{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZSFGZYSAKRIOIH537N6TRHF7Q7","short_pith_number":"pith:ZSFGZYSA","canonical_record":{"source":{"id":"1806.04370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-12T07:30:57Z","cross_cats_sorted":[],"title_canon_sha256":"1c538227829361c62d01cb4fed2dfbcf65f50a7a09931d1a7c4cdb735f89eec2","abstract_canon_sha256":"0d6211790eb3cc473a2f1062f6734a20d60b017f5b34e89aebb8bdeb2da7c5c5"},"schema_version":"1.0"},"canonical_sha256":"cc8a6ce2405450e41fbbfb7d389cbf87e2cef150560c7b1281cba790a758445a","source":{"kind":"arxiv","id":"1806.04370","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04370","created_at":"2026-05-18T00:13:35Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04370v1","created_at":"2026-05-18T00:13:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04370","created_at":"2026-05-18T00:13:35Z"},{"alias_kind":"pith_short_12","alias_value":"ZSFGZYSAKRIO","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZSFGZYSAKRIOIH53","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZSFGZYSA","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZSFGZYSAKRIOIH537N6TRHF7Q7","target":"record","payload":{"canonical_record":{"source":{"id":"1806.04370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-12T07:30:57Z","cross_cats_sorted":[],"title_canon_sha256":"1c538227829361c62d01cb4fed2dfbcf65f50a7a09931d1a7c4cdb735f89eec2","abstract_canon_sha256":"0d6211790eb3cc473a2f1062f6734a20d60b017f5b34e89aebb8bdeb2da7c5c5"},"schema_version":"1.0"},"canonical_sha256":"cc8a6ce2405450e41fbbfb7d389cbf87e2cef150560c7b1281cba790a758445a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:35.708632Z","signature_b64":"Km5dc/XBDEmPLmDjuTEgLYVPkVCOtHQSJA3NNeZmrKFQfbFqn/p0RW/jIy7mWF3IgKmULG9BafNmxRSgjLA3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc8a6ce2405450e41fbbfb7d389cbf87e2cef150560c7b1281cba790a758445a","last_reissued_at":"2026-05-18T00:13:35.707960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:35.707960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.04370","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":"2026-05-18T00:13:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"surayl0hUNOwanDV5UsqJcz//c7snfvK6PMs6OyYJ2zOnnsLrG0Wu4uHNyAToiH/d0W9VqJ16gR0KoF3ZR24CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:41:05.922736Z"},"content_sha256":"7f5cc13d05ee902cd18a1ef000ae80348d777566de3b0f46052775a07326a9f6","schema_version":"1.0","event_id":"sha256:7f5cc13d05ee902cd18a1ef000ae80348d777566de3b0f46052775a07326a9f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZSFGZYSAKRIOIH537N6TRHF7Q7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nilpotent groups of class two which underly a unique regular dessin","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kan Hu, Naer Wang, Roman Nedela","submitted_at":"2018-06-12T07:30:57Z","abstract_excerpt":"A dessin is an embedding of connected bipartite graph into an oriented closed surface. A dessin is regular if its group of colour- and orientation-preserving automorphisms acts transitively on the edges. In the present paper regular dessins with a nilpotent automorphism group are investigated, and attention are paid on those with the highest level of external symmetry. Depending on the algebraic theory of dessins and using group-theoretical methods, we present a classification of nilpotent groups of class two which underly a unique regular dessin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04370","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":"2026-05-18T00:13:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RYv7hU/iPpnesfXh6qZX1a7Idptr0+8CgSW8zt7zewq6h0W/MYWfktaij3CYpImzDZpM1rPZXUSYKYOqjI7zCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:41:05.923471Z"},"content_sha256":"31de25e631656f9ba6a3589775495f8f7847e53f31b9860db74d4d3ca2ecabb4","schema_version":"1.0","event_id":"sha256:31de25e631656f9ba6a3589775495f8f7847e53f31b9860db74d4d3ca2ecabb4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZSFGZYSAKRIOIH537N6TRHF7Q7/bundle.json","state_url":"https://pith.science/pith/ZSFGZYSAKRIOIH537N6TRHF7Q7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZSFGZYSAKRIOIH537N6TRHF7Q7/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":"2026-05-31T15:41:05Z","links":{"resolver":"https://pith.science/pith/ZSFGZYSAKRIOIH537N6TRHF7Q7","bundle":"https://pith.science/pith/ZSFGZYSAKRIOIH537N6TRHF7Q7/bundle.json","state":"https://pith.science/pith/ZSFGZYSAKRIOIH537N6TRHF7Q7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZSFGZYSAKRIOIH537N6TRHF7Q7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZSFGZYSAKRIOIH537N6TRHF7Q7","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":"0d6211790eb3cc473a2f1062f6734a20d60b017f5b34e89aebb8bdeb2da7c5c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-12T07:30:57Z","title_canon_sha256":"1c538227829361c62d01cb4fed2dfbcf65f50a7a09931d1a7c4cdb735f89eec2"},"schema_version":"1.0","source":{"id":"1806.04370","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04370","created_at":"2026-05-18T00:13:35Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04370v1","created_at":"2026-05-18T00:13:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04370","created_at":"2026-05-18T00:13:35Z"},{"alias_kind":"pith_short_12","alias_value":"ZSFGZYSAKRIO","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZSFGZYSAKRIOIH53","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZSFGZYSA","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:31de25e631656f9ba6a3589775495f8f7847e53f31b9860db74d4d3ca2ecabb4","target":"graph","created_at":"2026-05-18T00:13:35Z","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 dessin is an embedding of connected bipartite graph into an oriented closed surface. A dessin is regular if its group of colour- and orientation-preserving automorphisms acts transitively on the edges. In the present paper regular dessins with a nilpotent automorphism group are investigated, and attention are paid on those with the highest level of external symmetry. Depending on the algebraic theory of dessins and using group-theoretical methods, we present a classification of nilpotent groups of class two which underly a unique regular dessin.","authors_text":"Kan Hu, Naer Wang, Roman Nedela","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-12T07:30:57Z","title":"Nilpotent groups of class two which underly a unique regular dessin"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04370","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":"sha256:7f5cc13d05ee902cd18a1ef000ae80348d777566de3b0f46052775a07326a9f6","target":"record","created_at":"2026-05-18T00:13:35Z","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":"0d6211790eb3cc473a2f1062f6734a20d60b017f5b34e89aebb8bdeb2da7c5c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-12T07:30:57Z","title_canon_sha256":"1c538227829361c62d01cb4fed2dfbcf65f50a7a09931d1a7c4cdb735f89eec2"},"schema_version":"1.0","source":{"id":"1806.04370","kind":"arxiv","version":1}},"canonical_sha256":"cc8a6ce2405450e41fbbfb7d389cbf87e2cef150560c7b1281cba790a758445a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc8a6ce2405450e41fbbfb7d389cbf87e2cef150560c7b1281cba790a758445a","first_computed_at":"2026-05-18T00:13:35.707960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:35.707960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Km5dc/XBDEmPLmDjuTEgLYVPkVCOtHQSJA3NNeZmrKFQfbFqn/p0RW/jIy7mWF3IgKmULG9BafNmxRSgjLA3Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:35.708632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.04370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f5cc13d05ee902cd18a1ef000ae80348d777566de3b0f46052775a07326a9f6","sha256:31de25e631656f9ba6a3589775495f8f7847e53f31b9860db74d4d3ca2ecabb4"],"state_sha256":"c8e91e91f0d8f9f3c82aa4f3ffb2c85f8a4d2631465b9b1649a80371f17db883"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AIjDvpplGosW148G1gxUcVEyG/aQZ39vvcM8HynAWXHs+lgDslRPgfNpaLVWRpy52Hn86GU0Iy39Ve11LbTiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:41:05.926717Z","bundle_sha256":"6f84b9eafa483f16b75c2c43d327a998119f6ffd273b9debef1b4ec1f6258ffb"}}