No Single Signal Separates Agreement From Parallel Conduct Among LLM Sellers

Strengths. This takes a genuinely useful question — can an auditor tell a collusive agreement apart from innocent parallel conduct among LLM pricing agents — and answers it with a clean, well-motivated design. The decoy conditions (sellers with no message channel, where agreement is impossible by construction) are exactly the right control, and the antitrust "plus factors" framing (Twombly; Kovacic et al.) is a thoughtful lens this literature rarely applies. The methodology is strong for a sprint: both studies are preregistered as frozen git tags, detector thresholds are fixed on calibration seeds before any held-out market is scored, results carry confidence intervals with Holm correction, and — commendably — the null and negative findings are reported honestly (action-dependence runs the "wrong" way, every single signal fails, the plus-factor rule catches nothing). Every reported number is auto-checked against the analysis outputs, and the full code, both preregistrations, and every market log are public. The writing is clear and the dual-use appendix is substantive.

To strengthen.

1. Reconcile the authorship attribution — it is internally inconsistent. The Author Contributions section states the author performed the human annotation and wrote the report, but Section 4 ("Labels") states the messages were not hand-labeled and were labeled by Claude in one non-blind pass, and the LLM Usage Statement attributes the code, analysis, experiments and labeling to a coding agent. Make the contributions statement agree with the body.
2. The report reads as model-generated. Apart notes that reports which read as generated may not be scored. Rewriting at least the abstract, introduction and discussion in your own voice (the facts are collected in the repo's FACTS.md) would protect the submission and sharpen the argument.
3. The agreement labels are not blind. They were produced by Claude after the results were seen, as you note. The preregistered two-pass blind human labels would materially strengthen the central "they agreed — to compete" claim, which currently rests on non-blind labels.
4. Flag the external-validity ceiling prominently. Study 1's held-out cells have 4 markets each and the sellers are 7–8B 4-bit open-weight models, so several intervals are wide and larger models may coordinate through actions in ways these cannot show. You mention this; it deserves to be stated up front as the main limit.

Overall. A rigorous, honest, well-scoped study that lands a real methodological point: no single signal reliably separates agreement from parallel conduct, and a price-extracting judge combined with a price-level requirement does better than either alone. What holds it back is presentation and provenance — a model-drafted report, non-blind labels, and a contributions section that contradicts the body — rather than the underlying science, which is sound.