{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4EEP7SFNHSEI73BQ2ZUT3GL4SR","short_pith_number":"pith:4EEP7SFN","canonical_record":{"source":{"id":"1312.1106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-04T11:02:43Z","cross_cats_sorted":[],"title_canon_sha256":"6a60c43e6774628bf9e65a9c99c8cfd9af9db800f255f76a64b3ed787c10fa41","abstract_canon_sha256":"618894971278a1a8dfafcf232068de3229ed132749331afd0a6cddeb4f1a25ce"},"schema_version":"1.0"},"canonical_sha256":"e108ffc8ad3c888fec30d6693d997c94681ff65633329303947cb95de6500d85","source":{"kind":"arxiv","id":"1312.1106","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1106","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1106v1","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1106","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"4EEP7SFNHSEI","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"4EEP7SFNHSEI73BQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"4EEP7SFN","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4EEP7SFNHSEI73BQ2ZUT3GL4SR","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-04T11:02:43Z","cross_cats_sorted":[],"title_canon_sha256":"6a60c43e6774628bf9e65a9c99c8cfd9af9db800f255f76a64b3ed787c10fa41","abstract_canon_sha256":"618894971278a1a8dfafcf232068de3229ed132749331afd0a6cddeb4f1a25ce"},"schema_version":"1.0"},"canonical_sha256":"e108ffc8ad3c888fec30d6693d997c94681ff65633329303947cb95de6500d85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:34.972989Z","signature_b64":"wnYVx1TkaDsTqzjDKqSsd94NzIgfzA+XKok8ovJfBvmvxODiCLHFDG+Q+3ezwSgOJy6x+qw0/dIBWSXwp9kBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e108ffc8ad3c888fec30d6693d997c94681ff65633329303947cb95de6500d85","last_reissued_at":"2026-05-18T03:05:34.972636Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:34.972636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1106","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sf4C1vtWdcgHNVlrTpMyi7pMI7hJsH1CEQuJxAuHX4CUiemBAaSoFNkvL3ZMGKcEcmnLs9VrtBZC5alCPjMKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:42:22.219527Z"},"content_sha256":"b2679d59c7652aa550573ac50b8b2b76b3c2ff46de8662a5cb4f40e2e1e8d8b9","schema_version":"1.0","event_id":"sha256:b2679d59c7652aa550573ac50b8b2b76b3c2ff46de8662a5cb4f40e2e1e8d8b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4EEP7SFNHSEI73BQ2ZUT3GL4SR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Cycle Spectrum of Claw-free Hamiltonian Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dieter Rautenbach, Felix Joos, Jonas Eckert","submitted_at":"2013-12-04T11:02:43Z","abstract_excerpt":"If $G$ is a claw-free hamiltonian graph of order $n$ and maximum degree $\\Delta$ with $\\Delta\\geq 24$, then $G$ has cycles of at least $\\min\\left\\{ n,\\left\\lceil\\frac{3}{2}\\Delta\\right\\rceil\\right\\}-2$ many different lengths."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1106","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":""},"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":"2026-05-18T03:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eV3wIRw48cq4ZD9Fp91IosOGNaaz1hvQw24yNhaZS3KdQucEHT/9XALca1HfxywWxu/JH33Oc5d4yYbD2J2aCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:42:22.219869Z"},"content_sha256":"aab218eb69d17dbc6b94c1d2725dd56beddbdc852821eb5214751312fe7a9b6c","schema_version":"1.0","event_id":"sha256:aab218eb69d17dbc6b94c1d2725dd56beddbdc852821eb5214751312fe7a9b6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4EEP7SFNHSEI73BQ2ZUT3GL4SR/bundle.json","state_url":"https://pith.science/pith/4EEP7SFNHSEI73BQ2ZUT3GL4SR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4EEP7SFNHSEI73BQ2ZUT3GL4SR/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":"2026-06-04T03:42:22Z","links":{"resolver":"https://pith.science/pith/4EEP7SFNHSEI73BQ2ZUT3GL4SR","bundle":"https://pith.science/pith/4EEP7SFNHSEI73BQ2ZUT3GL4SR/bundle.json","state":"https://pith.science/pith/4EEP7SFNHSEI73BQ2ZUT3GL4SR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4EEP7SFNHSEI73BQ2ZUT3GL4SR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4EEP7SFNHSEI73BQ2ZUT3GL4SR","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":"618894971278a1a8dfafcf232068de3229ed132749331afd0a6cddeb4f1a25ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-04T11:02:43Z","title_canon_sha256":"6a60c43e6774628bf9e65a9c99c8cfd9af9db800f255f76a64b3ed787c10fa41"},"schema_version":"1.0","source":{"id":"1312.1106","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1106","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1106v1","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1106","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"4EEP7SFNHSEI","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"4EEP7SFNHSEI73BQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"4EEP7SFN","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:aab218eb69d17dbc6b94c1d2725dd56beddbdc852821eb5214751312fe7a9b6c","target":"graph","created_at":"2026-05-18T03:05:34Z","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":"If $G$ is a claw-free hamiltonian graph of order $n$ and maximum degree $\\Delta$ with $\\Delta\\geq 24$, then $G$ has cycles of at least $\\min\\left\\{ n,\\left\\lceil\\frac{3}{2}\\Delta\\right\\rceil\\right\\}-2$ many different lengths.","authors_text":"Dieter Rautenbach, Felix Joos, Jonas Eckert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-04T11:02:43Z","title":"The Cycle Spectrum of Claw-free Hamiltonian Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1106","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:b2679d59c7652aa550573ac50b8b2b76b3c2ff46de8662a5cb4f40e2e1e8d8b9","target":"record","created_at":"2026-05-18T03:05:34Z","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":"618894971278a1a8dfafcf232068de3229ed132749331afd0a6cddeb4f1a25ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-04T11:02:43Z","title_canon_sha256":"6a60c43e6774628bf9e65a9c99c8cfd9af9db800f255f76a64b3ed787c10fa41"},"schema_version":"1.0","source":{"id":"1312.1106","kind":"arxiv","version":1}},"canonical_sha256":"e108ffc8ad3c888fec30d6693d997c94681ff65633329303947cb95de6500d85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e108ffc8ad3c888fec30d6693d997c94681ff65633329303947cb95de6500d85","first_computed_at":"2026-05-18T03:05:34.972636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:34.972636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wnYVx1TkaDsTqzjDKqSsd94NzIgfzA+XKok8ovJfBvmvxODiCLHFDG+Q+3ezwSgOJy6x+qw0/dIBWSXwp9kBBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:34.972989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1106","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2679d59c7652aa550573ac50b8b2b76b3c2ff46de8662a5cb4f40e2e1e8d8b9","sha256:aab218eb69d17dbc6b94c1d2725dd56beddbdc852821eb5214751312fe7a9b6c"],"state_sha256":"33736748ec373a4045874101c2dd924d69343b1baacff97493f8b2ce7889d4ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EAszSlsDssnwwH587r1CNAM93zh0s0oYbunAOYlL+HdRp0/IPtWLbF0ThZPYOWI7hB73P1ylAROpd93G5Y1sDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:42:22.221811Z","bundle_sha256":"57e2a630467b9eddaa51d12e003d287a4b01895225ad388b99eb5f127cdaa9a2"}}