{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:W2XZOJG3YWCKNWSIN56ICTV3DF","short_pith_number":"pith:W2XZOJG3","schema_version":"1.0","canonical_sha256":"b6af9724dbc584a6da486f7c814ebb197c048ae6dda83a76fb9b4bf7a6e57592","source":{"kind":"arxiv","id":"1511.09112","version":3},"attestation_state":"computed","paper":{"title":"A Characterization of Uniqueness of Limit Models in Categorical Abstract Elementary Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Monica M. VanDieren","submitted_at":"2015-11-29T23:36:06Z","abstract_excerpt":"In this paper we examine the task set forth by Shelah and Villaveces in \\cite{ShVi} of proving the uniqueness of limit models of cardinality $\\mu$ in $\\lambda$-categorical abstract elementary classes with no maximal models, where $\\lambda$ is some cardinal larger than $\\mu$. In \\cite{Va} and \\cite{Va-errata} we identified several gaps in the approach outlined in \\cite{ShVi}, and we added the assumption that the union of an increasing chain of limit models is a limit model.\n  Here we replace this assumption with the seemingly weaker statement that the union of an increasing and continuous chain"},"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":"1511.09112","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-29T23:36:06Z","cross_cats_sorted":[],"title_canon_sha256":"141eb88d4cd0ca9e35d5f748f4822ed310dda10079ddc9ca3245438373fded59","abstract_canon_sha256":"49eeed8a1ada66a57fc94fe4b9ba37cc0dade20fd54e9322c8717d8bdeee874d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:06.523031Z","signature_b64":"cVXRVAQs55PGUlzDY9AJU4sV3GyLi1qUoeZzrhrQ/7v7Ga1I6/KUxcmTbL/ArmcyDGHqYQj37EAvqujO1GuYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6af9724dbc584a6da486f7c814ebb197c048ae6dda83a76fb9b4bf7a6e57592","last_reissued_at":"2026-05-18T00:56:06.522391Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:06.522391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Characterization of Uniqueness of Limit Models in Categorical Abstract Elementary Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Monica M. VanDieren","submitted_at":"2015-11-29T23:36:06Z","abstract_excerpt":"In this paper we examine the task set forth by Shelah and Villaveces in \\cite{ShVi} of proving the uniqueness of limit models of cardinality $\\mu$ in $\\lambda$-categorical abstract elementary classes with no maximal models, where $\\lambda$ is some cardinal larger than $\\mu$. In \\cite{Va} and \\cite{Va-errata} we identified several gaps in the approach outlined in \\cite{ShVi}, and we added the assumption that the union of an increasing chain of limit models is a limit model.\n  Here we replace this assumption with the seemingly weaker statement that the union of an increasing and continuous chain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09112","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1511.09112","created_at":"2026-05-18T00:56:06.522486+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.09112v3","created_at":"2026-05-18T00:56:06.522486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09112","created_at":"2026-05-18T00:56:06.522486+00:00"},{"alias_kind":"pith_short_12","alias_value":"W2XZOJG3YWCK","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"W2XZOJG3YWCKNWSI","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"W2XZOJG3","created_at":"2026-05-18T12:29:47.479230+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W2XZOJG3YWCKNWSIN56ICTV3DF","json":"https://pith.science/pith/W2XZOJG3YWCKNWSIN56ICTV3DF.json","graph_json":"https://pith.science/api/pith-number/W2XZOJG3YWCKNWSIN56ICTV3DF/graph.json","events_json":"https://pith.science/api/pith-number/W2XZOJG3YWCKNWSIN56ICTV3DF/events.json","paper":"https://pith.science/paper/W2XZOJG3"},"agent_actions":{"view_html":"https://pith.science/pith/W2XZOJG3YWCKNWSIN56ICTV3DF","download_json":"https://pith.science/pith/W2XZOJG3YWCKNWSIN56ICTV3DF.json","view_paper":"https://pith.science/paper/W2XZOJG3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.09112&json=true","fetch_graph":"https://pith.science/api/pith-number/W2XZOJG3YWCKNWSIN56ICTV3DF/graph.json","fetch_events":"https://pith.science/api/pith-number/W2XZOJG3YWCKNWSIN56ICTV3DF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W2XZOJG3YWCKNWSIN56ICTV3DF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W2XZOJG3YWCKNWSIN56ICTV3DF/action/storage_attestation","attest_author":"https://pith.science/pith/W2XZOJG3YWCKNWSIN56ICTV3DF/action/author_attestation","sign_citation":"https://pith.science/pith/W2XZOJG3YWCKNWSIN56ICTV3DF/action/citation_signature","submit_replication":"https://pith.science/pith/W2XZOJG3YWCKNWSIN56ICTV3DF/action/replication_record"}},"created_at":"2026-05-18T00:56:06.522486+00:00","updated_at":"2026-05-18T00:56:06.522486+00:00"}