{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4DIWASEXSCGNMKCYUIOAXQNK3H","short_pith_number":"pith:4DIWASEX","canonical_record":{"source":{"id":"1102.5156","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-25T04:52:59Z","cross_cats_sorted":[],"title_canon_sha256":"6ee29774e66ca635e8298180dd6e1dc2f1ecbc7b5f5e694082cc297d95cd034c","abstract_canon_sha256":"0e8915142bc0576dace7eafd5475e6568a521f06587f3cc71f2d07839335650a"},"schema_version":"1.0"},"canonical_sha256":"e0d1604897908cd62858a21c0bc1aad9d90debf638cc06a0d946e2ace822b00d","source":{"kind":"arxiv","id":"1102.5156","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5156","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5156v3","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5156","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"4DIWASEXSCGN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4DIWASEXSCGNMKCY","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4DIWASEX","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4DIWASEXSCGNMKCYUIOAXQNK3H","target":"record","payload":{"canonical_record":{"source":{"id":"1102.5156","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-25T04:52:59Z","cross_cats_sorted":[],"title_canon_sha256":"6ee29774e66ca635e8298180dd6e1dc2f1ecbc7b5f5e694082cc297d95cd034c","abstract_canon_sha256":"0e8915142bc0576dace7eafd5475e6568a521f06587f3cc71f2d07839335650a"},"schema_version":"1.0"},"canonical_sha256":"e0d1604897908cd62858a21c0bc1aad9d90debf638cc06a0d946e2ace822b00d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:12.500406Z","signature_b64":"qIIe/3oK9BOFqh+/xs30npfhCbQFj3YaYOCLucsGjCuEeyFJjEDq/Gj1Tx4wMRu5ynAMFTJB08EQBHr1kwaECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0d1604897908cd62858a21c0bc1aad9d90debf638cc06a0d946e2ace822b00d","last_reissued_at":"2026-05-18T03:52:12.499568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:12.499568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.5156","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":"2026-05-18T03:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFzyv+TY4+gK+spwasFmOZVQydS8no8XrdHiqI0lesZxBYnSwDps+I90yJR2oACfAHZ87WcRcNUOHpnTC1sBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:40:19.521398Z"},"content_sha256":"98dc111fec799dbb595a01cad86ecb6a9286f543e76309bd25983de61f95cc6f","schema_version":"1.0","event_id":"sha256:98dc111fec799dbb595a01cad86ecb6a9286f543e76309bd25983de61f95cc6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4DIWASEXSCGNMKCYUIOAXQNK3H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cayley graphs of order 30p are hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dave Witte Morris, Ebrahim Ghaderpour","submitted_at":"2011-02-25T04:52:59Z","abstract_excerpt":"Suppose G is a finite group of order 30p, where p is prime. We show that if S is any generating set of G, then there is a hamiltonian cycle in the corresponding Cayley graph Cay(G;S)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5156","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":"2026-05-18T03:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4HqbIoW2/lZdmYP/hKOTcQm+YkkgoXVd3WKYZ0i2ZH2ATXYW1EyyCJt6L9eHeH/MlctwmXn/EP4FXX/11n5mAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:40:19.521751Z"},"content_sha256":"2dadd306a390f9be47127b281ae6e2dbf01381f10d14b92330b2541c02029a93","schema_version":"1.0","event_id":"sha256:2dadd306a390f9be47127b281ae6e2dbf01381f10d14b92330b2541c02029a93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4DIWASEXSCGNMKCYUIOAXQNK3H/bundle.json","state_url":"https://pith.science/pith/4DIWASEXSCGNMKCYUIOAXQNK3H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4DIWASEXSCGNMKCYUIOAXQNK3H/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":"2026-06-24T09:40:19Z","links":{"resolver":"https://pith.science/pith/4DIWASEXSCGNMKCYUIOAXQNK3H","bundle":"https://pith.science/pith/4DIWASEXSCGNMKCYUIOAXQNK3H/bundle.json","state":"https://pith.science/pith/4DIWASEXSCGNMKCYUIOAXQNK3H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4DIWASEXSCGNMKCYUIOAXQNK3H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4DIWASEXSCGNMKCYUIOAXQNK3H","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":"0e8915142bc0576dace7eafd5475e6568a521f06587f3cc71f2d07839335650a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-25T04:52:59Z","title_canon_sha256":"6ee29774e66ca635e8298180dd6e1dc2f1ecbc7b5f5e694082cc297d95cd034c"},"schema_version":"1.0","source":{"id":"1102.5156","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5156","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5156v3","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5156","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"4DIWASEXSCGN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4DIWASEXSCGNMKCY","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4DIWASEX","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:2dadd306a390f9be47127b281ae6e2dbf01381f10d14b92330b2541c02029a93","target":"graph","created_at":"2026-05-18T03:52:12Z","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":"Suppose G is a finite group of order 30p, where p is prime. We show that if S is any generating set of G, then there is a hamiltonian cycle in the corresponding Cayley graph Cay(G;S).","authors_text":"Dave Witte Morris, Ebrahim Ghaderpour","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-25T04:52:59Z","title":"Cayley graphs of order 30p are hamiltonian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5156","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":"sha256:98dc111fec799dbb595a01cad86ecb6a9286f543e76309bd25983de61f95cc6f","target":"record","created_at":"2026-05-18T03:52:12Z","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":"0e8915142bc0576dace7eafd5475e6568a521f06587f3cc71f2d07839335650a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-25T04:52:59Z","title_canon_sha256":"6ee29774e66ca635e8298180dd6e1dc2f1ecbc7b5f5e694082cc297d95cd034c"},"schema_version":"1.0","source":{"id":"1102.5156","kind":"arxiv","version":3}},"canonical_sha256":"e0d1604897908cd62858a21c0bc1aad9d90debf638cc06a0d946e2ace822b00d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0d1604897908cd62858a21c0bc1aad9d90debf638cc06a0d946e2ace822b00d","first_computed_at":"2026-05-18T03:52:12.499568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:12.499568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qIIe/3oK9BOFqh+/xs30npfhCbQFj3YaYOCLucsGjCuEeyFJjEDq/Gj1Tx4wMRu5ynAMFTJB08EQBHr1kwaECg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:12.500406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5156","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98dc111fec799dbb595a01cad86ecb6a9286f543e76309bd25983de61f95cc6f","sha256:2dadd306a390f9be47127b281ae6e2dbf01381f10d14b92330b2541c02029a93"],"state_sha256":"1e0a0e8a9774c9976505cae90f43ce63164c4e1b198f929f405d4f65b8d9b71a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rblvs7SNYIof/N6hGM6lB+FDRkETD3B66sMkmvQ4VHVeCFl3VtZyAmFUQ3wGfMBLLgrSXV/NuZpr3EXsnZwwAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T09:40:19.523775Z","bundle_sha256":"f06e3449087d21ad5879f3e9e08659e636a033292e0d9d4960264c59f3dbe71d"}}