{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:CDJYD6WM3W6YNVUUIAAHHWZKZ6","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":"1ca145cf8a69c7d530a65d0845bafcfb7d64e7e4b72ecd4d70af11ece35cbe12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-26T15:40:28Z","title_canon_sha256":"895da9178dc016f7d4046483909a0d90759d38d57e9a76b2a7c5d9836852017e"},"schema_version":"1.0","source":{"id":"2010.13667","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.13667","created_at":"2026-07-05T01:48:13Z"},{"alias_kind":"arxiv_version","alias_value":"2010.13667v2","created_at":"2026-07-05T01:48:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.13667","created_at":"2026-07-05T01:48:13Z"},{"alias_kind":"pith_short_12","alias_value":"CDJYD6WM3W6Y","created_at":"2026-07-05T01:48:13Z"},{"alias_kind":"pith_short_16","alias_value":"CDJYD6WM3W6YNVUU","created_at":"2026-07-05T01:48:13Z"},{"alias_kind":"pith_short_8","alias_value":"CDJYD6WM","created_at":"2026-07-05T01:48:13Z"}],"graph_snapshots":[{"event_id":"sha256:a874b93f1432b2e48364a75943b9a3e3e7c1fea1be27f43fba8186265bbc4a49","target":"graph","created_at":"2026-07-05T01:48:13Z","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/2010.13667/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Combining P\\'{o}sa's rotation lemma with a technique of Kopylov in a novel approach, we prove a generalization of the Erd\\H{o}s-Gallai theorems on cycles and paths. This implies a clique version of the Erd\\H{o}s-Gallai stability theorems and also provides alternative proofs for some recent results.","authors_text":"Jie Ma, Long-tu Yuan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-26T15:40:28Z","title":"A clique version of the Erd\\H{o}s-Gallai stability theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.13667","kind":"arxiv","version":2},"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":"sha256:9999964addfb9060d4fe423dc77467a568b1f9d527532563aecc59ae7d9fddf6","target":"record","created_at":"2026-07-05T01:48:13Z","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":"1ca145cf8a69c7d530a65d0845bafcfb7d64e7e4b72ecd4d70af11ece35cbe12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-26T15:40:28Z","title_canon_sha256":"895da9178dc016f7d4046483909a0d90759d38d57e9a76b2a7c5d9836852017e"},"schema_version":"1.0","source":{"id":"2010.13667","kind":"arxiv","version":2}},"canonical_sha256":"10d381faccddbd86d694400073db2acf96443ffdd4dabc421d9e47a384691746","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10d381faccddbd86d694400073db2acf96443ffdd4dabc421d9e47a384691746","first_computed_at":"2026-07-05T01:48:13.943967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:48:13.943967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IBKxi34XfZWTP1qJdxIKOpA/+jojT7tvN6LPOfhqE9DUJFs1k89HSl0IPKqwp2mbISsZcjaIC7l+LQiyUKZCCA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:48:13.944410Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.13667","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9999964addfb9060d4fe423dc77467a568b1f9d527532563aecc59ae7d9fddf6","sha256:a874b93f1432b2e48364a75943b9a3e3e7c1fea1be27f43fba8186265bbc4a49"],"state_sha256":"3bc5d1a15df54cdf8e865726b65c0bf449b2d38d8bae3d6a64ec9144b74c055e"}