Cohler and Soon audit finds that the isotope argument does not establish fossil attribution bounds

Jonathan Cohler and Willie Soon argue that carbon-isotope measurements mathematically falsify a fossil-dominant explanation of rising atmospheric carbon dioxide. Our audit reproduces important numerical observations behind their argument, including the modern isotope intercept near −13.2‰. It finds that the claimed general attribution bounds do not follow from those observations and carbon conservation alone. The proof requires additional assumptions about sources, sinks and exchange that the paper does not establish. This assessment concerns the paper’s inference; it does not provide a new empirical estimate of the fossil contribution. Audited paper, DOI 10.53234/scc202612/05.

What the isotope observation shows

Carbon has two stable isotopes, carbon-12 and carbon-13. Their relative abundance carries information about sources and exchanges. A Keeling plot compares the isotope composition of atmospheric CO₂ with the reciprocal of its concentration. Under specified mixing conditions, the fitted intercept identifies the isotope composition of the added carbon.

The audit paired public Scripps concentration and isotope records at Point Barrow, La Jolla, Mauna Loa and South Pole. Seasonally adjusted annual regressions, using available observations within 1978–2022, produced intercepts of approximately −13.25, −13.34, −13.28 and −13.02‰. Monthly analyses using the publisher’s filled, adjusted series also closely recovered the cited station results. These are current-vintage reconstructions, rather than an exact replay of the earlier download and code. Scripps atmospheric data.

The basic mixing arithmetic is also sound when its conditions hold. At an effective signature of −13.2‰, a fossil signature of −28‰ and a natural signature of −8‰, a positive two-component mixture gives a fossil weight of 26%. Choosing zero for the natural signature gives approximately 47.1%. Exact isotope-ratio calculations change these central values only slightly. Small approximation errors are not the principal problem.

Why a net flux needs more than mixing arithmetic

The authors explicitly account for sinks in their definition of the net addition. The relevant question is whether the resulting quantity can be represented as two positive contributions with fixed isotope signatures.

A net flux is the difference between incoming and outgoing carbon. Its isotope composition is also calculated from differences. Such a residual need not lie between the signatures of the physical reservoirs involved. Exchange can change atmospheric isotope composition even when the net amount of carbon supplied by that exchange is zero.

The audit constructed an exact, synthetic example addressing the authors’ definition of net fossil-origin growth. Fossil input is 10 amount units and fossil output is 5. Natural-origin input and output are both 95. Total atmospheric growth is therefore 5, all of it growth in the fossil-origin stock. With ordinary positive isotope abundances and the same removal rate for all atmospheric carbon, the effective net signature can nevertheless be −13.2‰. Natural exchange changes the isotope balance while adding no net carbon.

This is a logical counterexample, not a reconstruction of Earth’s carbon budget. It demonstrates that conservation alone cannot supply the paper’s proposed universal bound. Determining the actual contribution requires further constraints on exchange, reservoirs and the precise meaning of attribution.

The five-century evidence has a different provenance

The paper describes a separate Caribbean sponge record as independent atmospheric corroboration extending over roughly five centuries. The cited analysis by Koutsoyiannis instead digitizes atmospheric concentration and isotope curves shown alongside sponge measurements in Böhm and colleagues’ Figure 4. Those atmospheric curves draw on ice, firn and air records; the isotope curve was scaled to fit the shallow-water sponge record for comparison. They are therefore not unaltered atmospheric samples or a separate atmospheric reconstruction from sponge measurements. The sponge measurements themselves concern marine carbonate. Koutsoyiannis 2024, §2, Böhm and colleagues 2002.

The reported agreement of aggregate intercepts remains a numerical result worth examining. It does not establish a separate sponge-derived atmospheric measurement or prove that the effective signature was constant in every subperiod. In a separate proxy-model calculation, Koutsoyiannis fixes −13.2‰ to the modern-site average; that calculation is not another independent estimate. The exact digitized atmospheric series was not located, so the audit does not claim to have reproduced that regression or resolved how the scaling was handled.

The Law Dome citation is numerically accurate: Köhler and colleagues report an intercept of −13.1‰ and an R² of 0.96. Their paper also explains why long-term exchange with other reservoirs can make a Keeling intercept differ from the original emission signature. Agreement with their number does not settle the attribution interpretation. Köhler and colleagues 2006, Figure 1 and discussion.

Even a perfectly constant effective intercept would not, by itself, fix the natural residual signature. Within the paper’s own approximate mixture equation, a fossil weight rising from zero to 26% can retain an intercept of −13.2‰ if the natural signature moves from −13.2 to −8‰. An independent constraint is needed to exclude that possibility.

Several later numerical checks reproduce

The audit also examined the paper’s criticism of a model by van Wijngaarden and Happer. Using public emissions and atmospheric data with explicitly recorded integration choices, the reconstruction recovered several reported CO₂ diagnostics:

These results support examining variability beyond a shared long-term trend. A high correlation alone does not establish causation, and a model can reproduce a broad rise while missing year-to-year changes. Poor residual performance of that model, however, does not logically establish a negligible human contribution to the long-term increase.

The reported isotope residual correlation of −0.45 was not recovered. The audit’s documented firn-and-Bermuda annual reconstruction gave about −0.075, with results changing under different sampling choices. The paper’s exact replication package was not located in the checked public locations. That discrepancy remains unresolved; it is not evidence of fabrication or proof that no such package exists. The audit also disclosed a missing isotope factor in the competing model’s printed discrete formula and used its governing equation instead. Neither model’s causal adequacy is certified here. Van Wijngaarden and Happer 2026.

Residence time does not determine the whole response

The paper’s short-lifetime calculation can also be reproduced approximately under its assumptions: historical emissions plus an explicitly assumed 2025 input give about 39 gigatonnes of carbon for a 3.8-year one-way lifetime and 148 gigatonnes for 17.2 years. These are conditional model calculations, not measured fossil-origin inventories. Global Carbon Budget 2025 data.

The one-way calculation omits carbon returning from other reservoirs. A molecule can leave the atmosphere and later return without losing its origin. Moreover, the fraction of atmospheric atoms originally emitted from fossil fuel is different from the atmospheric increase caused by fossil emissions.

An exchanging reservoir system can have a short first-exit residence time and a much longer response to a perturbation, even when transport treats all origins identically. The audit demonstrates this with explicit two-reservoir equations. This defeats a general claim that identical molecules require one system response time; it does not validate any particular competing model’s parameters.

Audit conclusion and limits

The observed intercept, several model-comparison diagnostics and the conditional mixture arithmetic survive scrutiny. The general fossil bounds and near-zero human-contribution conclusion do not follow without additional assumptions about signed residuals, time variation and reservoir exchange.

The audit preserves its analytical derivations, executable scripts, downloaded source data, individual reviews and reconciliation. Its uncertainty calculations do not fully propagate calibration, chronology, correlated observations or model-identification error. Some historical full-text methods and exact author inputs remain unavailable. The result is a scoped scientific assessment of this paper, not a complete independent attribution study or formal proof certification.

The mathematical and carbon-source first reviews were separate AI assessments under the same provider. A separate AI challenge reviewer from the same provider examined the reconciled report and article with inherited context and access to the earlier work; this was not a blind review. Its source and wording corrections were applied and checked. Prior exposure and the targeted post-review source addendum are documented. This is not external human peer review or author endorsement. Richard Janutka of Qonduit Limited, New Zealand, commissioned the audit. Haivian’s audit service and the Haivian Validation Journal share organizational control.

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