The isotopic signature was assembled, not observed.

Jonathan Cohler (Lexington, MA) and Willie Soon (EPSS Sopron). Under review 25 August 2026. Acknowledgments: Demetris Koutsoyiannis for the intercept papers this builds on; Claude 4.7 and Grok 4.5 as writing aids. No external funding. No new data were generated.

Three measurement chains, none of them this lab’s flasks: Scripps CO₂ Program δ¹³C at Barrow, La Jolla, Mauna Loa and the South Pole (via Koutsoyiannis 2024a); Caribbean sclerosponge DIC from Böhm et al. 2002; Law Dome ice via Köhler et al. 2006. Endmembers: Andres et al. 2000 fossil mix ≈ −28‰; Mook 1986 / Zhang 1995 ocean-outgassing ≈ −8‰.

Method: derive the Keeling relation from conservation of each isotope (their Eqs. 1–4), read δI off a linear regression of δ¹³C on 1/C, then substitute into the mixture equation. No ocean chemistry, no biosphere parameterisation, no transport scheme.

Two-endmember mix. The paper’s engine. δI = f·δF + (1−f)·δN is a definition, not a climate model.

Isoflux inversion. The official story’s extra reservoir of free parameters. Not one of the paper’s three inputs. This lab names it in the verdict: it is how −13 becomes −28 without rejecting the flasks.

Residence vs Bern IRF. Independent cross-check in §9.2: RRR τres ≈ 3.8 yr, bomb-¹⁴C τrel ≈ 17.2 yr. Convolution of GCB emissions leaves 39 or 147 GtC fossil in a 907 GtC air reservoir (4.3% / 16.2%) — not the Bern ~50% hangover.

Ice pipeline. Not in this paper. Gravity, firn diffusion, blanks and CG92 live in §02 of this lab.

If f were large, δI would walk toward −28‰ as fossil emissions rose from essentially zero (1500) to ~10 GtC/yr. The intercept did not walk. At the pre-industrial end, f ≈ 0, so δI(t₀) = δN(t₀) ≈ −13‰. Holding δN there, the modern mix is

fmodern = (−13.2 + 13) / (−28 + 13) ≈ 0.013

That is 1.3%, inside the ±0.2‰ intercept noise. The instrumental band [0, 0.26] collapses to a point. This lab’s honesty check: Böhm is a DIC proxy, not a flask, and we do not have a public table — see the continuity row.

1. Mass conservation. The Keeling relation and the mixture equation are algebra.
2. Standard endmembers. Fossil ≈ −28‰, ocean outgassing ≈ −8‰ — the values IPCC assessments already use.
3. The records. Scripps four-site δ¹³C and the Böhm sclerosponge. Rejecting them rejects the measurement chain the attribution also rests on.

This lab names a fourth way out, which the paper’s dilemma omits: an isoflux in a carbon inversion. Extra land and ocean terms with free signatures can always make −13‰ air look like −28‰ fuel. That term is not in the flask. It is the assembled signature.

Fossil carbon rose from about 3 GtC/yr in the 1960s to more than 10 GtC/yr now. If that pulse stayed in the air, each year’s increment would scale with emissions (1 ppm ≈ 2.12 GtC). In this window the observed rise is 112.1 ppm; the fossil total, if it all stayed, is 201.4 ppm. The leftover fraction is the usual airborne identity. The shape is the issue: r(annual growth, fossil GtC) at this station is 0.78. Pinatubo, El Niño, and the seasonal bite do not sit on the rust staircase.

Mean seasonal amplitude here is 5.8 ppm — a biosphere exchange of order 10+ GtC, comparable to or larger than a year of fossil. Zoom to two years. That is what the atmosphere is doing. The publication smooth erases it.

IPCC AR4 itself puts the turnover time of CO₂ in air at about 4 years — the mean wait before a molecule is taken up by ocean or land. The 100-year figure is a different quantity, the adjustment time of a leftover concentration anomaly in a buffered ocean. The bomb-¹⁴C pulse is the experiment: after 1963 the excess ¹⁴CO₂ left the troposphere on an e-folding of order 10 years (Hua et al. 2013; Levin et al.). Essenhigh (2009) and Starr (1993) recover 4–15 years from mass balance. A short cycle for anthropogenic carbon is not a crank number. It is the turnover IPCC already published, plus the bomb tracer.

• IPCC AR4 WG1 FAQ 7.1 / Ch. 7Turnover time of CO₂ in the atmosphere is about 4 years (exchange with ocean and biosphere). IPCC distinguishes this from a longer ‘adjustment time’ of a concentration perturbation.
• Essenhigh, R.H. (2009), Energy & Fuels 23:2773–2784Mass-balance residence time of anthropogenically sourced CO₂ in the range 5–15 years, centred near 5–10.
• Starr, C. (1993), Energy 18:1297–1310Atmospheric residence time 4–5 years from carbon-cycle mass balance.
• Hua, Barbetti & Rakowski (2013), Radiocarbon 55:2059–2072Bomb-¹⁴C tropospheric excess (the 1963 pulse) declines on an e-folding of order 10 years as ¹⁴CO₂ mixes into the ocean and biosphere — an empirical tracer of CO₂ leaving the air.
• Levin et al. (2010), Tellus B / Radiocarbon bomb-¹⁴C recordsPost-test-ban Δ¹⁴C in clean air falls with a multi-year e-folding as the bomb pulse is taken up, not a century-scale hangover.
• Stallinga (2023), Atmosphere 14:473, reviewing SolomonResidence time of carbon atoms in the atmosphere of order 10 years.

Nikolov & Zeller reconstruct GSAT from TSI and Bond albedo only (their Equation 16 has no greenhouse-gas term; R² 0.84, Mar 2000–Jul 2026). Goessling, Rackow & Jung, using CERES and ERA5, find that the 2023 surge left a ~0.2 K hole after anthropogenic warming and El Niño, and that a record-low planetary albedo — fewer low clouds in the northern mid-latitudes and tropics — closed it. Polar ice is a sideshow. TSI is a sideshow. That is an independent verification of the albedo change, not a CSIRO file.

Over the CERES era the directional fact is the same: the planet reflected less sunlight, absorbed more, and warmed. The 2023 floor sits on a multi-annual low-cloud decline (Goessling: −1.27%/decade from 2013–2022), not on a solar-constant step.

Goessling et al. still sit inside a GHG + feedback + aerosol + variability frame. They treat the albedo drop as a 0.2 K patch that intensifies a greenhouse-plus-El-Niño budget, and they leave open whether the low-cloud trend is internal variability, aerosol cleanup, or an emerging cloud feedback.

Nikolov & Zeller treat the same drop as the budget. Surface temperature tracks absorbed sunlight, not the TOA energy imbalance. Apparent EEI is what you get after the atmosphere adiabatically attenuates longwave (TEFAC 0.477). Sensitivity to ASR is modest (~0.30 K per W m⁻²). If a greenhouse term were required, a solar-plus-albedo reconstruction would miss the 26-year slope. In the atlas, it does not.

Plant photosynthesis discriminates against ¹³C, so coal, oil and gas — buried plants — sit near −25 to −44‰. Burning them should dilute atmospheric δ¹³C. Francey 1999 supplies the 1000-year curve; Allison’s Cape Grim flasks lock the modern end; IPCC inversions close the budget with airborne fraction ~0.45 plus ocean and land isofluxes large enough that the observed −13‰ intercept can still be blamed on −28‰ fuel.

That last clause is the whole trick. The fingerprint is inferred after a model of exchange fluxes that are not measured at the precision of the flasks.

Mass balance on the atmosphere alone — Keeling’s own plot, without a second reservoir of free parameters — gives a net source/sink signature of about −13.3‰ at every background station, and in the ice–firn join back to the 16th century (Koutsoyiannis 2024). Seasonal loops reach −25‰, which is the biosphere, and they do not grow as fossil emissions double.

A genuine fossil takeover would drag the intercept toward −28‰ as the natural-gas share rose. The series does the opposite in the high-emission decades. Koutsoyiannis’s carbon-cycle close is that temperature-driven natural [CO₂] changes already exceed fossil by more than 3×, with human carbon ≤4% of the gross flux — so the 2019 spline is a biosphere-on-temperature curve, not a fuel chromatogram. Two ramps of [CO₂] and T are the misunderstanding; the increment follows T once the ramp is stripped. See Conclusions and T → CO₂. A companion CERES atlas finds the same pattern in the energy budget: 26 years of satellite warming track Bond albedo, not greenhouse forcing — the overlap of Nikolov & Zeller with Goessling, Rackow & Jung. Sister desks take the same rule to ice versus stomata, both poles versus 1988, the instrumental stack, and the ocean heat cycle.