{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DKWJMSC2DYZWLUGVIP27GRCM4X","short_pith_number":"pith:DKWJMSC2","canonical_record":{"source":{"id":"1906.09367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-22T02:06:46Z","cross_cats_sorted":[],"title_canon_sha256":"6970e9df9b32d4acbfbe614dd92474f712eb490dcc24f2d0854f7328287d7d75","abstract_canon_sha256":"bf564521b40eff4c8dc912de512800fb9eb247b43a46003941e657ffe7900cd9"},"schema_version":"1.0"},"canonical_sha256":"1aac96485a1e3365d0d543f5f3444ce5c68c7e30081bfbea7e932519f4c5c1e3","source":{"kind":"arxiv","id":"1906.09367","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09367","created_at":"2026-05-17T23:42:38Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09367v1","created_at":"2026-05-17T23:42:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09367","created_at":"2026-05-17T23:42:38Z"},{"alias_kind":"pith_short_12","alias_value":"DKWJMSC2DYZW","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DKWJMSC2DYZWLUGV","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DKWJMSC2","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DKWJMSC2DYZWLUGVIP27GRCM4X","target":"record","payload":{"canonical_record":{"source":{"id":"1906.09367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-22T02:06:46Z","cross_cats_sorted":[],"title_canon_sha256":"6970e9df9b32d4acbfbe614dd92474f712eb490dcc24f2d0854f7328287d7d75","abstract_canon_sha256":"bf564521b40eff4c8dc912de512800fb9eb247b43a46003941e657ffe7900cd9"},"schema_version":"1.0"},"canonical_sha256":"1aac96485a1e3365d0d543f5f3444ce5c68c7e30081bfbea7e932519f4c5c1e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:38.362597Z","signature_b64":"mUToX/sLzygfOTkVLqUAK2iVRy9eU02507+uwJh7Ps1BmkUZPZcNjgPtHRlXc+JPL8gfoTWi9zqX1KAAkiTEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1aac96485a1e3365d0d543f5f3444ce5c68c7e30081bfbea7e932519f4c5c1e3","last_reissued_at":"2026-05-17T23:42:38.361919Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:38.361919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.09367","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":"2026-05-17T23:42:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yHkRpJm0Fg21qtdpoj/xE1OiYK+1KHf5UAzrIpFA5AHyGJBhtJFYK6jI8iOPpBmHjS9sFu6ZxTGWp/zE0mc+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:55:10.500639Z"},"content_sha256":"21d626149193a60eef444dbb4a37011dd661abd094a55a068b0bc9599f0e32f2","schema_version":"1.0","event_id":"sha256:21d626149193a60eef444dbb4a37011dd661abd094a55a068b0bc9599f0e32f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DKWJMSC2DYZWLUGVIP27GRCM4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trivalent dihedrants and bi-dihedrants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jin-Xin Zhou, Mi-Mi Zhang","submitted_at":"2019-06-22T02:06:46Z","abstract_excerpt":"A Cayley (resp. bi-Cayley) graph on a dihedral group is called a {\\em dihedrant} (resp. {\\em bi-dihedrant}). In 2000, a classification of trivalent arc-transitive dihedrants was given by Maru\\v si\\v c and Pisanski, and several years later, trivalent non-arc-transitive dihedrants of order $4p$ or $8p$ $(p$ a prime) were classified by Feng et al. As a generalization of these results, our first result presents a classification of trivalent non-arc-transitive dihedrants. Using this, a complete classification of trivalent vertex-transitive non-Cayley bi-dihedrants is given, thus completing the stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09367","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":"2026-05-17T23:42:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8te4EjFVZ7pO+DaSUnhiQf6SoQHrL19LGgqqolpnl4MG/ywiLnOPMFn+84csjmqBbiEFYpBQLf402Uh3UkanCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:55:10.500985Z"},"content_sha256":"7d81ec8a5f357476d18ca4e4b15c377b2295a058d7e775bd18c7dc31713dea2d","schema_version":"1.0","event_id":"sha256:7d81ec8a5f357476d18ca4e4b15c377b2295a058d7e775bd18c7dc31713dea2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKWJMSC2DYZWLUGVIP27GRCM4X/bundle.json","state_url":"https://pith.science/pith/DKWJMSC2DYZWLUGVIP27GRCM4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKWJMSC2DYZWLUGVIP27GRCM4X/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":"2026-06-26T16:55:10Z","links":{"resolver":"https://pith.science/pith/DKWJMSC2DYZWLUGVIP27GRCM4X","bundle":"https://pith.science/pith/DKWJMSC2DYZWLUGVIP27GRCM4X/bundle.json","state":"https://pith.science/pith/DKWJMSC2DYZWLUGVIP27GRCM4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKWJMSC2DYZWLUGVIP27GRCM4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DKWJMSC2DYZWLUGVIP27GRCM4X","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":"bf564521b40eff4c8dc912de512800fb9eb247b43a46003941e657ffe7900cd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-22T02:06:46Z","title_canon_sha256":"6970e9df9b32d4acbfbe614dd92474f712eb490dcc24f2d0854f7328287d7d75"},"schema_version":"1.0","source":{"id":"1906.09367","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09367","created_at":"2026-05-17T23:42:38Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09367v1","created_at":"2026-05-17T23:42:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09367","created_at":"2026-05-17T23:42:38Z"},{"alias_kind":"pith_short_12","alias_value":"DKWJMSC2DYZW","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DKWJMSC2DYZWLUGV","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DKWJMSC2","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:7d81ec8a5f357476d18ca4e4b15c377b2295a058d7e775bd18c7dc31713dea2d","target":"graph","created_at":"2026-05-17T23:42:38Z","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 Cayley (resp. bi-Cayley) graph on a dihedral group is called a {\\em dihedrant} (resp. {\\em bi-dihedrant}). In 2000, a classification of trivalent arc-transitive dihedrants was given by Maru\\v si\\v c and Pisanski, and several years later, trivalent non-arc-transitive dihedrants of order $4p$ or $8p$ $(p$ a prime) were classified by Feng et al. As a generalization of these results, our first result presents a classification of trivalent non-arc-transitive dihedrants. Using this, a complete classification of trivalent vertex-transitive non-Cayley bi-dihedrants is given, thus completing the stud","authors_text":"Jin-Xin Zhou, Mi-Mi Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-22T02:06:46Z","title":"Trivalent dihedrants and bi-dihedrants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09367","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":"sha256:21d626149193a60eef444dbb4a37011dd661abd094a55a068b0bc9599f0e32f2","target":"record","created_at":"2026-05-17T23:42:38Z","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":"bf564521b40eff4c8dc912de512800fb9eb247b43a46003941e657ffe7900cd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-22T02:06:46Z","title_canon_sha256":"6970e9df9b32d4acbfbe614dd92474f712eb490dcc24f2d0854f7328287d7d75"},"schema_version":"1.0","source":{"id":"1906.09367","kind":"arxiv","version":1}},"canonical_sha256":"1aac96485a1e3365d0d543f5f3444ce5c68c7e30081bfbea7e932519f4c5c1e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1aac96485a1e3365d0d543f5f3444ce5c68c7e30081bfbea7e932519f4c5c1e3","first_computed_at":"2026-05-17T23:42:38.361919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:38.361919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mUToX/sLzygfOTkVLqUAK2iVRy9eU02507+uwJh7Ps1BmkUZPZcNjgPtHRlXc+JPL8gfoTWi9zqX1KAAkiTEDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:38.362597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09367","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21d626149193a60eef444dbb4a37011dd661abd094a55a068b0bc9599f0e32f2","sha256:7d81ec8a5f357476d18ca4e4b15c377b2295a058d7e775bd18c7dc31713dea2d"],"state_sha256":"7bda124c57b65c48b5f0ab2ebb39edf0284bd1efc0e29082b3e0870b218ad7c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W8+alJ/y+T7RT7pcRGaGZzU4B3ZgnANmu7sO3MImB+dhUoPKqOwtNDg45B/HFjzZp4II7IWbmhIyieLz1nEXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T16:55:10.502895Z","bundle_sha256":"0d4876ac19081053881b0b3f9ed54eea9fa7deb8e4c24d25dcb20e2548bf7fa7"}}