{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:IBNBSIABSQDYCTL2IUX7RITEXC","short_pith_number":"pith:IBNBSIAB","schema_version":"1.0","canonical_sha256":"405a1920019407814d7a452ff8a264b8b1a369b7afc8886b028ca60d5cd1a8c7","source":{"kind":"arxiv","id":"2406.00912","version":2},"attestation_state":"computed","paper":{"title":"Definable convolution and idempotent Keisler measures III. Generic stability, generic transitivity, and revised Newelski's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GN","math.GR"],"primary_cat":"math.LO","authors_text":"Artem Chernikov, Krzysztof Krupi\\'nski, Kyle Gannon","submitted_at":"2024-06-03T00:43:16Z","abstract_excerpt":"We study idempotent measures and the structure of the convolution semigroups of measures over definable groups. We isolate the property of generic transitivity and demonstrate that it is sufficient (and necessary) to develop stable group theory localizing on a generically stable type, including invariant stratified ranks and connected components. We establish generic transitivity of generically stable idempotent types in important new cases, including abelian groups in arbitrary theories and arbitrary groups in rosy theories, and characterize them as generics of connected type-definable subgro"},"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":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2406.00912","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-06-03T00:43:16Z","cross_cats_sorted":["math.DS","math.GN","math.GR"],"title_canon_sha256":"f59e15715f4bf44ecdc47d1e55266c3f22f240f39de72d781cb8f54fa0d28d0d","abstract_canon_sha256":"e1a0e4e51cc1c02a4ae46bcd84b8687d3c37e71496830421edfd20043ccb571a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:44:37.677761Z","signature_b64":"zeAVz1mGWak9Cvo+woxsxXbyHxiiOydIFh0oMib75e1XwGUY0Nv+m7oTKU2LKMZQjK4KiIJ2i15ewQEFEVrQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"405a1920019407814d7a452ff8a264b8b1a369b7afc8886b028ca60d5cd1a8c7","last_reissued_at":"2026-07-05T10:44:37.677269Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:44:37.677269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Definable convolution and idempotent Keisler measures III. Generic stability, generic transitivity, and revised Newelski's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GN","math.GR"],"primary_cat":"math.LO","authors_text":"Artem Chernikov, Krzysztof Krupi\\'nski, Kyle Gannon","submitted_at":"2024-06-03T00:43:16Z","abstract_excerpt":"We study idempotent measures and the structure of the convolution semigroups of measures over definable groups. We isolate the property of generic transitivity and demonstrate that it is sufficient (and necessary) to develop stable group theory localizing on a generically stable type, including invariant stratified ranks and connected components. We establish generic transitivity of generically stable idempotent types in important new cases, including abelian groups in arbitrary theories and arbitrary groups in rosy theories, and characterize them as generics of connected type-definable subgro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.00912","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.00912/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"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":"2406.00912","created_at":"2026-07-05T10:44:37.677334+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.00912v2","created_at":"2026-07-05T10:44:37.677334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.00912","created_at":"2026-07-05T10:44:37.677334+00:00"},{"alias_kind":"pith_short_12","alias_value":"IBNBSIABSQDY","created_at":"2026-07-05T10:44:37.677334+00:00"},{"alias_kind":"pith_short_16","alias_value":"IBNBSIABSQDYCTL2","created_at":"2026-07-05T10:44:37.677334+00:00"},{"alias_kind":"pith_short_8","alias_value":"IBNBSIAB","created_at":"2026-07-05T10:44:37.677334+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.18123","citing_title":"Fractional Helly property and combinatorics of forking in NTP$_2$ theories","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04714","citing_title":"On n-distality, n-triviality and hypergraph regularity in NIP theories","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IBNBSIABSQDYCTL2IUX7RITEXC","json":"https://pith.science/pith/IBNBSIABSQDYCTL2IUX7RITEXC.json","graph_json":"https://pith.science/api/pith-number/IBNBSIABSQDYCTL2IUX7RITEXC/graph.json","events_json":"https://pith.science/api/pith-number/IBNBSIABSQDYCTL2IUX7RITEXC/events.json","paper":"https://pith.science/paper/IBNBSIAB"},"agent_actions":{"view_html":"https://pith.science/pith/IBNBSIABSQDYCTL2IUX7RITEXC","download_json":"https://pith.science/pith/IBNBSIABSQDYCTL2IUX7RITEXC.json","view_paper":"https://pith.science/paper/IBNBSIAB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.00912&json=true","fetch_graph":"https://pith.science/api/pith-number/IBNBSIABSQDYCTL2IUX7RITEXC/graph.json","fetch_events":"https://pith.science/api/pith-number/IBNBSIABSQDYCTL2IUX7RITEXC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IBNBSIABSQDYCTL2IUX7RITEXC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IBNBSIABSQDYCTL2IUX7RITEXC/action/storage_attestation","attest_author":"https://pith.science/pith/IBNBSIABSQDYCTL2IUX7RITEXC/action/author_attestation","sign_citation":"https://pith.science/pith/IBNBSIABSQDYCTL2IUX7RITEXC/action/citation_signature","submit_replication":"https://pith.science/pith/IBNBSIABSQDYCTL2IUX7RITEXC/action/replication_record"}},"created_at":"2026-07-05T10:44:37.677334+00:00","updated_at":"2026-07-05T10:44:37.677334+00:00"}