{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AMZA6HQNQTBPMWKICMTQNK5CNO","short_pith_number":"pith:AMZA6HQN","canonical_record":{"source":{"id":"1509.00941","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-03T04:19:28Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"789e19886d60eb1b57a28d42f606c820fc6c7b1ce2bb74e7abd5a0731cc9d3ba","abstract_canon_sha256":"2fd282ebaae191ea53755c004faeb9a8b50544b6bf19e539ac710c1d6f992ee3"},"schema_version":"1.0"},"canonical_sha256":"03320f1e0d84c2f65948132706aba26b8206625d7b4a69521b4b060db032c7e1","source":{"kind":"arxiv","id":"1509.00941","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00941","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00941v2","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00941","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"AMZA6HQNQTBP","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AMZA6HQNQTBPMWKI","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AMZA6HQN","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AMZA6HQNQTBPMWKICMTQNK5CNO","target":"record","payload":{"canonical_record":{"source":{"id":"1509.00941","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-03T04:19:28Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"789e19886d60eb1b57a28d42f606c820fc6c7b1ce2bb74e7abd5a0731cc9d3ba","abstract_canon_sha256":"2fd282ebaae191ea53755c004faeb9a8b50544b6bf19e539ac710c1d6f992ee3"},"schema_version":"1.0"},"canonical_sha256":"03320f1e0d84c2f65948132706aba26b8206625d7b4a69521b4b060db032c7e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:38.294147Z","signature_b64":"w9DRSEs8QjnpqCIcOvHWW7qcRlMDfQMYTuqFHl2Wpd6QzhXJe6836ZeNbqs0nxCLuzCAp1Z7Hw4l5l/Dq4RvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03320f1e0d84c2f65948132706aba26b8206625d7b4a69521b4b060db032c7e1","last_reissued_at":"2026-05-18T00:13:38.293505Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:38.293505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.00941","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZRXJei13KwYfSD6Qmu2WNch6LVJzljU4yXQnvy5euujlFlMmscls3/2zVjYw0Do6a1nOiDfm0qCY0a7v+1AkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T00:57:43.494057Z"},"content_sha256":"398dc7e926197e88eccbd8f1e5cc195affd0026740339fcdd2b4944f06f4e1dd","schema_version":"1.0","event_id":"sha256:398dc7e926197e88eccbd8f1e5cc195affd0026740339fcdd2b4944f06f4e1dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AMZA6HQNQTBPMWKICMTQNK5CNO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abelian regular coverings of the quaternion hypermap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Kan Hu, Na-Er Wang","submitted_at":"2015-09-03T04:19:28Z","abstract_excerpt":"A hypermap is an embedding of a connected hypergraph into an orientable closed surface. A covering between hypermaps is a homomorphism between the embedded hypergraphs which extends to an orientation-preserving covering of the supporting surfaces. A covering of a hypermap onto itself is an automorphism, and a hypermap is regular if its automorphism group acts transitively on the brins. Depending on the algebraic theory of regular hypermaps and hypermap operations, the abelian regular coverings over the quaternion hypermap are investigated. We define normalized multicyclic coverings between reg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00941","kind":"arxiv","version":2},"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":"2026-05-18T00:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Aynpq7Ea0lZRNyTwS3tOTImHhjjMUE4vtIP43lXW0Sk0/9BAuIQdeuFam+iHJusjhbMlhcsL1O78IH4FQoyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T00:57:43.494447Z"},"content_sha256":"fe479f0b4bd8156463d88c46554399dd340d6866ac6710263e584a22c2a13be9","schema_version":"1.0","event_id":"sha256:fe479f0b4bd8156463d88c46554399dd340d6866ac6710263e584a22c2a13be9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AMZA6HQNQTBPMWKICMTQNK5CNO/bundle.json","state_url":"https://pith.science/pith/AMZA6HQNQTBPMWKICMTQNK5CNO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AMZA6HQNQTBPMWKICMTQNK5CNO/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":"2026-06-06T00:57:43Z","links":{"resolver":"https://pith.science/pith/AMZA6HQNQTBPMWKICMTQNK5CNO","bundle":"https://pith.science/pith/AMZA6HQNQTBPMWKICMTQNK5CNO/bundle.json","state":"https://pith.science/pith/AMZA6HQNQTBPMWKICMTQNK5CNO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AMZA6HQNQTBPMWKICMTQNK5CNO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AMZA6HQNQTBPMWKICMTQNK5CNO","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":"2fd282ebaae191ea53755c004faeb9a8b50544b6bf19e539ac710c1d6f992ee3","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-03T04:19:28Z","title_canon_sha256":"789e19886d60eb1b57a28d42f606c820fc6c7b1ce2bb74e7abd5a0731cc9d3ba"},"schema_version":"1.0","source":{"id":"1509.00941","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00941","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00941v2","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00941","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"AMZA6HQNQTBP","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AMZA6HQNQTBPMWKI","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AMZA6HQN","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:fe479f0b4bd8156463d88c46554399dd340d6866ac6710263e584a22c2a13be9","target":"graph","created_at":"2026-05-18T00:13:38Z","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 hypermap is an embedding of a connected hypergraph into an orientable closed surface. A covering between hypermaps is a homomorphism between the embedded hypergraphs which extends to an orientation-preserving covering of the supporting surfaces. A covering of a hypermap onto itself is an automorphism, and a hypermap is regular if its automorphism group acts transitively on the brins. Depending on the algebraic theory of regular hypermaps and hypermap operations, the abelian regular coverings over the quaternion hypermap are investigated. We define normalized multicyclic coverings between reg","authors_text":"Kan Hu, Na-Er Wang","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-03T04:19:28Z","title":"Abelian regular coverings of the quaternion hypermap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00941","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":"sha256:398dc7e926197e88eccbd8f1e5cc195affd0026740339fcdd2b4944f06f4e1dd","target":"record","created_at":"2026-05-18T00:13:38Z","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":"2fd282ebaae191ea53755c004faeb9a8b50544b6bf19e539ac710c1d6f992ee3","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-03T04:19:28Z","title_canon_sha256":"789e19886d60eb1b57a28d42f606c820fc6c7b1ce2bb74e7abd5a0731cc9d3ba"},"schema_version":"1.0","source":{"id":"1509.00941","kind":"arxiv","version":2}},"canonical_sha256":"03320f1e0d84c2f65948132706aba26b8206625d7b4a69521b4b060db032c7e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03320f1e0d84c2f65948132706aba26b8206625d7b4a69521b4b060db032c7e1","first_computed_at":"2026-05-18T00:13:38.293505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:38.293505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w9DRSEs8QjnpqCIcOvHWW7qcRlMDfQMYTuqFHl2Wpd6QzhXJe6836ZeNbqs0nxCLuzCAp1Z7Hw4l5l/Dq4RvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:38.294147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00941","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:398dc7e926197e88eccbd8f1e5cc195affd0026740339fcdd2b4944f06f4e1dd","sha256:fe479f0b4bd8156463d88c46554399dd340d6866ac6710263e584a22c2a13be9"],"state_sha256":"4cca29a061bc81833bf5296e1fcd0d46918a698ed0ca58fb52cf6e4f12a5520f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KHKbWtCfvBIhD4xjWvp4w3GJKe3pbwzHd7SCxkph0j4M2L52c8+rBE6nGO/6mPFK+eyF1I4vTC5FLkrYaUZfDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T00:57:43.496559Z","bundle_sha256":"9d7d4d9645729f4ae5a4d7135ec9cb9c44cab5cc50c939d77ff2a12e7105eae6"}}