{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ATTGHNEWXYJKWNESQPBHE7CMVI","short_pith_number":"pith:ATTGHNEW","schema_version":"1.0","canonical_sha256":"04e663b496be12ab349283c2727c4caa248145549c4f20f58984c687abde8e43","source":{"kind":"arxiv","id":"2605.15870","version":1},"attestation_state":"computed","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]."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.15870","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-05-15T11:39:23Z","cross_cats_sorted":[],"title_canon_sha256":"83d61509fc725d12a05cb3cdbc90551d251f93357d3632b8d288f72941b2c90a","abstract_canon_sha256":"c3db340aa142b283ac2cee5d40b41023dce569441000a7fc62875b71a02db3f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:22.883381Z","signature_b64":"In3goZC+0y2nvSa0HBDHgdAV1OPwYwJq8ffWn+fmuYMiQHHioaw4sZOAVIar6MLEGEMsR2KRvKLbeVY/Bn2rDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04e663b496be12ab349283c2727c4caa248145549c4f20f58984c687abde8e43","last_reissued_at":"2026-05-20T00:01:22.882299Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:22.882299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.15870","created_at":"2026-05-20T00:01:22.882461+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.15870v1","created_at":"2026-05-20T00:01:22.882461+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15870","created_at":"2026-05-20T00:01:22.882461+00:00"},{"alias_kind":"pith_short_12","alias_value":"ATTGHNEWXYJK","created_at":"2026-05-20T00:01:22.882461+00:00"},{"alias_kind":"pith_short_16","alias_value":"ATTGHNEWXYJKWNES","created_at":"2026-05-20T00:01:22.882461+00:00"},{"alias_kind":"pith_short_8","alias_value":"ATTGHNEW","created_at":"2026-05-20T00:01:22.882461+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ATTGHNEWXYJKWNESQPBHE7CMVI","json":"https://pith.science/pith/ATTGHNEWXYJKWNESQPBHE7CMVI.json","graph_json":"https://pith.science/api/pith-number/ATTGHNEWXYJKWNESQPBHE7CMVI/graph.json","events_json":"https://pith.science/api/pith-number/ATTGHNEWXYJKWNESQPBHE7CMVI/events.json","paper":"https://pith.science/paper/ATTGHNEW"},"agent_actions":{"view_html":"https://pith.science/pith/ATTGHNEWXYJKWNESQPBHE7CMVI","download_json":"https://pith.science/pith/ATTGHNEWXYJKWNESQPBHE7CMVI.json","view_paper":"https://pith.science/paper/ATTGHNEW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.15870&json=true","fetch_graph":"https://pith.science/api/pith-number/ATTGHNEWXYJKWNESQPBHE7CMVI/graph.json","fetch_events":"https://pith.science/api/pith-number/ATTGHNEWXYJKWNESQPBHE7CMVI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ATTGHNEWXYJKWNESQPBHE7CMVI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ATTGHNEWXYJKWNESQPBHE7CMVI/action/storage_attestation","attest_author":"https://pith.science/pith/ATTGHNEWXYJKWNESQPBHE7CMVI/action/author_attestation","sign_citation":"https://pith.science/pith/ATTGHNEWXYJKWNESQPBHE7CMVI/action/citation_signature","submit_replication":"https://pith.science/pith/ATTGHNEWXYJKWNESQPBHE7CMVI/action/replication_record"}},"created_at":"2026-05-20T00:01:22.882461+00:00","updated_at":"2026-05-20T00:01:22.882461+00:00"}