{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JFHVGYY2JCYKQJPOUTL7ZBRVRG","short_pith_number":"pith:JFHVGYY2","canonical_record":{"source":{"id":"1301.6224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-26T08:58:01Z","cross_cats_sorted":[],"title_canon_sha256":"72837ac765728b910dd6c579fb0cb3badfc19bd410b0048f57f5281a600ac61a","abstract_canon_sha256":"4c84388de8dbb4f62fd7296f01e3aa1364e20b88d08350d19068ee0ff1cef507"},"schema_version":"1.0"},"canonical_sha256":"494f53631a48b0a825eea4d7fc863589b81c7aeff91d1e34f572559da35974b2","source":{"kind":"arxiv","id":"1301.6224","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6224","created_at":"2026-05-18T03:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6224v1","created_at":"2026-05-18T03:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6224","created_at":"2026-05-18T03:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"JFHVGYY2JCYK","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JFHVGYY2JCYKQJPO","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JFHVGYY2","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JFHVGYY2JCYKQJPOUTL7ZBRVRG","target":"record","payload":{"canonical_record":{"source":{"id":"1301.6224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-26T08:58:01Z","cross_cats_sorted":[],"title_canon_sha256":"72837ac765728b910dd6c579fb0cb3badfc19bd410b0048f57f5281a600ac61a","abstract_canon_sha256":"4c84388de8dbb4f62fd7296f01e3aa1364e20b88d08350d19068ee0ff1cef507"},"schema_version":"1.0"},"canonical_sha256":"494f53631a48b0a825eea4d7fc863589b81c7aeff91d1e34f572559da35974b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:24.693713Z","signature_b64":"LUqTuS4dnuFIpbRTaHaqrGo7wRenn7RBe418VsW674z7vjdcUqhBQq/8GFfykT2m9U9ek9E9H88gET5DuQaGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"494f53631a48b0a825eea4d7fc863589b81c7aeff91d1e34f572559da35974b2","last_reissued_at":"2026-05-18T03:35:24.693069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:24.693069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.6224","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":"2026-05-18T03:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vo7jtHs7QgJ/qRBH73866wXOVWqGAWoZgOL6AGLFKyAq7RSAN3autEWSQ/zV8rPIYzhBoOLM1jgz+y16sQ2+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:04:04.719876Z"},"content_sha256":"266127f952d0198a269facd757ba80ace4d9af449f3815a61a7a3440ca32949f","schema_version":"1.0","event_id":"sha256:266127f952d0198a269facd757ba80ace4d9af449f3815a61a7a3440ca32949f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JFHVGYY2JCYKQJPOUTL7ZBRVRG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The skew energy of random oriented graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huishu Lian, Xiaolin Chen, Xueliang Li","submitted_at":"2013-01-26T08:58:01Z","abstract_excerpt":"Given a graph $G$, let $G^\\sigma$ be an oriented graph of $G$ with the orientation $\\sigma$ and skew-adjacency matrix $S(G^\\sigma)$. The skew energy of the oriented graph $G^\\sigma$, denoted by $\\mathcal{E}_S(G^\\sigma)$, is defined as the sum of the absolute values of all the eigenvalues of $S(G^\\sigma)$. In this paper, we study the skew energy of random oriented graphs and formulate an exact estimate of the skew energy for almost all oriented graphs by generalizing Wigner's semicircle law. Moreover, we consider the skew energy of random regular oriented graphs $G_{n,d}^\\sigma$, and get an exa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6224","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":"2026-05-18T03:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pJB53rt2LRSSH+AFbAZNI96jrOlXxmLIVGq4ibUvk4Y58QSMcSWYKBDseh87ZIPjzUaVTK6JRysZmk5sGDkfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:04:04.720219Z"},"content_sha256":"ceacf593afea8e08bb86bd8865c6cb02152e5e61d6704232d6bd5c63b244899d","schema_version":"1.0","event_id":"sha256:ceacf593afea8e08bb86bd8865c6cb02152e5e61d6704232d6bd5c63b244899d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JFHVGYY2JCYKQJPOUTL7ZBRVRG/bundle.json","state_url":"https://pith.science/pith/JFHVGYY2JCYKQJPOUTL7ZBRVRG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JFHVGYY2JCYKQJPOUTL7ZBRVRG/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":"2026-06-02T02:04:04Z","links":{"resolver":"https://pith.science/pith/JFHVGYY2JCYKQJPOUTL7ZBRVRG","bundle":"https://pith.science/pith/JFHVGYY2JCYKQJPOUTL7ZBRVRG/bundle.json","state":"https://pith.science/pith/JFHVGYY2JCYKQJPOUTL7ZBRVRG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JFHVGYY2JCYKQJPOUTL7ZBRVRG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JFHVGYY2JCYKQJPOUTL7ZBRVRG","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":"4c84388de8dbb4f62fd7296f01e3aa1364e20b88d08350d19068ee0ff1cef507","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-26T08:58:01Z","title_canon_sha256":"72837ac765728b910dd6c579fb0cb3badfc19bd410b0048f57f5281a600ac61a"},"schema_version":"1.0","source":{"id":"1301.6224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6224","created_at":"2026-05-18T03:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6224v1","created_at":"2026-05-18T03:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6224","created_at":"2026-05-18T03:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"JFHVGYY2JCYK","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JFHVGYY2JCYKQJPO","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JFHVGYY2","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:ceacf593afea8e08bb86bd8865c6cb02152e5e61d6704232d6bd5c63b244899d","target":"graph","created_at":"2026-05-18T03:35:24Z","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":"Given a graph $G$, let $G^\\sigma$ be an oriented graph of $G$ with the orientation $\\sigma$ and skew-adjacency matrix $S(G^\\sigma)$. The skew energy of the oriented graph $G^\\sigma$, denoted by $\\mathcal{E}_S(G^\\sigma)$, is defined as the sum of the absolute values of all the eigenvalues of $S(G^\\sigma)$. In this paper, we study the skew energy of random oriented graphs and formulate an exact estimate of the skew energy for almost all oriented graphs by generalizing Wigner's semicircle law. Moreover, we consider the skew energy of random regular oriented graphs $G_{n,d}^\\sigma$, and get an exa","authors_text":"Huishu Lian, Xiaolin Chen, Xueliang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-26T08:58:01Z","title":"The skew energy of random oriented graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6224","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":"sha256:266127f952d0198a269facd757ba80ace4d9af449f3815a61a7a3440ca32949f","target":"record","created_at":"2026-05-18T03:35:24Z","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":"4c84388de8dbb4f62fd7296f01e3aa1364e20b88d08350d19068ee0ff1cef507","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-26T08:58:01Z","title_canon_sha256":"72837ac765728b910dd6c579fb0cb3badfc19bd410b0048f57f5281a600ac61a"},"schema_version":"1.0","source":{"id":"1301.6224","kind":"arxiv","version":1}},"canonical_sha256":"494f53631a48b0a825eea4d7fc863589b81c7aeff91d1e34f572559da35974b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"494f53631a48b0a825eea4d7fc863589b81c7aeff91d1e34f572559da35974b2","first_computed_at":"2026-05-18T03:35:24.693069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:24.693069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LUqTuS4dnuFIpbRTaHaqrGo7wRenn7RBe418VsW674z7vjdcUqhBQq/8GFfykT2m9U9ek9E9H88gET5DuQaGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:24.693713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.6224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:266127f952d0198a269facd757ba80ace4d9af449f3815a61a7a3440ca32949f","sha256:ceacf593afea8e08bb86bd8865c6cb02152e5e61d6704232d6bd5c63b244899d"],"state_sha256":"3b32fad3faf1b59233b97a366dcbb0403503599c7ec190b742d4a5c13e2660b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u6ad3t0I/HO/jDzQKSCJ9NnL0GSwODFhWHR2jkEQ/nTOifuBIyJAp2jltjKuZmSLCymWJvd6kYKNfk9303L7CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:04:04.722272Z","bundle_sha256":"8e662aefdbcdb4213b54b90621c890e6e2d23b051267dbb08eca8e802180c38d"}}