.8 -15.2 -9.2 -8.9 -19.5 -3.9 -12.0 2.2 -14.9	-0.19 -0.14 -0.21 -0.24 -0.19 -0.19 -0.19 -0.23 -0.26 -0.18 -0.20 -0.23 -0.25 -0.21
	CAS 26	-10.8	-0.24
	CAS 28	-19.1	-0.17
	CAS 29	-13.5	-0.24
	CAS 30	-15.9	-0.14
	CAS 31	-11.0	-0.19
	CAS 33	-10.6	-0.25
	CAS 34	-10.3	-0.23
	CAS 35	-2.9	-0.30

  , and 2) since 2.4 Ga, ∆ 17 O of sulfate indicates a stable ozone layer[START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF]. Therefore, we suggest that the indication of positive ∆ 33 S and negative ∆ 17 O anomalies from Kazput barite at ~2.3 Ga are most readily explained by sedimentary recycling of ∆ 33 S anomalies under an oxygenated atmosphere of at least 10 -2 PAL O 2 , which is consistent with the evidence for irreversible oxygenation by ca. 2.4 Ga (e.g.,[START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF][START_REF] Warke | The Great Oxidation Event preceded a Paleoproterozoic "snowball Earth[END_REF], and waning signals of recycled sulfur anomalies until a maximum of ca. 2.2 Ga[START_REF] Reinhard | Long-term sedimentary recycling of rare sulphur isotope anomalies[END_REF][START_REF] Philippot | Globally asynchronous sulphur isotope signals require redefinition of the Great Oxidation Event[END_REF].As pO 2 , pCO 2 , and GPP are all effective 'levers' on ∆ 17 O O2 variation, additional constraints are needed to return unique inverse model solutions from a given ∆ 17 O O2 value. As has been done before, for example by[START_REF] Crockford | Claypool continued: Extending the isotopic record of sedimentary sulfate[END_REF], we assume that the flux of bioO2 is proportional to GPP. The model is then inverted to solve for GPP from a given O-isotope composition by applying our sulfate isotope constraints on O 2 from Kazput barite, then resampling the model with a Monte Carlo treatment to constrain ranges of GPP. The Kazput barite-constrained ∆ 17 O O2 used in the model is -0.43 +0.03

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ACKNOWLEDGEMENTS

The use of trade or product names does not imply endorsement by the U.S. Government.

J o u r n a l P r e -p r o o f

FUNDING

This research was supported in part by funding from Fundação Amparo à Pesquisa do Estado de São Paulo (FAPESP grant 2015/16235-2 to P.P.) and the European Union's Horizon 2020 research and innovation program (Marie Sklodowska-Curie grant 708117 to B.K.).

lower 1σ of the data regression curve (see also Fig. S3). Under those conditions, if respiration were 2/3 of modern the minimum GPP would be 4.2 times present levels.

Though unrealistic, we test the sensitivity to respiration efficiency by dropping respiration to zero, making the starting biological O 2 purely photosynthetic, before it is affected by mixing with stratospheric O 2 . With no respiration, our constraints require a minimum GPP of 2.8 times present levels. Surprisingly, both cases affirm the requirement of higher GPP than modern for the early Paleoproterozoic, with slightly lower GPP than the minimum of 6 times present levels estimated in our prior simplified model runs.

CONCLUSION

Here, we provide a new framework in which to evaluate triple oxygen isotope records of sulfate. We show that triple oxygen isotope compositions of sulfate should be evaluated without pre-assigning the O 2 /H 2 O oxygen source ratio of sulfate, and that sulfate may contain a range of oxygen sources spanning 100 % H 2 O-oxygen to 100 % O 2 * -oxygen (fractionated O 2 -oxygen). Given additional constraints, distinguishing between the stratosphere and biosphere effects on ∆ 17 O O2 and δ 18 O O2 , and an accounting of the ancient Dole Effect via sulfate records, may now be more fully realized in the framework provided here. As an example, using sulfate ∆ 17 O and δ 18 O constraints, we estimate early Paleoproterozoic gross primary productivity to be 6 to 160 modern levels, with a bare minimum threshold of 3 times modern levels. Such estimates of high productivity may reflect life's efficient expansion in an oxygenated world or that significant sources of O 2 remain to be accounted for. The authors declare no competing interests.

On behalf of the authors,

Bryan Killingsworth USGS

J o u r n a l P r e -p r o o f