{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OYVS2BHV63CDWBTLREACLIHIUZ","short_pith_number":"pith:OYVS2BHV","canonical_record":{"source":{"id":"1506.02795","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T06:36:54Z","cross_cats_sorted":[],"title_canon_sha256":"d24332f43af61efb9839e4b58e18fa40a8e0023b9d376bd46a2bd18bc86626fb","abstract_canon_sha256":"a6e35059480670ce8c779f027e58fdd5506b1ae1b1f01dc3702f399583a94ab7"},"schema_version":"1.0"},"canonical_sha256":"762b2d04f5f6c43b066b890025a0e8a66d3087932ed5fd3c64b13db024145b0a","source":{"kind":"arxiv","id":"1506.02795","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02795","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02795v3","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02795","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"OYVS2BHV63CD","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OYVS2BHV63CDWBTL","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OYVS2BHV","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OYVS2BHV63CDWBTLREACLIHIUZ","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02795","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T06:36:54Z","cross_cats_sorted":[],"title_canon_sha256":"d24332f43af61efb9839e4b58e18fa40a8e0023b9d376bd46a2bd18bc86626fb","abstract_canon_sha256":"a6e35059480670ce8c779f027e58fdd5506b1ae1b1f01dc3702f399583a94ab7"},"schema_version":"1.0"},"canonical_sha256":"762b2d04f5f6c43b066b890025a0e8a66d3087932ed5fd3c64b13db024145b0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:13.602207Z","signature_b64":"/ytD3gQySd0HGmzGLVX13ucV6DAOPM+xn0Ya0X8Vx53A538eo32P3BuM76cTe282VAhYa+A1p/eIzqb5P9cjCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"762b2d04f5f6c43b066b890025a0e8a66d3087932ed5fd3c64b13db024145b0a","last_reissued_at":"2026-05-18T00:42:13.601614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:13.601614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02795","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gd60IKG9Ry3R3H8iI7wf7qQw7JCzB1PoE9UftKYJOHGmw8m+kFLcDjH3T1uErQH4OOXXLiv349ISJnpVv4NIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:05:52.346304Z"},"content_sha256":"1101f1370f6b6da6768e739f2fdebe277055807ad6480b0a50e18ba2dd3180fb","schema_version":"1.0","event_id":"sha256:1101f1370f6b6da6768e739f2fdebe277055807ad6480b0a50e18ba2dd3180fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OYVS2BHV63CDWBTLREACLIHIUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heavy subgraphs, stability and hamiltonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Binlong Li, Bo Ning","submitted_at":"2015-06-09T06:36:54Z","abstract_excerpt":"Let $G$ be a graph. Adopting the terminology of Broersma et al. and \\v{C}ada, respectively, we say that $G$ is 2-heavy if every induced claw ($K_{1,3}$) of $G$ contains two end-vertices each one has degree at least $|V(G)|/2$; and $G$ is o-heavy if every induced claw of $G$ contains two end-vertices with degree sum at least $|V(G)|$ in $G$. In this paper, we introduce a new concept, and say that $G$ is \\emph{$S$-c-heavy} if for a given graph $S$ and every induced subgraph $G'$ of $G$ isomorphic to $S$ and every maximal clique $C$ of $G'$, every non-trivial component of $G'-C$ contains a vertex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02795","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MyuKrfPxtES/s74KfxayWUklgGecAOU3zayDMTS0tDc4KP7J7i/50zNGkYWnfvw2R6YAn+5/2MMEwbtEhOtXCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:05:52.346678Z"},"content_sha256":"e88419a7e2e7ab22207227a6bae762e32efd7da3fb93f9b93e42107e7c56aae1","schema_version":"1.0","event_id":"sha256:e88419a7e2e7ab22207227a6bae762e32efd7da3fb93f9b93e42107e7c56aae1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OYVS2BHV63CDWBTLREACLIHIUZ/bundle.json","state_url":"https://pith.science/pith/OYVS2BHV63CDWBTLREACLIHIUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OYVS2BHV63CDWBTLREACLIHIUZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T19:05:52Z","links":{"resolver":"https://pith.science/pith/OYVS2BHV63CDWBTLREACLIHIUZ","bundle":"https://pith.science/pith/OYVS2BHV63CDWBTLREACLIHIUZ/bundle.json","state":"https://pith.science/pith/OYVS2BHV63CDWBTLREACLIHIUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OYVS2BHV63CDWBTLREACLIHIUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OYVS2BHV63CDWBTLREACLIHIUZ","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":"a6e35059480670ce8c779f027e58fdd5506b1ae1b1f01dc3702f399583a94ab7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T06:36:54Z","title_canon_sha256":"d24332f43af61efb9839e4b58e18fa40a8e0023b9d376bd46a2bd18bc86626fb"},"schema_version":"1.0","source":{"id":"1506.02795","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02795","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02795v3","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02795","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"OYVS2BHV63CD","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OYVS2BHV63CDWBTL","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OYVS2BHV","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:e88419a7e2e7ab22207227a6bae762e32efd7da3fb93f9b93e42107e7c56aae1","target":"graph","created_at":"2026-05-18T00:42:13Z","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"},"paper":{"abstract_excerpt":"Let $G$ be a graph. Adopting the terminology of Broersma et al. and \\v{C}ada, respectively, we say that $G$ is 2-heavy if every induced claw ($K_{1,3}$) of $G$ contains two end-vertices each one has degree at least $|V(G)|/2$; and $G$ is o-heavy if every induced claw of $G$ contains two end-vertices with degree sum at least $|V(G)|$ in $G$. In this paper, we introduce a new concept, and say that $G$ is \\emph{$S$-c-heavy} if for a given graph $S$ and every induced subgraph $G'$ of $G$ isomorphic to $S$ and every maximal clique $C$ of $G'$, every non-trivial component of $G'-C$ contains a vertex","authors_text":"Binlong Li, Bo Ning","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T06:36:54Z","title":"Heavy subgraphs, stability and hamiltonicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02795","kind":"arxiv","version":3},"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":"sha256:1101f1370f6b6da6768e739f2fdebe277055807ad6480b0a50e18ba2dd3180fb","target":"record","created_at":"2026-05-18T00:42:13Z","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":"a6e35059480670ce8c779f027e58fdd5506b1ae1b1f01dc3702f399583a94ab7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T06:36:54Z","title_canon_sha256":"d24332f43af61efb9839e4b58e18fa40a8e0023b9d376bd46a2bd18bc86626fb"},"schema_version":"1.0","source":{"id":"1506.02795","kind":"arxiv","version":3}},"canonical_sha256":"762b2d04f5f6c43b066b890025a0e8a66d3087932ed5fd3c64b13db024145b0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"762b2d04f5f6c43b066b890025a0e8a66d3087932ed5fd3c64b13db024145b0a","first_computed_at":"2026-05-18T00:42:13.601614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:13.601614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/ytD3gQySd0HGmzGLVX13ucV6DAOPM+xn0Ya0X8Vx53A538eo32P3BuM76cTe282VAhYa+A1p/eIzqb5P9cjCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:13.602207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02795","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1101f1370f6b6da6768e739f2fdebe277055807ad6480b0a50e18ba2dd3180fb","sha256:e88419a7e2e7ab22207227a6bae762e32efd7da3fb93f9b93e42107e7c56aae1"],"state_sha256":"f24972b979869ddfb0c3ffb9823497af8ecc8a2ffd7461fef58b27c04f125af7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"McahL5VVA7Kzo+SBzCDVrY+Ne5hqeO469MkcXRdBAEG9+VYxC4Ziv3jCw3kKehb2Bbw2fEunDk7GPrlap74VDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:05:52.348694Z","bundle_sha256":"11ef716f883724f34cdad3a373a7f6f73433d34344c2181a387b770455870509"}}