{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UEKYUIQOXG4HFWI5RIKZ6N3KTJ","short_pith_number":"pith:UEKYUIQO","canonical_record":{"source":{"id":"1201.5317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-25T16:22:20Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b65eca6adf3f4c4f7d33aa24e4cf021420baaa8493c2047430994c8bfe21ebf0","abstract_canon_sha256":"abb90da96c11108308ea8a8a376a8dea24350e3a3953adde2cb1c369c6aff073"},"schema_version":"1.0"},"canonical_sha256":"a1158a220eb9b872d91d8a159f376a9a6d54725cf65cc16d4045cd94b7de9139","source":{"kind":"arxiv","id":"1201.5317","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5317","created_at":"2026-05-18T04:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5317v1","created_at":"2026-05-18T04:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5317","created_at":"2026-05-18T04:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"UEKYUIQOXG4H","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UEKYUIQOXG4HFWI5","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UEKYUIQO","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UEKYUIQOXG4HFWI5RIKZ6N3KTJ","target":"record","payload":{"canonical_record":{"source":{"id":"1201.5317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-25T16:22:20Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b65eca6adf3f4c4f7d33aa24e4cf021420baaa8493c2047430994c8bfe21ebf0","abstract_canon_sha256":"abb90da96c11108308ea8a8a376a8dea24350e3a3953adde2cb1c369c6aff073"},"schema_version":"1.0"},"canonical_sha256":"a1158a220eb9b872d91d8a159f376a9a6d54725cf65cc16d4045cd94b7de9139","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:55.064158Z","signature_b64":"tcSQl+lMdF2U8xL5uKf2wCuLaXDp8u+oTxVwP+PJ+LPeu3wOWV8aOX+enRxTl7LvYpM+RQzDqqcBMR7PA21wAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1158a220eb9b872d91d8a159f376a9a6d54725cf65cc16d4045cd94b7de9139","last_reissued_at":"2026-05-18T04:03:55.063459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:55.063459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.5317","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":"2026-05-18T04:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xQILqG9Onxq3jpyNs5a+7bGp6ZaffsI81CfNEXQ7/8AF6XFHtYL0EtnkVMRxHht6lxzxEobNj1doycPeE75BBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:19:35.302811Z"},"content_sha256":"ba61d5223df4965fe45423d714460534f7ad07614b391765817f7a6af5e81a1c","schema_version":"1.0","event_id":"sha256:ba61d5223df4965fe45423d714460534f7ad07614b391765817f7a6af5e81a1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UEKYUIQOXG4HFWI5RIKZ6N3KTJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cubic vertex-transitive graphs on up to 1280 vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Gabriel Verret, Pablo Spiga, Primoz Potocnik","submitted_at":"2012-01-25T16:22:20Z","abstract_excerpt":"A graph is called cubic and tetravalent if all of its vertices have valency 3 and 4, respectively. It is called vertex-transitive and arc-transitive if its automorphism group acts transitively on its vertex-set and on its arc- set, respectively. In this paper, we combine some new theoretical results with computer calculations to construct all cubic vertex-transitive graphs of order at most 1280. In the process, we also construct all tetravalent arc-transitive graphs of order at most 640."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5317","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":"2026-05-18T04:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g3SdKgSn8fxtehpgCJq7pyKyWQKcpFOs97WKBddtZM/DVnF0HLPQLAdDdU+mYsGjhU2sXygn2eSG2jPwyDS9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:19:35.303159Z"},"content_sha256":"848bb94c19ebfeaef2569c0e8bdb9f2e6881c0663ba81d2c444685609ea4eb58","schema_version":"1.0","event_id":"sha256:848bb94c19ebfeaef2569c0e8bdb9f2e6881c0663ba81d2c444685609ea4eb58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEKYUIQOXG4HFWI5RIKZ6N3KTJ/bundle.json","state_url":"https://pith.science/pith/UEKYUIQOXG4HFWI5RIKZ6N3KTJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEKYUIQOXG4HFWI5RIKZ6N3KTJ/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":"2026-06-20T11:19:35Z","links":{"resolver":"https://pith.science/pith/UEKYUIQOXG4HFWI5RIKZ6N3KTJ","bundle":"https://pith.science/pith/UEKYUIQOXG4HFWI5RIKZ6N3KTJ/bundle.json","state":"https://pith.science/pith/UEKYUIQOXG4HFWI5RIKZ6N3KTJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEKYUIQOXG4HFWI5RIKZ6N3KTJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UEKYUIQOXG4HFWI5RIKZ6N3KTJ","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":"abb90da96c11108308ea8a8a376a8dea24350e3a3953adde2cb1c369c6aff073","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-25T16:22:20Z","title_canon_sha256":"b65eca6adf3f4c4f7d33aa24e4cf021420baaa8493c2047430994c8bfe21ebf0"},"schema_version":"1.0","source":{"id":"1201.5317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5317","created_at":"2026-05-18T04:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5317v1","created_at":"2026-05-18T04:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5317","created_at":"2026-05-18T04:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"UEKYUIQOXG4H","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UEKYUIQOXG4HFWI5","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UEKYUIQO","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:848bb94c19ebfeaef2569c0e8bdb9f2e6881c0663ba81d2c444685609ea4eb58","target":"graph","created_at":"2026-05-18T04:03:55Z","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 graph is called cubic and tetravalent if all of its vertices have valency 3 and 4, respectively. It is called vertex-transitive and arc-transitive if its automorphism group acts transitively on its vertex-set and on its arc- set, respectively. In this paper, we combine some new theoretical results with computer calculations to construct all cubic vertex-transitive graphs of order at most 1280. In the process, we also construct all tetravalent arc-transitive graphs of order at most 640.","authors_text":"Gabriel Verret, Pablo Spiga, Primoz Potocnik","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-25T16:22:20Z","title":"Cubic vertex-transitive graphs on up to 1280 vertices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5317","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:ba61d5223df4965fe45423d714460534f7ad07614b391765817f7a6af5e81a1c","target":"record","created_at":"2026-05-18T04:03:55Z","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":"abb90da96c11108308ea8a8a376a8dea24350e3a3953adde2cb1c369c6aff073","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-25T16:22:20Z","title_canon_sha256":"b65eca6adf3f4c4f7d33aa24e4cf021420baaa8493c2047430994c8bfe21ebf0"},"schema_version":"1.0","source":{"id":"1201.5317","kind":"arxiv","version":1}},"canonical_sha256":"a1158a220eb9b872d91d8a159f376a9a6d54725cf65cc16d4045cd94b7de9139","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1158a220eb9b872d91d8a159f376a9a6d54725cf65cc16d4045cd94b7de9139","first_computed_at":"2026-05-18T04:03:55.063459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:55.063459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tcSQl+lMdF2U8xL5uKf2wCuLaXDp8u+oTxVwP+PJ+LPeu3wOWV8aOX+enRxTl7LvYpM+RQzDqqcBMR7PA21wAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:55.064158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba61d5223df4965fe45423d714460534f7ad07614b391765817f7a6af5e81a1c","sha256:848bb94c19ebfeaef2569c0e8bdb9f2e6881c0663ba81d2c444685609ea4eb58"],"state_sha256":"85e2fe588489579b65054462a53465af43b614f2056cc7e36219a9e633c50298"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IikBScgpizCOadQgYMhLL7rH82uXv8TvhHF0TQmGHweSw2aXOLhOp2WfgyuWdDbcIE/lnK3f2qp3pUCdb01+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T11:19:35.305111Z","bundle_sha256":"549331b66a95a6339c723d3ad68fa3fff5f8a22acdaa506246c940f575e4f91d"}}