COHLER–SOON / DOI 10.53234/scc202612/05
SEPARATE CRITICAL CHALLENGE OF THE RECONCILED AUDIT
6 November 2026, Pacific/Auckland
Reviewer: independent_challenge, delegated AI reviewer

DISPOSITION

The draft's central conclusion is defensible: the paper does not establish its
general mathematical falsification of fossil dominance. The positive-mixture
arithmetic and several observed correlations should remain explicitly credited.
No critical mathematical or computational error was found in the audit's central
reasoning during this challenge. Resolve CH1–CH3 below before freezing the packet.
CH1 is a substantive source-provenance qualification; CH2–CH3 are precision edits.
No new first-pass review, complete rerun or framework is needed to resolve them.

I do not certify the actual atmospheric attribution fraction, a competing carbon
model, all original inputs, or comprehensive statistical confidence coverage.
The unresolved author inputs must remain visible in the final disposition.

EXPOSURE AND INDEPENDENCE

This was a separate critical assessment of an existing draft, not a blind review.
I inherited the manager's history, source summaries, prior reviews and interim
results before checking them. I am an AI under the same provider/configuration;
this is not external human or different-provider corroboration. My task was to
challenge the audit rather than duplicate either original source-first review.
The first reviewers' independence statements describe their own earlier work and
are not statements of my independence. No authors or third parties were contacted.

MATERIAL EXAMINED

COMMISSION.txt, CLAIM-MAP.txt; TECHNICAL-REPORT.txt draft; publication/ARTICLE.md;
the frozen mathematical and carbon/source reports and mathematical addendum;
REPRODUCIBILITY.txt and CLAIM-EVIDENCE-LEDGER.json; relevant retained primary
source text from the Cohler–Soon target, Koutsoyiannis2024 and Köhler2006; the
math-check, Scripps, extended-reconstruction and final-check scripts/results.

Source examination concentrated on the target's original balance, definition of
f, net-growth discussion and later defenses (pp82–87,93–96); Koutsoyiannis §2,
§5.3 and Table4; and the distinction between source agreement and source
identification. I relied on the disclosed targeted mathematical addendum for the
visual check of the W-H printed Eq74 omission; I did not perform a new whole-paper
review of W-H. Full historical methods access limits remain those in the ledger.

I inspected code and saved numerical results, and independently executed a
bounded set of checks described below. This is not a second full empirical replay.

ACTIONABLE CHALLENGES

CH1 — MODERATE: Include the atmospheric-curve scaling step in the proxy provenance.
Locations: technical report §6, public article “The five-century evidence has a
different provenance”, claim-ledger C03 where appropriate.

The audit correctly says that Koutsoyiannis digitized atmospheric curves from
Böhm Figure4 rather than independently measuring an atmospheric endmember from
sponge DIC. However Koutsoyiannis §2 also explicitly describes scaling the
atmospheric isotope curve using its preindustrial mean and minimum to fit the
shallow-water sponge record. The draft omits that intermediate operation.
An atmospheric origin is not proof that digitized plotted values are untouched
raw atmospheric observations. Exact handling/reversal of scaling is unresolved
without the original coordinates and procedures.

Required remedy: state the reported scaling/digitization step and that its exact
handling is unresolved. Keep the justified narrower conclusion: this is not an
independent sponge-derived atmospheric laboratory chain. Do not assert that the
scaling necessarily invalidates the regression or was necessarily left uncorrected.
The source-review ledger already notes scaling for display; reconcile the main
report and article with that evidence. Retaining the author-hosted-v4/version
limitation is also appropriate.

Suggested public sentence: “The cited account also describes scaling the plotted
atmospheric isotope curve to the sponge record; without the exact digitized
series, the audit could not determine how that scaling was handled.”

CH2 — MINOR: Historical GCB series are estimates, not direct observations.
Location: technical report §7, “historical annual observations end2024”.
Required remedy: use “historical annual estimates end2024”. The calculations
correctly use the verified workbook and separately label assumed2025 forcing.
No computation changes follow from this wording correction.

CH3 — MINOR: Keep author-package availability wording bounded to the search.
Location: CLAIM-EVIDENCE-LEDGER.json C08 limitation, “Author package absent”.
Required remedy: use “author package not located in checked public locations”.
The report and article already make the appropriate distinction between not
retrieved and nonexistent. Align the ledger so a condensed handoff does not
overstate what the search establishes.

These corrections do not reverse the central verdict. The draft's temporary
“provisional”/“challenge pending” status must of course be updated only after
resolution, with this report retained and an item-by-item resolution recorded.

CENTRAL MATHEMATICAL CHALLENGE

I re-derived the abundance balance independently:
N*q'=H-q*G, q=r/(1+r), delta=1000(r/s-1).
It gives N*delta'=G*(1+r)/(1+r_I)*(delta_I-delta). The draft's exact expression
and constant-q_I integration are correct. Tiny isotope-ratio corrections do not
create or remove the decisive non-identification problem.

I challenged whether the snapshot origin-tag example merely changes a gross
emission/growth ratio or depends on an accidental numerical cancellation. It
does neither. Exact Fraction arithmetic gives zero residual for the isotope13
balance. Fossil NET stock growth equals total growth even with identical
nonfractionating removal for both provenance tags. Natural net carbon is zero
but natural isotope exchange is nonzero. The example addresses the authors'
stronger §9.3 definition rather than ignoring their stock/flux distinction.

I also challenged whether a local snapshot suffices for the paper's fit-window
claim. A finite-duration analytical extension exists. In amount units, set
N(t)=1000+5t, Nf(t)=50+5t, Nn=950, qf=q(-28), qi=q(-13.2), qa0=q(-8.5).
Set qn0=[qa0-.05*qf]/.95 and
  qn(t)=qn0+(5t/950)*(qi-qf).
With total output100 and common per-atom removal100/N(t), choose
  Of=100*Nf/N; On=100*Nn/N;
  Ef=5+Of; In=On;
  qn_input=qn(t)+5*(qi-qf)/In.
Then Nf'=5, Nn'=0, H=5*qi identically, and
  N(t)*qa(t)=1000*qa0+5t*qi.
Thus f=1 throughout and the exact constant-net-signature trajectory holds over
the whole interval. On 0<=t<=20, natural input delta runs approximately -6.694
to -5.058; all inventories, gross flows and isotope abundances remain positive.
I checked the identities with exact rational arithmetic at all integer times,
and the displayed algebra establishes the continuous formula. Fossil input
changes from10 to18.636 across this constructed interval; no historical forcing
match is claimed. It is a designed logical test, not an empirical Earth model.

Nor does the issue depend solely on an undefined signature at zero natural
net growth. Retain the snapshot stocks/removal and set natural net growth
J=5/9. Total growth is50/9, fossil net growth5 and f=.9. Choosing the natural
input abundance to balance H=G*qi gives gross natural input delta=-6.73210 while
the effective natural NET delta is+120.21835. All gross signatures remain finite
and negative. A physical reservoir at+120 is not required. This directly checks
the draft's statement that finite ordinary gross signatures can produce a large
signed residual. It also shows why merely relaxing a physical endmember bound
to zero does not restore a general residual bound.

These extensions strengthen a logical conclusion only. They need not satisfy
all empirical terrestrial/oceanic exchange constraints, and cannot be presented
as proof of a particular actual f. The draft already states that distinction.

The two-box return formula and 60-year ramp were also independently recalculated:
A(30)=.0910629427 for k=1/3.8,l=1/38, versus the much smaller first-exit survival;
the stated ramp gives421.6343966GtC, not445. The latter remains a minor arithmetic
clarification under the specified ramp, not the central physical objection.

EMPIRICAL CHALLENGE

Using the original saved Scripps CSV bytes, a separate parser and np.polyfit
against1/C, I reproduced the filled-adjusted monthly1978–2022 fits:
PTB n480: -13.2102681458;
LJO n528: -13.3098474777;
MLO n516: -13.2868873087;
SPO n528: -12.9737597533.
Maximum difference from the retained calculation is below7e-14per mil. These
checks support the draft's positive numerical result, not an attribution bound.

The Scripps script explicitly selects paired values and has a minimum annual
sample count. The draft correctly discloses that HAC/blocks use observation rows
across gaps and that uncertainty is conditional/descriptive. No actual coverage
guarantee or station independence follows; this should not be lost in copy edits.

The extended reconstruction implements its stated constant-input convolution,
separate detrending and isotope splice. Its source-vintage, start-state and
year-end/annual-mean caveats are material. The saved CO2 correlations support the
reported substantive reproduction; they are not calibration-independent fixed
prediction skill, and the draft now distinguishes these metrics. I did not rerun
every extended parameter/sampling combination. The isotope residual discrepancy
is appropriately unresolved rather than called an error in the target paper.
No author package or exact53-point proxy coordinates were supplied to this review.

The first extended run's Law Dome column mistake was preserved and corrected;
the report uses the corrected run. The current Law Dome regressions are properly
labeled diagnostic, not reproductions of a different historical vintage. The
sparse early regression must not become a claimed preindustrial source signature.

The 2025 short-lifetime calculations are approximate conditional reconstructions
using an assumed extension. Calling147.62 “about148” in the public draft is
consistent with its actual result; it should not be advertised as exact recovery
of the target's147 or of actual2025 fossil stock.

SOURCE AND CLAIM CHALLENGE

The source chain supports distinguishing Koutsoyiannis's diagnostic intercept
from its fixed-input proxy modeling. The latter is an explicit test of a selected
modern signature against a historical series, not an independent optimization.
It remains evidence about fit; lack of independent optimization does not mean
the test has no evidential value. The draft keeps aggregate agreement visible.

Köhler's numerical Law Dome agreement and interpretative limitations are both
retained. The assessment of IPCC/NOAA/NASA is appropriately a check of what they
claim, not an appeal to their authority as proof of attribution. The short public
article need not reproduce every agency citation or quantify new attribution.

The phrase “not established” is better supported than an unqualified assertion
that every result or all physical reasoning in the target is false. The draft
uses the former and preserves successful calculations. It also evaluates the
later turnover/model defenses instead of treating the paper as unaware of sinks.

EXECUTION AND ARTIFACTS

analysis/challenge_checks.py — separate bounded-check script.
analysis/challenge/results.json — exact residuals, finite-interval rows,
positive-natural-growth example, independent Scripps fits, ramp/response values,
input hashes and runtime.
Original captured execution output is preserved but not distributed here.
One execution, exit0, Python3.12.14, numpy2.3.5, standard-library Fraction.
No new data acquisition, first-pass rerun or report/article edit occurred.
The script hash and reviewed source/review hashes are retained in results.json.

RESIDUAL DISAGREEMENT AND COMPLETION CONDITION

No substantive dissent remains about the narrowed central disposition. The audit
does not settle unavailable-input questions by mathematical counterexample.
CH1–CH3 require explicit resolution, after which this challenge does not require
another scientific execution. Completion means a transparent bounded assessment
with the listed uncertainties, not proof that every requested historical artifact
was available.
