CARBON-CYCLE AND SOURCE REVIEW — FIRST INDEPENDENT REPORT
Frozen Cohler & Soon (2026), DOI 10.53234/scc202612/05, pp81–99
Prepared 6 November 2026, Pacific/Auckland
Reviewer: carbon_source_review, same-provider AI delegated scientific reviewer

INDEPENDENCE AND SCOPE
I read COMMISSION.txt and the full frozen paper, including the later defenses in §9 (pp88–96), before reading any other reviewer findings. I have not read the mathematical-review report or the manager's empirical results. Audit editor messages concerned source acquisition, filenames and reproduction plans; my outbound checkpoints disclosed source findings. I am an OpenAI AI reviewer under the inherited configuration, not an external human or different-provider reviewer. Prior general training exposure to carbon-cycle arguments is possible and cannot be exhaustively inventoried. Incidental search results included third-party criticism and social posts; these were not used as scientific evidence. This is a source-first review, not a complete remeasurement of climate attribution.

The journal PDF hash is 7df483cdab73904ba5839f53eef5589cb84a7ce4c9e5e9e01667440d8a6d6822. The current author-hosted PDF was separately downloaded and has the identical hash. No separate Appendix exists in those 19 pages. I also read the cited Koutsoyiannis Appendix A. Scoped journal/author searches did not locate a separate later reply or the promised analysis.py package. Absence from these searches is not proof that no package exists.

DISPOSITION
The reported near −13 per mil effective intercept deserves empirical reproduction. The cited literature does not establish that this intercept supplies the claimed model-independent fossil fraction, five-century invariant natural endmember, or negligible anthropogenic forcing. Major premises are unsupported, and one central source chain is described incorrectly. This conclusion concerns the paper's proof; it does not itself measure the actual anthropogenic fraction or establish an alternative climate model.

STRONGEST DEFENSIBLE READING
The authors expressly define a net addition after sinks; they are not simply unaware that sinks exist. They distinguish gross input, atmospheric stock, and net-growth fractions in §9.3. A constant effective isotopic ratio of net addition can produce a Keeling line, and the arithmetic 0.26 and 0.471 follows from their stated positive two-component mixture and chosen endmembers. Their criticism that a fit to shared secular trends alone does not prove causality is valid in that limited form. Neither measurement precision nor an attractive regression settles the inverse attribution problem.

The scientific issue is whether the effective signed residual can be represented by those two positive components with independently known signatures and stable weights. Saying that sinks have already been included does not prove that representation.

FINDING CS1 — MAJOR: PROXY IDENTITY AND CLAIMED INDEPENDENCE
Target: §4.2–4.3, pp84–85; abstract; five-century premise of §7.
The atmospheric series used by Koutsoyiannis is not an independent atmospheric reconstruction obtained from sponge DIC. See source ledger K24 and B02. It is therefore incorrect to count the cited analysis as a separate sponge-based laboratory chain independently corroborating Law Dome. Both analyses draw on atmospheric ice/firn records; exact record overlap needs sample-level documentation, but independence is already unestablished.

This does not invalidate the sponge measurements. Those measurements can independently constrain marine carbon-cycle history. They do not by themselves supply atmospheric CO2 concentrations or a fixed atmosphere–marine transfer calibration. Replacing the atmospheric series with sponge δ13C and retaining an atmospheric C series would create a new analysis requiring chronology, scaling and exchange assumptions, not reproduce the stated source.

FINDING CS2 — MAJOR: FIVE-CENTURY CONSTANCY IS STRONGER THAN THE SOURCE RESULT
Target: §4.2 and §7; collapse from finite upper bound to f approximately zero.
K24's aggregate agreement is real as a reported numerical result, but its proxy modeling and subperiod analysis do not establish a time-invariant natural residual independent of fossil emissions. Failure to reject a trend is not an equivalence test with a physically meaningful small bound. A record spanning five centuries can be dominated by a short recent interval's concentration range. Different dates, sparse early sampling, digitization, smoothing and age uncertainty change its inferential precision.

Even exact constancy of an effective intercept does not establish constancy of every source, sink or their weighted residual. To infer f approximately zero, the natural contribution must be fixed independently of the observed total. Setting it equal to a preindustrial effective intercept and carrying it unchanged into the modern period is an additional carbon-cycle hypothesis. Preindustrial fossil emissions being negligible does not eliminate preindustrial sinks, disequilibrium or changing land/ocean exchange.

FINDING CS3 — CRITICAL TO THE CLAIMED PROOF: RESERVOIR LIMITS DO NOT BOUND A SIGNED NET RESIDUAL
Target: §5–7, Eqs7–12, pp85–87.
For inputs Ij and outputs Ok, the effective net isotope signature in the paper's first-order delta convention is
  delta_net = (sum Ij*delta_j - sum Ok*delta_k)/(sum Ij - sum Ok).
A positive reservoir-mixture bound holds for nonnegative normalized weights. This signed expression lacks that property. Its denominator can be small even when every individual flux is ordinary. The effective signature can lie beyond every physical reservoir signature; this does not require a reservoir with that signature.

Analytical illustration only, not empirical reconstruction: natural input 100 units at −8 per mil and removal 90 at −10 leave net input 10 with effective signature +10 per mil. All gross fluxes are positive. The residual's +10 is not a claimed natural reservoir. Exact isotope-abundance algebra can replace delta linearization without restoring convexity; the mathematical reviewer owns exact quantitative checks.

Alternatively, emission E>0 and combined environmental net uptake N<0 yield E/(E+N)>1 when atmospheric growth is positive. A causal fossil contribution to growth need not be a convex fraction bounded by one. It is possible to define a retained-origin stock fraction in [0,1], but its accompanying flux signature and dynamics must then be derived, not assigned the original fuel value by fiat.

K24 Appendix A explicitly includes a negative weight in its rise/fall-cycle net signature. Thus this objection addresses the paper's defended net interpretation, not a gross-input substitute. The −8 upper limit from ocean outgassing is not a global theorem about the non-fossil net residual. The 0 per mil sensitivity does not repair the missing bound. The paper's claim that signatures above +1.6 are impossible on Earth is also overbroad even on its own terms: it discusses positive marine DIC; sponge aragonite is more positive still. Neither is necessarily an atmospheric source flux.

FINDING CS4 — MAJOR: EFFECTIVE INTERCEPT IS NOT THE ORIGINAL EMISSION END MEMBER
Target: §4.3, §5, §9.1.
K06 confirms the Law Dome numerical result but explicitly treats ocean/land exchange as a reason the long-term intercept differs from emitted carbon. Its relevance cannot be reduced to a number while omitting the physical conditions that number describes. An effective intercept is a useful observational constraint, but source identification requires assumptions about exchanges, fractionation and evolving reservoir states.

The approximate −28 fuel signature is not itself the principal problem. Even accepting it exactly leaves the inverse problem underdetermined. Conversely, isotope fractionation is real and process-specific, not an arbitrary fitting correction. This review does not claim an unconstrained fractionation knob can fit anything.

FINDING CS5 — MAJOR: IDENTICAL MOLECULES DO NOT IMPLY ONE GLOBAL RESPONSE TIME
Target: §9.2–9.3, pp89–95.
The strongest author argument is that fossil and natural CO2 share physical transfer laws. That premise is compatible with multiple reservoirs and return fluxes. Consider an illustrative linear two-reservoir perturbation system:
  dA/dt = -k*A + r*O + E; dO/dt = k*A - (r+s)*O.
The same transfer law applies to every carbon label. Atmospheric A nevertheless generally contains two decay modes. A first-exit survival probability exp(-k*t) does not include returns; the atmospheric perturbation response does. Adding isotope-specific fractionation yields an additional set of coupled equations, not a requirement that total carbon and isotope anomalies have identical apparent relaxation times.

Consequently the one-box Nf equation in §9.3 is not a general provenance accounting law if fossil-origin carbon can return from other reservoirs. Its calculated 4.3% or 16.2% stock fraction is conditional on that truncation and chosen lifetime. A small surviving atmospheric provenance fraction would in any case not imply a small causal change in the atmospheric stock. The author explicitly distinguishes fractions numerically, but the final causal/forcing inference still needs a counterfactual system calculation. J13 defines its impulse response as an emission perturbation, not the probability that a tagged atom has never exited the atmosphere.

A static Revelle factor alone indeed does not specify a rate, as the authors say. Carbon chemistry coupled to exchange and storage can alter response modes without introducing different molecular treatment by provenance. The audit need not validate every Bern parameter to reject the claimed impossibility theorem.

FINDING CS6 — MODERATE: UNCERTAINTY AND TARGET CLAIM NEED CORRECTION
Target: §4.1, §§9.3–9.5 and opening agency attribution.
The paper initially identifies ±0.2 as inter-site variation/residual scatter, then uses it as measurement precision when multiplying predicted isotope discrepancies. These are different quantities. A pooled estimate, time dependence, calibration errors, smoothing dependence and correlated residuals need separate treatment. K24's table is not a formal ±0.2 confidence interval on every period's source signature.

The agencies' actual proposition is human-caused increase, primarily fossil combustion with land-use and industrial contributions, together with environmental uptake. It is not generally that every increment is a surviving fossil-origin molecule or that the effective net-growth isotope signature must equal fuel. NOAA's educational isotope page does use simplified fossil-cause wording; this is a legitimate target for clarification. It does not establish the much stronger literal proposition attributed to all agencies. I do not use their authority as proof: the ledger documents what claim is being tested. Full independent verification of their oxygen, radiocarbon, inventory and ocean-storage evidence exceeds this single-paper source review.

EMPIRICAL AND REPRODUCIBILITY STATUS
The manager owns actual Scripps regressions, uncertainty analysis and execution; no independent empirical fit is claimed here. Current data need end-date truncation and revised-vintage labeling. Exact early atmospheric digitized coordinates used by K24 were not located. Original sponge data are preserved, with parsing advice in DATA-NOTES.txt. They must not be substituted for those coordinates.

The frozen paper's §9 later defenses were reviewed, including its detrending, isotope/time-constant and residence-time arguments. The promised executable package was not found on the journal landing page, linked-datasets page or current author page. Thus the reported Wang–Huang reproduction/detrending numbers remain unverified here. Trend removal may reveal inadequate variability prediction, but failure to fit detrended fluctuations alone cannot prove zero causal secular contribution.

G25's 2025 values are described as projections/preliminary estimates, not final annual observations. Its October 2026 corrigendum concerns Table6 ocean-interior estimates, not the other results. Preserve the version when using annual fossil totals and distinguish fossil/industry from total anthropogenic emissions. A fixed −28 for a changing fossil mix and cement contribution requires its own sensitivity analysis.

LIMITATIONS AND REQUIRED PUBLIC WORDING
Full Keeling1958, Mook1986, Zhang1995 and Ciais1995 methods were not obtained; abstracts/metadata and separately identified accessible primary sources were used only within their access limits. Do not describe this as an exhaustive literature review or exact reproduction of inaccessible author code. Do not call the sponge record fabricated, the intercept nonexistent, the whole paper circular, or the agency attribution proved merely by citation.

Defensible wording: the empirical intercept may be reproducible, but the claimed general fossil bound and negligible-human conclusion require unproved constraints on signed residual fluxes and response dynamics; the asserted independent five-century sponge evidence is not the data chain used in the cited analysis. The mathematical report and executed empirical checks must be reconciled before final publication disposition.

