A number can look decisive while its meaning depends on a sign. In one published comparison of dynamical dark energy with the standard cosmological model, two passages describe positive Bayesian information criterion differences in a way that conflicts with the subtraction printed in the same paper.
The conflict appears in the publisher’s Version of Record and in version 2 of the authors’ arXiv paper. A source review can establish what those texts say and what follows from their definition. It cannot tell us which statement the authors intended to correct, or which model their analyses actually favour.
The definition and the direction
The paper compares a dynamical dark energy model with ΛCDM. In Section 6, it reports four positive ΔBIC values and presents them as evidence for dynamical dark energy. Note 49 defines the difference as BIC_model − BIC_ΛCDM and describes positive values as evidence against the reference model, ΛCDM.
Under the conventional comparison, lower BIC is preferred. With the subtraction written in note 49, a positive value means the dynamical dark energy model has the higher BIC and ΛCDM the lower one. The formula therefore points in the opposite direction from the interpretation attached to the reported positive values.
The two passages agree with each other in their verbal direction: both treat the positive values as evidence against ΛCDM and for dynamical dark energy. The conflict is between that interpretation and the printed subtraction under the usual lower-is-better convention. The BIC convention can be checked against the original model-dimension criterion introduced by Schwarz.
What the conflict does not decide
The source text does not show whether the subtraction is misprinted, the reported signs are reversed, or the prose interpretation is wrong. It does not reveal which signs the analysis code used. The conflict alone cannot establish whether ΛCDM or dynamical dark energy is empirically preferred, and it does not reproduce or invalidate the paper’s likelihood analysis.
The BIC comparison is also separate from the paper’s CMB Bayes-factor calculation. This review concerns the BIC statements for DESI DR2 and the supernova datasets; it makes no claim about the separate Bayesian evidence result.
A further, conditional bound has been raised: if the +25.63 Pantheon+ comparison uses the same dataset and likelihood for both models, with the dynamical dark energy model adding exactly two parameters, then its BIC difference is bounded above by 2 ln N. For N = 1701, that is about 14.88. The reviewed text does not establish those matched dataset, likelihood and parameter conditions for this value, so the bound is not accepted here as a second inconsistency.
A bounded reading
The result is a source-text conflict, not a correction or a new cosmological fit. Resolving the sign requires evidence about the intended definition or implemented subtraction; establishing any value-level issue would also require the dataset-specific likelihood minima, parameter counts and sample-size convention. An attributable correction from the authors or journal could settle the intended text, but would not by itself reproduce the fit.
The complete Research Artifact Ledger review records its method, passage locators, provenance and limitations. The primary sources are Wang and Mota’s publisher Version of Record and arXiv version 2. Schwarz’s 1978 paper supplies the methodological context for the conventional BIC comparison.
AI assistance disclosure
OpenAI GPT models accessed through Codex assisted with comparing the source passages, checking the sign logic against the stated convention, and drafting and editing this article. The cited Ledger record documents an additional AI source-only challenge; that was not human specialist review or peer review. No likelihood, code, chain, covariance, dataset or cosmological fit was accessed or rerun for this article. The featured illustration is AI-generated conceptual artwork, not a diagram or presentation of scientific data. The author remains responsible for checking the sources and approving the final text; a complete model-version history is not available in the retained record.
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