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Prior work derived these SFRD correlations with a simplifying assumption that neglected the difference between the correlations of the components of the velocity parallel and perpendicular to the separation between the two points being correlated. Here we calculate the full joint PDF of the squares of the peculiar velocity at two different points. 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Prior work derived these SFRD correlations with a simplifying assumption that neglected the difference between the correlations of the components of the velocity parallel and perpendicular to the separation between the two points being correlated. Here we calculate the full joint PDF of the squares of the peculiar velocity at two different points. The error tha"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The error that arises in predictions for 21-cm fluctuations if this subtlety is overlooked is generally less than a few percent, but it can be larger for some values of wavenumber k and redshift z if there are cancellations between different contributions to the total signal.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The peculiar velocity field follows the two-point statistics derived from linear perturbation theory in the standard cosmological model, allowing the joint PDF of velocity squares to be computed from the parallel and perpendicular components (as described in the abstract's account of the velocity correlations and prior simplifying assumption).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives the joint PDF for squared peculiar velocities at separated points and shows that neglecting directional anisotropy in velocity correlations causes errors of a few percent or less in 21-cm fluctuation predictions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Accounting for the difference between parallel and perpendicular peculiar-velocity correlations improves 21-cm fluctuation predictions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"75a23ad66a35222d19386e6803889a3debef3e43de365f253e068894f7991b2c"},"source":{"id":"2605.15287","kind":"arxiv","version":1},"verdict":{"id":"354a56e9-47b4-4de2-9246-2535d590d101","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T16:18:45.694130Z","strongest_claim":"The error that arises in predictions for 21-cm fluctuations if this subtlety is overlooked is generally less than a few percent, but it can be larger for some values of wavenumber k and redshift z if there are cancellations between different contributions to the total signal.","one_line_summary":"Derives the joint PDF for squared peculiar velocities at separated points and shows that neglecting directional anisotropy in velocity correlations causes errors of a few percent or less in 21-cm fluctuation predictions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The peculiar velocity field follows the two-point statistics derived from linear perturbation theory in the standard cosmological model, allowing the joint PDF of velocity squares to be computed from the parallel and perpendicular components (as described in the abstract's account of the velocity correlations and prior simplifying assumption).","pith_extraction_headline":"Accounting for the difference between parallel and perpendicular peculiar-velocity correlations improves 21-cm fluctuation predictions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15287/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T16:31:18.370541Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T16:27:05.244425Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T14:41:54.243094Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.788817Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1131eac8d1cbabcf495e626f329808af401e0b0ad0377cc8480865b1edb81647"},"references":{"count":11,"sample":[{"doi":"","year":2023,"title":"Givans, Jahmour J. and Kamionkowski, Marc. 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