{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AUT66WRSLSK7OUNFRW34XSSGDO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"071ccda705b5298a232d3fe98ae070e58fcce8e009eb6d90ed5a63697fd503f3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-09-18T13:05:30Z","title_canon_sha256":"ff2cf01a6970c5e0da9a59e0486c1ddede5ceee0359cd2fbeb41de6fc978c0de"},"schema_version":"1.0","source":{"id":"2409.11950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.11950","created_at":"2026-07-05T09:08:40Z"},{"alias_kind":"arxiv_version","alias_value":"2409.11950v1","created_at":"2026-07-05T09:08:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.11950","created_at":"2026-07-05T09:08:40Z"},{"alias_kind":"pith_short_12","alias_value":"AUT66WRSLSK7","created_at":"2026-07-05T09:08:40Z"},{"alias_kind":"pith_short_16","alias_value":"AUT66WRSLSK7OUNF","created_at":"2026-07-05T09:08:40Z"},{"alias_kind":"pith_short_8","alias_value":"AUT66WRS","created_at":"2026-07-05T09:08:40Z"}],"graph_snapshots":[{"event_id":"sha256:d2b4540dd05e3db54d1a834cf5dfb7674faf3d72287bd1480e0786e5d8a5bc08","target":"graph","created_at":"2026-07-05T09:08:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.11950/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Caiyun Hu, Jianfeng Hou, Xizhi Liu, Zian Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-09-18T13:05:30Z","title":"Generalized Andr\\'{a}sfai--Erd\\H{o}s--S\\'{o}s theorems for odd cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.11950","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c3cc52cf5afbd1b3a4fe40403e83bdefb381d6edb52630856d96ed6c45b90bb7","target":"record","created_at":"2026-07-05T09:08:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"071ccda705b5298a232d3fe98ae070e58fcce8e009eb6d90ed5a63697fd503f3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-09-18T13:05:30Z","title_canon_sha256":"ff2cf01a6970c5e0da9a59e0486c1ddede5ceee0359cd2fbeb41de6fc978c0de"},"schema_version":"1.0","source":{"id":"2409.11950","kind":"arxiv","version":1}},"canonical_sha256":"0527ef5a325c95f751a58db7cbca461bba57195577c07efeca69a04c1d6d3eb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0527ef5a325c95f751a58db7cbca461bba57195577c07efeca69a04c1d6d3eb3","first_computed_at":"2026-07-05T09:08:40.102321Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:08:40.102321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kmtXXBBAvkaiKFXT1FCvnUSEBx8nU4zl3Ur0IpUV6pz3MlGT+lpuuH7uMSDrCB/wFSAsf/KY8wLxSORpXLdEAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:08:40.102820Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.11950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3cc52cf5afbd1b3a4fe40403e83bdefb381d6edb52630856d96ed6c45b90bb7","sha256:d2b4540dd05e3db54d1a834cf5dfb7674faf3d72287bd1480e0786e5d8a5bc08"],"state_sha256":"0b24df6ca8920946f0c0debe3de4f57371600ed4a8cf680d495a7614b3e49f6b"}