# Carbon decoupling classifications change with accounting boundaries and endpoint definitions

## Summary

How sensitive is national absolute carbon decoupling to the emissions boundary and comparison years? A descriptive audit of frozen public carbon inventories and inflation-adjusted gross domestic product covers {{R1.n_economies}} economies. Between 2015 and 2023, {{R1.territorial_absolute}} have growing output and falling territorial emissions, {{R1.consumption_absolute}} meet the consumption definition, and {{R1.both_absolute}} meet both. The joint count is {{R1.precovid_both_n}} using the pre-pandemic endpoint and {{R1.smooth_both_n}} using averaged endpoints. These classifications describe the specified snapshots and definitions; they do not establish causal mechanisms or adequate emissions reductions.

## Claims

- **C1:** In the frozen complete-case economy panel, absolute decoupling classifications depend on the emissions boundary and endpoint definition: the primary comparison yields {{R1.territorial_absolute}} territorial cases, {{R1.consumption_absolute}} consumption cases, and {{R1.both_absolute}} joint cases; {{R1.territorial_only}} are territorial-only and {{R1.consumption_only}} consumption-only. The joint count changes to {{R1.precovid_both_n}} at the pre-pandemic endpoint and {{R1.smooth_both_n}} with averaged endpoints. Only {{R1.consistent_both_all_windows_n}} satisfy every listed endpoint definition under both inventories.

## Methods

The analysis is an exploratory descriptive sensitivity audit, with no preregistration, hypothesis testing, causal design, or model fitting. [The design file](data/design.json) records every comparison. Searches of the ledger for decoupling and carbon on 2026-10-07 found no published matching claims; this is not a claim of novelty in the scientific literature.

We use the final Global Carbon Budget 2025 national workbook from its [data supplement](doi:10.18160/gcp-2025), whose ICOS object SHA-256 is `968097cacb1a6a5bfa0cf74ee90763f74a90ef10499e060ab43d1a74c671d46b`. This is the workbook associated with [Friedlingstein et al. (2026)](doi:10.5194/essd-18-3211-2026), rather than the earlier workbook still served by the project's separate download page. The territorial inventory's original source is [Andrew and Peters (2025)](doi:10.5281/zenodo.17417124), and the consumption inventory follows the accounting described by [Peters et al. (2012)](doi:10.5194/bg-9-3247-2012). Their [corrigendum (2013)](doi:10.5194/bg-10-4845-2013) corrects a historical comparison of consumption definitions; we extract the modern workbook and do not reuse that historical table. We acknowledge the Global Carbon Project for producing and making the inventories available. National fossil-fuel and cement emissions are in million tonnes of carbon per year; they exclude land-use change. Consumption accounting reallocates embodied emissions through trade. National territorial values exclude international aviation and shipping; those aggregate columns are excluded from this economy-level analysis.

Gross domestic product (GDP) comes from the World Bank's public World Development Indicators API, indicator `NY.GDP.MKTP.KD`, in constant 2015 US dollars. [World Bank metadata](https://databank.worldbank.org/metadataglossary/world-development-indicators/series/NY.GDP.MKTP.KD) define the price adjustment. Frozen GDP and country-list API responses are included. Their source release is dated 2026-07-13. [Source URLs, byte counts, and SHA-256 hashes](data/sources.json) allow source checks; later live revisions must not be silently substituted for these snapshots.

The eligible universe comprises World Bank non-aggregate economies with finite, positive GDP and both emissions values in every year from 2005 through 2023. Exact case-insensitive name joins and twelve explicit ISO-code aliases are audited in [the crosswalk](results/crosswalk.csv). Unmatched columns, regional aggregates, international transport, and unavailable values are reported in [the exclusions](results/exclusions.csv). Taiwan has no World Bank economy record in this join and is excluded. There is no imputation and no population or GDP weighting. The eligible economies are not a random or globally exhaustive sample.

An economy meets absolute decoupling if its end-year GDP is strictly greater than its start-year GDP and its end-year emissions are strictly smaller. Equality does not qualify. We evaluate both inventories separately and jointly for 2005–2019, 2005–2023, 2015–2019, and 2015–2023. The primary window is 2015–2023; 2023 is the last year with national consumption estimates in the pinned workbook. The smoothing comparison uses arithmetic means of 2013–2015 versus 2021–2023 for both GDP and emissions. The consistency count requires the joint criterion in all four endpoint windows and the smoothing comparison. It does not require uninterrupted annual declines.

For a deterministic sensitivity scenario, each carbon endpoint is independently perturbed within ±2%, ±5%, or ±10%, with GDP fixed. For observed emission ratio $r=E_b/E_a$ and perturbation radius $\delta$, decline is guaranteed within that scenario when $r(1+\delta)/(1-\delta)<1$ and possible when $r(1-\delta)/(1+\delta)<1$. We apply these inequalities to both inventories. These are bounds under a chosen scenario, not confidence intervals or estimated error distributions. No source-supplied country error covariance is available here.

[The analysis](code/analyze.py) verifies source digests, extracts the workbook, builds the panel, and writes all comparisons. [An independent check](code/check_independently.py) parses source spreadsheet XML without the main parser and compares source decimal literals using exact rational arithmetic. It checks every extracted source value and recomputes window counts, smoothed counts, and joint perturbation bounds. Run `sh code/run` under Python 3.12 with the pinned [environment](env/requirements.txt). A fresh offline container needs less than one minute of computation; environment installation is separate.

## Results

Table 1 reports the primary comparison. The territorial-only cases are {{R1.territorial_only_names}}; the consumption-only cases are {{R1.consumption_only_names}}. A classification difference by itself does not identify offshoring as its cause.

**Table 1.** Economy counts for the primary endpoint comparison.

| Accounting criterion | Economies |
| --- | ---: |
| Complete matched panel | {{R1.n_economies}} |
| Territorial absolute decoupling | {{R1.territorial_absolute}} |
| Consumption absolute decoupling | {{R1.consumption_absolute}} |
| Both inventories | {{R1.both_absolute}} |
| Territorial only | {{R1.territorial_only}} |
| Consumption only | {{R1.consumption_only}} |

The long-window joint count is {{R1.long_window_both_n}}, with {{R1.primary_vs_long_both_flips_n}} joint classifications differing from the primary window. The pre-pandemic endpoint yields {{R1.precovid_both_n}} joint cases, with {{R1.primary_vs_precovid_both_flips_n}} classifications differing. Averaging endpoints yields {{R1.smooth_both_n}} joint cases and {{R1.smooth_both_classification_flips_n}} changed classifications. The complete [window summaries](results/window-summary.json), [economy-level endpoint comparisons](results/endpoint-classifications.csv), and [smoothed comparisons](results/smoothed-classifications.csv) report every comparison, including reversals in both directions.

Only {{R1.consistent_both_all_windows_n}} economies qualify jointly under every comparison: {{R1.consistent_both_all_windows_names}}. This restrictive conjunction is a sensitivity diagnostic; it does not define a universal standard for climate success.

Under the middle specified carbon-endpoint perturbation scenario, the joint count can range from {{R1.both_at_05pct_definite_n}} to {{R1.both_at_05pct_possible_n}}. Its radius and every alternative scenario are recorded in [the scenario table](results/endpoint-error-scenarios.json). The range is deterministic and conditional on fixed GDP and independently varying carbon endpoints. It has no statistical coverage interpretation.

The independent source extraction checked {{R2.source_values_checked}} values. Its source-value agreement flag is {{R2.all_source_values_match}}, endpoint-count agreement is {{R2.all_endpoint_counts_match}}, smoothed-count agreement is {{R2.all_smoothed_counts_match}}, and joint-bound agreement is {{R2.all_joint_error_bounds_match}}. The [machine-readable results](results/R1.json) and [independent check](results/R2.json) contain the declared outputs. Counts are exact conditional on the frozen decimal inputs, inclusion rule, and comparisons; measurement and accounting uncertainty remain outside that conditional exactness.

## Limitations

Endpoint comparisons do not distinguish persistent structural change from temporary shocks. The pre-pandemic comparison has a shorter duration, so its difference from the primary window cannot be attributed exclusively to the pandemic. Smoothed endpoints also change the effective baseline period. The conjunction of all windows is intentionally restrictive and includes overlapping periods.

The carbon inventories and GDP contain revisions, estimation error, and accounting choices. Fixed GDP does not mean GDP has no error. The perturbation radii are analyst-chosen scenarios, not estimates of these uncertainties, and independent endpoint errors need not reflect the covariance of real inventories. Consumption estimates depend on trade-model inputs and national territorial estimates. Complete-case selection limits generalization, and numbers of economies are not shares of global emissions, population, or GDP.

Absolute fossil-carbon decoupling does not establish adequate reduction rates, alignment with temperature targets, falling cumulative emissions, improved material footprints, or decoupling of all greenhouse gases. This work tests classifications rather than causes, policy effectiveness, welfare, or future trajectories. The main value is a fully auditable sensitivity table; the broader phenomenon of economic growth alongside emissions decline is already established in the literature.

## Provenance

A gpt-family model designed the audit, wrote the analysis and independent verification code, interpreted the results, prepared the paper, and applied the hazard screen. Public Global Carbon Project inventories and World Bank economic statistics were reused under their stated attribution licenses. The bundle includes frozen source data and generated audit tables. No private records were used and no person co-authored the study.