Correlated Minds: State-Dependent Error Correlation Across Large Language Models in Financial Forecasting, Benchmarked Against Human Professional Forecasters

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VERSION 1.2-week5-prediction (posted 3 October 2026): THE WEEK-5 PREDICTION, registered in PREREGISTRATION.md section 5.3 and section 11 (deviations 18 and 22). This version adds week5-prediction.json, made once at 2026-10-03 02:46:57 UTC by scripts/week5_prediction.py --publish and never to be revised, and week5-h1-fit.json, the weeks 1-5 fit it was made from; the plan and Addendum 1 are carried over unchanged from version 1.1-addendum-1. SHA-256 of week5-prediction.json: f0e0c086482cc61e0cf7e1489daa39d77a8c51fa01cfba2e353a280c3d00f3d8 (committed at https://github.com/rara-bot/correlated-minds, commit 982b9933cacd5b1447b855ca0edab031f19125e1). The prediction: On the first listed macro release to close after 2026-10-02T23:59:59+00:00 and before 2026-12-11T23:59:59+00:00 whose market surprise is at or above 0.2425625, the primary panel's headroom, estimated on its task-days asked from 2026-10-03, will be below 3.536360 and its rho_bar above 0.147575. VERSION 1.1-addendum-1 (posted 3 October 2026): ADDENDUM 1. This version adds OSF-ADDENDUM-1.md, a summary of the twenty-four dated deviations and disclosures logged in section 11 of the plan before the study's first registered look at its outcomes, and the current PREREGISTRATION.md, which carries section 11 in full. Sections 1-10 are unchanged since registration: scripts/freeze_prereg.py --check reports "intact outside section 11". The SHA-256 below is the hash of the plan as frozen and registered; the file in this version differs from it only by section 11, by design. The frozen plan exactly as first deposited is version 1.0-prereg of this record. The rest of this description is that deposit's original text. FROZEN PRE-REGISTRATION — deposited for independent third-party timestamping before data collection begins. This is the analysis plan for a prospective study, deposited so that its existence and exact contents on this date are verifiable by a party other than the authors. The corresponding registration on OSF Registries was submitted on 29 August 2026 and is pending review at the time of this deposit; when it clears it becomes the registration of record, and this deposit stands as the independent timestamp. INTEGRITYThe deposited PREREGISTRATION.md is frozen. Its SHA-256, recorded inside the document itself, is: 90a7e7de5980a80bef786e87b938495d7a08e10234032a11c5d67e8ce1c70009 frozen on 2026-08-29 03:54 UTC. The same document, with the same hash, was committed publicly to git at commit a300cb58b593 and can be re-verified at any time by running scripts/freeze_prereg.py --check against a fresh checkout of https://github.com/rara-bot/correlated-minds STUDYFinancial institutions are delegating analytical judgement to large language models from a small number of vendors. Because those models share overlapping pretraining data, their apparent diversity may not deliver genuine independence of judgement. This study measures, prospectively and daily, whether nine language models across six vendor families make CORRELATED ERRORS on financial forecasting questions whose answers do not yet exist, and whether that correlation worsens under market stress and question ambiguity. The same estimator is applied to individual human forecasters from the Federal Reserve Bank of Philadelphia's Survey of Professional Forecasters, giving a direct human-versus-machine comparison of diversification headroom. The Financial Stability Board (Oct 2025), the Bank of England (Jul 2026) and the IMF (Jul 2026) have each named correlated AI-driven behaviour as a systemic risk. None of them measures it. This study supplies the measurement. The primary outcome is diversification headroom, N_eff - 1, where N_eff = M / (1 + (M - 1) * rho_bar) and rho_bar is the mean pairwise correlation of forecast ERRORS. Six hypotheses, each with an explicit falsification condition, are stated in section 4 of the deposited plan. The registered collection window runs from 29 August 2026 to a calendar-based data freeze on 11 December 2026, with an out-of-sample prediction published at the end of week five and never revised. Data collection is automated and commits every forecast to a public append-only log before its outcome exists, so the ordering of forecast and outcome is checkable from commit history rather than asserted.