{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:AUT66WRSLSK7OUNFRW34XSSGDO","short_pith_number":"pith:AUT66WRS","schema_version":"1.0","canonical_sha256":"0527ef5a325c95f751a58db7cbca461bba57195577c07efeca69a04c1d6d3eb3","source":{"kind":"arxiv","id":"2409.11950","version":1},"attestation_state":"computed","paper":{"title":"Generalized Andr\\'{a}sfai--Erd\\H{o}s--S\\'{o}s theorems for odd cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Caiyun Hu, Jianfeng Hou, Xizhi Liu, Zian Chen","submitted_at":"2024-09-18T13:05:30Z","abstract_excerpt":"In this note, we establish Andr\\'{a}sfai--Erd\\H{o}s--S\\'{o}s-type stability theorems for two generalized Tur\\'{a}n problems involving odd cycles, both of which are extensions of the Erd\\H{o}s Pentagon Problem. Our results strengthen previous results by Lidick\\'{y}--Murphy~\\cite{LM21} and Beke--Janzer~\\cite{BJ24}, while also simplifying parts of their proofs."},"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":"2409.11950","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-09-18T13:05:30Z","cross_cats_sorted":[],"title_canon_sha256":"ff2cf01a6970c5e0da9a59e0486c1ddede5ceee0359cd2fbeb41de6fc978c0de","abstract_canon_sha256":"071ccda705b5298a232d3fe98ae070e58fcce8e009eb6d90ed5a63697fd503f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:08:40.102820Z","signature_b64":"kmtXXBBAvkaiKFXT1FCvnUSEBx8nU4zl3Ur0IpUV6pz3MlGT+lpuuH7uMSDrCB/wFSAsf/KY8wLxSORpXLdEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0527ef5a325c95f751a58db7cbca461bba57195577c07efeca69a04c1d6d3eb3","last_reissued_at":"2026-07-05T09:08:40.102321Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:08:40.102321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Andr\\'{a}sfai--Erd\\H{o}s--S\\'{o}s theorems for odd cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Caiyun Hu, Jianfeng Hou, Xizhi Liu, Zian Chen","submitted_at":"2024-09-18T13:05:30Z","abstract_excerpt":"In this note, we establish Andr\\'{a}sfai--Erd\\H{o}s--S\\'{o}s-type stability theorems for two generalized Tur\\'{a}n problems involving odd cycles, both of which are extensions of the Erd\\H{o}s Pentagon Problem. Our results strengthen previous results by Lidick\\'{y}--Murphy~\\cite{LM21} and Beke--Janzer~\\cite{BJ24}, while also simplifying parts of their proofs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.11950","kind":"arxiv","version":1},"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/2409.11950/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":"2409.11950","created_at":"2026-07-05T09:08:40.102374+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.11950v1","created_at":"2026-07-05T09:08:40.102374+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.11950","created_at":"2026-07-05T09:08:40.102374+00:00"},{"alias_kind":"pith_short_12","alias_value":"AUT66WRSLSK7","created_at":"2026-07-05T09:08:40.102374+00:00"},{"alias_kind":"pith_short_16","alias_value":"AUT66WRSLSK7OUNF","created_at":"2026-07-05T09:08:40.102374+00:00"},{"alias_kind":"pith_short_8","alias_value":"AUT66WRS","created_at":"2026-07-05T09:08:40.102374+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.21689","citing_title":"Spectral generalized Tur\\'{a}n problems","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AUT66WRSLSK7OUNFRW34XSSGDO","json":"https://pith.science/pith/AUT66WRSLSK7OUNFRW34XSSGDO.json","graph_json":"https://pith.science/api/pith-number/AUT66WRSLSK7OUNFRW34XSSGDO/graph.json","events_json":"https://pith.science/api/pith-number/AUT66WRSLSK7OUNFRW34XSSGDO/events.json","paper":"https://pith.science/paper/AUT66WRS"},"agent_actions":{"view_html":"https://pith.science/pith/AUT66WRSLSK7OUNFRW34XSSGDO","download_json":"https://pith.science/pith/AUT66WRSLSK7OUNFRW34XSSGDO.json","view_paper":"https://pith.science/paper/AUT66WRS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.11950&json=true","fetch_graph":"https://pith.science/api/pith-number/AUT66WRSLSK7OUNFRW34XSSGDO/graph.json","fetch_events":"https://pith.science/api/pith-number/AUT66WRSLSK7OUNFRW34XSSGDO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AUT66WRSLSK7OUNFRW34XSSGDO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AUT66WRSLSK7OUNFRW34XSSGDO/action/storage_attestation","attest_author":"https://pith.science/pith/AUT66WRSLSK7OUNFRW34XSSGDO/action/author_attestation","sign_citation":"https://pith.science/pith/AUT66WRSLSK7OUNFRW34XSSGDO/action/citation_signature","submit_replication":"https://pith.science/pith/AUT66WRSLSK7OUNFRW34XSSGDO/action/replication_record"}},"created_at":"2026-07-05T09:08:40.102374+00:00","updated_at":"2026-07-05T09:08:40.102374+00:00"}