{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:G35JSI55NVSWDDZEIKOB63A7MJ","short_pith_number":"pith:G35JSI55","canonical_record":{"source":{"id":"1301.1512","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-08T12:42:57Z","cross_cats_sorted":[],"title_canon_sha256":"d3173570a67eda374e49107291117e884840ccdda278607c6af86171186d73cc","abstract_canon_sha256":"7c3e8ceff8c343c9c0889d69392c635445fc5d29f9fee6c9c06f0832a7d1ce9a"},"schema_version":"1.0"},"canonical_sha256":"36fa9923bd6d65618f24429c1f6c1f6265e805d429f07ce27860c181f681d892","source":{"kind":"arxiv","id":"1301.1512","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1512","created_at":"2026-05-18T03:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1512v4","created_at":"2026-05-18T03:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1512","created_at":"2026-05-18T03:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"G35JSI55NVSW","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G35JSI55NVSWDDZE","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G35JSI55","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:G35JSI55NVSWDDZEIKOB63A7MJ","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1512","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-08T12:42:57Z","cross_cats_sorted":[],"title_canon_sha256":"d3173570a67eda374e49107291117e884840ccdda278607c6af86171186d73cc","abstract_canon_sha256":"7c3e8ceff8c343c9c0889d69392c635445fc5d29f9fee6c9c06f0832a7d1ce9a"},"schema_version":"1.0"},"canonical_sha256":"36fa9923bd6d65618f24429c1f6c1f6265e805d429f07ce27860c181f681d892","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:13.916994Z","signature_b64":"4yo1eoh58KtPCJESJmbVcYxL6FI2tye9iYZY2gRo6pKOcYpcw0b/hd8LrPHKvD5Ep2tXur4b+cpNKidPbfkOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36fa9923bd6d65618f24429c1f6c1f6265e805d429f07ce27860c181f681d892","last_reissued_at":"2026-05-18T03:04:13.916511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:13.916511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1512","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bYG9H7wUyjA8BQbhovBPCnqBWU2W0Hu4XMkVeZAd/HeQwfDH63XRINfHfykNLC257N+pCa5y1pOYYYSfHgCBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:02:05.410895Z"},"content_sha256":"29a66dd0f0f766efaaca9a70c31a39fcaf9ebce64299b8a0d8020d746ea88e72","schema_version":"1.0","event_id":"sha256:29a66dd0f0f766efaaca9a70c31a39fcaf9ebce64299b8a0d8020d746ea88e72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:G35JSI55NVSWDDZEIKOB63A7MJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pairs of Fan-type heavy subgraphs for pancyclicity of 2-connected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Ning","submitted_at":"2013-01-08T12:42:57Z","abstract_excerpt":"A graph $G$ on $n$ vertices is Hamiltonian if it contains a spanning cycle, and pancyclic if it contains cycles of all lengths from 3 to $n$. In 1984, Fan presented a degree condition involving every pair of vertices at distance two for a 2-connected graph to be Hamiltonian. Motivated by Fan's result, we say that an induced subgraph $H$ of $G$ is $f_1$-heavy if for every pair of vertices $u,v\\in V(H)$, $d_{H}(u,v)=2$ implies $\\max\\{d(u),d(v)\\}\\geq (n+1)/2$. For a given graph $R$, $G$ is called $R$-$f_1$-heavy if every induced subgraph of $G$ isomorphic to $R$ is $f_1$-heavy. In this paper we s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1512","kind":"arxiv","version":4},"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":"2026-05-18T03:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0n72Uu0ZD0PQooD3f1fzuEyhM7NigYcuq47kK5P2xKnIhJvhGPmgcQEfn6SRCxRMiNsWnadrLgt0/3+9BGm2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:02:05.411241Z"},"content_sha256":"83a837078038141b7056ec9e94d51c76eb3721041cfb117ea54138fa73bd67f8","schema_version":"1.0","event_id":"sha256:83a837078038141b7056ec9e94d51c76eb3721041cfb117ea54138fa73bd67f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G35JSI55NVSWDDZEIKOB63A7MJ/bundle.json","state_url":"https://pith.science/pith/G35JSI55NVSWDDZEIKOB63A7MJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G35JSI55NVSWDDZEIKOB63A7MJ/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":"2026-06-04T17:02:05Z","links":{"resolver":"https://pith.science/pith/G35JSI55NVSWDDZEIKOB63A7MJ","bundle":"https://pith.science/pith/G35JSI55NVSWDDZEIKOB63A7MJ/bundle.json","state":"https://pith.science/pith/G35JSI55NVSWDDZEIKOB63A7MJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G35JSI55NVSWDDZEIKOB63A7MJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:G35JSI55NVSWDDZEIKOB63A7MJ","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":"7c3e8ceff8c343c9c0889d69392c635445fc5d29f9fee6c9c06f0832a7d1ce9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-08T12:42:57Z","title_canon_sha256":"d3173570a67eda374e49107291117e884840ccdda278607c6af86171186d73cc"},"schema_version":"1.0","source":{"id":"1301.1512","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1512","created_at":"2026-05-18T03:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1512v4","created_at":"2026-05-18T03:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1512","created_at":"2026-05-18T03:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"G35JSI55NVSW","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G35JSI55NVSWDDZE","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G35JSI55","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:83a837078038141b7056ec9e94d51c76eb3721041cfb117ea54138fa73bd67f8","target":"graph","created_at":"2026-05-18T03:04:13Z","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":"A graph $G$ on $n$ vertices is Hamiltonian if it contains a spanning cycle, and pancyclic if it contains cycles of all lengths from 3 to $n$. In 1984, Fan presented a degree condition involving every pair of vertices at distance two for a 2-connected graph to be Hamiltonian. Motivated by Fan's result, we say that an induced subgraph $H$ of $G$ is $f_1$-heavy if for every pair of vertices $u,v\\in V(H)$, $d_{H}(u,v)=2$ implies $\\max\\{d(u),d(v)\\}\\geq (n+1)/2$. For a given graph $R$, $G$ is called $R$-$f_1$-heavy if every induced subgraph of $G$ isomorphic to $R$ is $f_1$-heavy. In this paper we s","authors_text":"Bo Ning","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-08T12:42:57Z","title":"Pairs of Fan-type heavy subgraphs for pancyclicity of 2-connected graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1512","kind":"arxiv","version":4},"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":"sha256:29a66dd0f0f766efaaca9a70c31a39fcaf9ebce64299b8a0d8020d746ea88e72","target":"record","created_at":"2026-05-18T03:04:13Z","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":"7c3e8ceff8c343c9c0889d69392c635445fc5d29f9fee6c9c06f0832a7d1ce9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-08T12:42:57Z","title_canon_sha256":"d3173570a67eda374e49107291117e884840ccdda278607c6af86171186d73cc"},"schema_version":"1.0","source":{"id":"1301.1512","kind":"arxiv","version":4}},"canonical_sha256":"36fa9923bd6d65618f24429c1f6c1f6265e805d429f07ce27860c181f681d892","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36fa9923bd6d65618f24429c1f6c1f6265e805d429f07ce27860c181f681d892","first_computed_at":"2026-05-18T03:04:13.916511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:13.916511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4yo1eoh58KtPCJESJmbVcYxL6FI2tye9iYZY2gRo6pKOcYpcw0b/hd8LrPHKvD5Ep2tXur4b+cpNKidPbfkOBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:13.916994Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1512","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29a66dd0f0f766efaaca9a70c31a39fcaf9ebce64299b8a0d8020d746ea88e72","sha256:83a837078038141b7056ec9e94d51c76eb3721041cfb117ea54138fa73bd67f8"],"state_sha256":"0f325862c819f1406ec2f3590c9515fbc0d32ed08fa3548a7882fad1ef7bb908"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CR4POaQCgkL4uuq0Ke3JmHY/1hV19RUJnBwAelgQR8KVJ2dxe2bEDxjdmkS+mjXea8TeU1hnKxy2YaqwxPUYCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:02:05.413256Z","bundle_sha256":"771867171a245d46625acd7e309815fa4f32f2cc01d3b1148736424b2553d610"}}