{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KFSIOWVCJBYZRJ3VJS4XNFAVVO","short_pith_number":"pith:KFSIOWVC","canonical_record":{"source":{"id":"1704.06867","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2017-04-23T00:59:49Z","cross_cats_sorted":[],"title_canon_sha256":"1cc748eb9beaaa79479ed6b0e21b2c146dd927b2e3faefb1ad35672261360d86","abstract_canon_sha256":"60ea1a0083f64e3efe39d88576844b7d3bb9f4955382dda3217a9f97bab54a07"},"schema_version":"1.0"},"canonical_sha256":"5164875aa2487198a7754cb9769415ab83597e97c24d6d8b5364dc1aff3f03ce","source":{"kind":"arxiv","id":"1704.06867","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06867","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06867v1","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06867","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"KFSIOWVCJBYZ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KFSIOWVCJBYZRJ3V","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KFSIOWVC","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KFSIOWVCJBYZRJ3VJS4XNFAVVO","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06867","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2017-04-23T00:59:49Z","cross_cats_sorted":[],"title_canon_sha256":"1cc748eb9beaaa79479ed6b0e21b2c146dd927b2e3faefb1ad35672261360d86","abstract_canon_sha256":"60ea1a0083f64e3efe39d88576844b7d3bb9f4955382dda3217a9f97bab54a07"},"schema_version":"1.0"},"canonical_sha256":"5164875aa2487198a7754cb9769415ab83597e97c24d6d8b5364dc1aff3f03ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:55.522965Z","signature_b64":"SadxS9/EKcJ+E5v3BmOxdQJSPRN+eHkPXHJIdsffpJHPeYhlX2Xcd2ADa/r+Esr2MsnoV53/XPq9UVTpCj2QDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5164875aa2487198a7754cb9769415ab83597e97c24d6d8b5364dc1aff3f03ce","last_reissued_at":"2026-05-18T00:45:55.522539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:55.522539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06867","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":"2026-05-18T00:45:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7BaWtzcci0CQvTp+1kKyS/vb+8wRmvNUiL1lkK1egS0/dj1afRKepS1egYJQx9DNNtlr/tjyI4q8FSsynjs4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:23:34.769870Z"},"content_sha256":"5a16720359364f768bb3b9a31eb8be83e380a57a72d57bef918dbf1838d681c7","schema_version":"1.0","event_id":"sha256:5a16720359364f768bb3b9a31eb8be83e380a57a72d57bef918dbf1838d681c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KFSIOWVCJBYZRJ3VJS4XNFAVVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relation between the skew-rank of an oriented graph and the independence number of its underlying graph","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"H. Wang, J. Huang, S.C. Li","submitted_at":"2017-04-23T00:59:49Z","abstract_excerpt":"An oriented graph $G^\\sigma$ is a digraph without loops or multiple arcs whose underlying graph is $G$. Let $S\\left(G^\\sigma\\right)$ be the skew-adjacency matrix of $G^\\sigma$ and $\\alpha(G)$ be the independence number of $G$. The rank of $S(G^\\sigma)$ is called the skew-rank of $G^\\sigma$, denoted by $sr(G^\\sigma)$. Wong et al. [European J. Combin. 54 (2016) 76-86] studied the relationship between the skew-rank of an oriented graph and the rank of its underlying graph. In this paper, the correlation involving the skew-rank, the independence number, and some other parameters are considered. Fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06867","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":"2026-05-18T00:45:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h5ujp1/EyqVcEtEk9IptnmqwdSkKsarD9FfUPGbb6RQdb+RckVIQwoRctNNz7tUEMpMVa8wjMlC2eQm0EfUXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:23:34.770285Z"},"content_sha256":"a93738efa56052bc9cc0906e281dd86c4eeee64192bbe4556eb51b6cc1627878","schema_version":"1.0","event_id":"sha256:a93738efa56052bc9cc0906e281dd86c4eeee64192bbe4556eb51b6cc1627878"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KFSIOWVCJBYZRJ3VJS4XNFAVVO/bundle.json","state_url":"https://pith.science/pith/KFSIOWVCJBYZRJ3VJS4XNFAVVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KFSIOWVCJBYZRJ3VJS4XNFAVVO/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":"2026-06-01T13:23:34Z","links":{"resolver":"https://pith.science/pith/KFSIOWVCJBYZRJ3VJS4XNFAVVO","bundle":"https://pith.science/pith/KFSIOWVCJBYZRJ3VJS4XNFAVVO/bundle.json","state":"https://pith.science/pith/KFSIOWVCJBYZRJ3VJS4XNFAVVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KFSIOWVCJBYZRJ3VJS4XNFAVVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KFSIOWVCJBYZRJ3VJS4XNFAVVO","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":"60ea1a0083f64e3efe39d88576844b7d3bb9f4955382dda3217a9f97bab54a07","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2017-04-23T00:59:49Z","title_canon_sha256":"1cc748eb9beaaa79479ed6b0e21b2c146dd927b2e3faefb1ad35672261360d86"},"schema_version":"1.0","source":{"id":"1704.06867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06867","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06867v1","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06867","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"KFSIOWVCJBYZ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KFSIOWVCJBYZRJ3V","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KFSIOWVC","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:a93738efa56052bc9cc0906e281dd86c4eeee64192bbe4556eb51b6cc1627878","target":"graph","created_at":"2026-05-18T00:45:55Z","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":"An oriented graph $G^\\sigma$ is a digraph without loops or multiple arcs whose underlying graph is $G$. Let $S\\left(G^\\sigma\\right)$ be the skew-adjacency matrix of $G^\\sigma$ and $\\alpha(G)$ be the independence number of $G$. The rank of $S(G^\\sigma)$ is called the skew-rank of $G^\\sigma$, denoted by $sr(G^\\sigma)$. Wong et al. [European J. Combin. 54 (2016) 76-86] studied the relationship between the skew-rank of an oriented graph and the rank of its underlying graph. In this paper, the correlation involving the skew-rank, the independence number, and some other parameters are considered. Fi","authors_text":"H. Wang, J. Huang, S.C. Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2017-04-23T00:59:49Z","title":"Relation between the skew-rank of an oriented graph and the independence number of its underlying graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06867","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":"sha256:5a16720359364f768bb3b9a31eb8be83e380a57a72d57bef918dbf1838d681c7","target":"record","created_at":"2026-05-18T00:45:55Z","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":"60ea1a0083f64e3efe39d88576844b7d3bb9f4955382dda3217a9f97bab54a07","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2017-04-23T00:59:49Z","title_canon_sha256":"1cc748eb9beaaa79479ed6b0e21b2c146dd927b2e3faefb1ad35672261360d86"},"schema_version":"1.0","source":{"id":"1704.06867","kind":"arxiv","version":1}},"canonical_sha256":"5164875aa2487198a7754cb9769415ab83597e97c24d6d8b5364dc1aff3f03ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5164875aa2487198a7754cb9769415ab83597e97c24d6d8b5364dc1aff3f03ce","first_computed_at":"2026-05-18T00:45:55.522539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:55.522539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SadxS9/EKcJ+E5v3BmOxdQJSPRN+eHkPXHJIdsffpJHPeYhlX2Xcd2ADa/r+Esr2MsnoV53/XPq9UVTpCj2QDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:55.522965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a16720359364f768bb3b9a31eb8be83e380a57a72d57bef918dbf1838d681c7","sha256:a93738efa56052bc9cc0906e281dd86c4eeee64192bbe4556eb51b6cc1627878"],"state_sha256":"009d24d9c5cf1258d57d900bb4931a68ce923f17cdf21a64b219912363d41593"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6CKGePoQmidoVL2G4Ah+I4sUM0nWKG4pScQsis1hZ/qA7YuPNIJMc/QI1fayaOChy9uSFrKUhy2O5MwL0LPTDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:23:34.772732Z","bundle_sha256":"3647435a4ac0cfd40f6dfc76bede87eebba2c616649675a1f5ce2ab34c774168"}}