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For general conditional densities, we show that inverse-Fisher-scaled conditional scores arise as local Gaussian posterior corrections based on Fisher scoring and precision discounting. For conjugate natural"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For conjugate natural exponential families, the classical discounted Bayesian recursion has an exact score-driven representation: with steady-state precision discounting and expectation-space inverse-Fisher scaling, the score-driven correction equals the Bayesian posterior mean before transition dynamics are imposed.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The derivations rely on the conditional densities belonging to natural exponential families for the exact equivalence and on Fisher scoring yielding a valid local Gaussian posterior correction for general densities; if these modeling choices do not hold, the claimed representation between score-driven and Bayesian updates fails.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Score-driven models equal Bayesian posterior mean updates in conjugate natural exponential families under steady-state precision discounting and inverse-Fisher scaling.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Score-driven updates match Bayesian posterior corrections exactly for conjugate natural exponential families under steady-state precision discounting and inverse-Fisher scaling.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f589063f898bd74332e5135acf74da84f26faf26db7c0e7b79b6ee586ff86f93"},"source":{"id":"2605.15902","kind":"arxiv","version":1},"verdict":{"id":"8d6c4aea-c752-42d6-9af0-31f1c5a4c489","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:19:02.636065Z","strongest_claim":"For conjugate natural exponential families, the classical discounted Bayesian recursion has an exact score-driven representation: with steady-state precision discounting and expectation-space inverse-Fisher scaling, the score-driven correction equals the Bayesian posterior mean before transition dynamics are imposed.","one_line_summary":"Score-driven models equal Bayesian posterior mean updates in conjugate natural exponential families under steady-state precision discounting and inverse-Fisher scaling.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The derivations rely on the conditional densities belonging to natural exponential families for the exact equivalence and on Fisher scoring yielding a valid local Gaussian posterior correction for general densities; if these modeling choices do not hold, the claimed representation between score-driven and Bayesian updates fails.","pith_extraction_headline":"Score-driven updates match Bayesian posterior corrections exactly for conjugate natural exponential families under steady-state precision discounting and inverse-Fisher scaling."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15902/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T18:31:24.050232Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T18:31:18.762509Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:46.564001Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.771463Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"131704fea678be358bdf29801b807f4c9e5c04455fa68ce3775b1dd67fb904b0"},"references":{"count":20,"sample":[{"doi":"","year":2022,"title":"Artemova, M., Blasques, F., van Brummelen, J., and Koopman, S. 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