{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:J5ELNFICPF4OC5RKPNZM7NK6IO","short_pith_number":"pith:J5ELNFIC","canonical_record":{"source":{"id":"1211.4642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-11-20T01:03:50Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ac554174a5b713751bdc14d64920acc25e4eae3bcf9bc3d2afdef9ceb76f8feb","abstract_canon_sha256":"c490d41072ee931e5eef39322a028dfe77c677b3299838390b522d0ac98883df"},"schema_version":"1.0"},"canonical_sha256":"4f48b695027978e1762a7b72cfb55e43aa63d2b1c1be3a878e0d89d54420ab61","source":{"kind":"arxiv","id":"1211.4642","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4642","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4642v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4642","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"J5ELNFICPF4O","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"J5ELNFICPF4OC5RK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"J5ELNFIC","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:J5ELNFICPF4OC5RKPNZM7NK6IO","target":"record","payload":{"canonical_record":{"source":{"id":"1211.4642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-11-20T01:03:50Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ac554174a5b713751bdc14d64920acc25e4eae3bcf9bc3d2afdef9ceb76f8feb","abstract_canon_sha256":"c490d41072ee931e5eef39322a028dfe77c677b3299838390b522d0ac98883df"},"schema_version":"1.0"},"canonical_sha256":"4f48b695027978e1762a7b72cfb55e43aa63d2b1c1be3a878e0d89d54420ab61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:26.072382Z","signature_b64":"Ph/vqHZhrX550MCxw69PXRx6v7+sZ456xfUNUsjnZfslR2NOB0y8EJ3I8oMKuEjWBcIKDjgmXQBA3A4PG8jiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f48b695027978e1762a7b72cfb55e43aa63d2b1c1be3a878e0d89d54420ab61","last_reissued_at":"2026-05-18T03:40:26.071779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:26.071779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.4642","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":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FZPoCEk0C1m2aRgZFP5mDrJtdryValQuIt7JpMTHMqps6sVat1UkSk8FkPMExgpQvkbCqQhXh+K/elTaP5PTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:40:58.738369Z"},"content_sha256":"80fc85c86baf99ae13c7a3fb411f49d70c8c1d910fa6947aef44faca78d652f4","schema_version":"1.0","event_id":"sha256:80fc85c86baf99ae13c7a3fb411f49d70c8c1d910fa6947aef44faca78d652f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:J5ELNFICPF4OC5RKPNZM7NK6IO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The crossing number of pancake graph $P_4$ is six","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Baigong Zheng, Bo Lv, Ke Zhang, Xirong Xu, Yuansheng Yang","submitted_at":"2012-11-20T01:03:50Z","abstract_excerpt":"The {\\it crossing number} of a graph $G$ is the least number of pairwise crossings of edges among all the drawings of $G$ in the plane. The pancake graph is an important topology for interconnecting processors in parallel computers. In this paper, we prove the exact value of the crossing number of pancake graph $P_4$ is six."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4642","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":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TvhdYvPkWQi7m3FK/zIH0GjQsWofEjTXISZqKXy9dBB8LK6WP794e6ySwkIcCxQqsPwGj7g92P8WvZI7uSWdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:40:58.738726Z"},"content_sha256":"bd7c64cda50f703bb1fa36d6a48ad99fff156483ee20a8727809576939dd8eca","schema_version":"1.0","event_id":"sha256:bd7c64cda50f703bb1fa36d6a48ad99fff156483ee20a8727809576939dd8eca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J5ELNFICPF4OC5RKPNZM7NK6IO/bundle.json","state_url":"https://pith.science/pith/J5ELNFICPF4OC5RKPNZM7NK6IO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J5ELNFICPF4OC5RKPNZM7NK6IO/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":"2026-06-01T19:40:58Z","links":{"resolver":"https://pith.science/pith/J5ELNFICPF4OC5RKPNZM7NK6IO","bundle":"https://pith.science/pith/J5ELNFICPF4OC5RKPNZM7NK6IO/bundle.json","state":"https://pith.science/pith/J5ELNFICPF4OC5RKPNZM7NK6IO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J5ELNFICPF4OC5RKPNZM7NK6IO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:J5ELNFICPF4OC5RKPNZM7NK6IO","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":"c490d41072ee931e5eef39322a028dfe77c677b3299838390b522d0ac98883df","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-11-20T01:03:50Z","title_canon_sha256":"ac554174a5b713751bdc14d64920acc25e4eae3bcf9bc3d2afdef9ceb76f8feb"},"schema_version":"1.0","source":{"id":"1211.4642","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4642","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4642v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4642","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"J5ELNFICPF4O","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"J5ELNFICPF4OC5RK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"J5ELNFIC","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:bd7c64cda50f703bb1fa36d6a48ad99fff156483ee20a8727809576939dd8eca","target":"graph","created_at":"2026-05-18T03:40:26Z","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":"The {\\it crossing number} of a graph $G$ is the least number of pairwise crossings of edges among all the drawings of $G$ in the plane. The pancake graph is an important topology for interconnecting processors in parallel computers. In this paper, we prove the exact value of the crossing number of pancake graph $P_4$ is six.","authors_text":"Baigong Zheng, Bo Lv, Ke Zhang, Xirong Xu, Yuansheng Yang","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-11-20T01:03:50Z","title":"The crossing number of pancake graph $P_4$ is six"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4642","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":"sha256:80fc85c86baf99ae13c7a3fb411f49d70c8c1d910fa6947aef44faca78d652f4","target":"record","created_at":"2026-05-18T03:40:26Z","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":"c490d41072ee931e5eef39322a028dfe77c677b3299838390b522d0ac98883df","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-11-20T01:03:50Z","title_canon_sha256":"ac554174a5b713751bdc14d64920acc25e4eae3bcf9bc3d2afdef9ceb76f8feb"},"schema_version":"1.0","source":{"id":"1211.4642","kind":"arxiv","version":1}},"canonical_sha256":"4f48b695027978e1762a7b72cfb55e43aa63d2b1c1be3a878e0d89d54420ab61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f48b695027978e1762a7b72cfb55e43aa63d2b1c1be3a878e0d89d54420ab61","first_computed_at":"2026-05-18T03:40:26.071779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:26.071779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ph/vqHZhrX550MCxw69PXRx6v7+sZ456xfUNUsjnZfslR2NOB0y8EJ3I8oMKuEjWBcIKDjgmXQBA3A4PG8jiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:26.072382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4642","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80fc85c86baf99ae13c7a3fb411f49d70c8c1d910fa6947aef44faca78d652f4","sha256:bd7c64cda50f703bb1fa36d6a48ad99fff156483ee20a8727809576939dd8eca"],"state_sha256":"60fe73fffc93981dc3c4fd00faee2eba682c3618b10db561b8192fbc92635ce1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I8WNP2R8vdDHacvHfbDzwcXkb7tamkEuKeRc/bCAUC2Tgdz8izG+dhHXMo9XeHVzF4PxL9mt3Qv9zsdGTutZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:40:58.740799Z","bundle_sha256":"5c18492d6a1dabba726d7d0880a6058a36a0f05a07bb812b3793799e22ec9945"}}