{"paper":{"title":"Remarks on generic stability and random types","license":"http://creativecommons.org/licenses/by/4.0/","headline":"rgs and irgs for Keisler measures are equivalent to generically stable random type extensions","cross_cats":[],"primary_cat":"math.LO","authors_text":"Karim Khanaki","submitted_at":"2026-05-15T11:39:23Z","abstract_excerpt":"We introduce the notions of $rgs$ and $irgs$ as properties of a Keisler measure $\\mu$, and prove that they are respectively equivalent to the existence of a generically stable random type that extends $\\mu$ and to the fact that its canonical extension, namely the random type $r_\\mu$, is generically stable. We compare these notions with the known concepts of $fim$, $fam$, and self-averaging, and in particular we show that every $irgs$ measure is dependent in the sense of [10]."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"rgs is equivalent to the existence of a generically stable random type extending μ, and irgs to the canonical extension r_μ being generically stable. Every irgs measure is dependent in the sense of [10].","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The standard background definitions of Keisler measures, random types, generic stability, and the canonical extension r_μ from model theory literature hold and are applicable here.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces rgs and irgs for Keisler measures with equivalences to generic stability of random types and proves irgs implies dependence.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"rgs and irgs for Keisler measures are equivalent to generically stable random type extensions","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d1f2535427a1f0f4b6214e5152e2fe8c9e5e727b1eca78d2a885c867367a696d"},"source":{"id":"2605.15870","kind":"arxiv","version":1},"verdict":{"id":"bc19a7e1-d636-47ae-997f-36fef664ddee","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:19:50.732821Z","strongest_claim":"rgs is equivalent to the existence of a generically stable random type extending μ, and irgs to the canonical extension r_μ being generically stable. Every irgs measure is dependent in the sense of [10].","one_line_summary":"Introduces rgs and irgs for Keisler measures with equivalences to generic stability of random types and proves irgs implies dependence.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The standard background definitions of Keisler measures, random types, generic stability, and the canonical extension r_μ from model theory literature hold and are applicable here.","pith_extraction_headline":"rgs and irgs for Keisler measures are equivalent to generically stable random type extensions"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15870/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.075796Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:31:11.859195Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.694469Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.807304Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7a794f45ba9a330377d763f461f62ce3f12267d8006be023e2cbf77b6c129245"},"references":{"count":14,"sample":[{"doi":"","year":2008,"title":"Ben Yaacov,Transfer of properties between measures and random types, Unpublished research note, 2008","work_id":"96d7c930-e06e-4c68-85f3-ab7e38aaf840","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"I. Ben Yaacov, A. Berenstein, C. W. Henson, and A. Usvyatsov,Model theory for metric structures, inModel Theory with Applications to Al- gebra and Analysis, vol. 2, London Mathematical Society Lecture","work_id":"ef1a8450-18a7-4299-babc-f13f4632c0e6","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Ben Yaacov and H","work_id":"9c8d52fa-2ed8-4bec-8f93-1062073157c2","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.2140/mt.2023.2.1","year":2023,"title":"G. Conant, K. Gannon, and J. Hanson,Keisler measures in the wild, Model Theory, vol. 2, no. 1, pp. 1–67, 2023. doi:10.2140/mt.2023.2.1","work_id":"3098e401-5d60-4cf5-8c7d-073a016bfb9f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"G. Conant, K. Gannon, and J. Hanson,Generic stability, randomiza- tions, and NIP formulas, arXiv preprint arXiv:2308.01801, 2023","work_id":"1e00660d-af4f-44a0-8066-20d414ca38a6","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":14,"snapshot_sha256":"fca9e983a1f3bbce0be6e711e7efc028d5e54f09ed8dc1faf0dea30c5176a5d8","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"693355d62fdcfdfa0ea077c44275a5518f78f2fb9de7f461f5bac4c1ea0a8c9e"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}