{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z5XOMRYSSDQOXJCA6NVMUI6MGL","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":"5910c3d43d3946ee8559ecd1440dd35a004929d7614189c83022c022f9e3c492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-09T05:42:20Z","title_canon_sha256":"748930fdc982879633c8b022bf8dc45af1ef745a0dd4a4d276ea54c20df222b9"},"schema_version":"1.0","source":{"id":"1304.2458","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2458","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2458v1","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2458","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"pith_short_12","alias_value":"Z5XOMRYSSDQO","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z5XOMRYSSDQOXJCA","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z5XOMRYS","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:4ea96c45b0b0dd1f670b441b242234033778dc7fcf9e0a3cc3f4ffe34652ae1c","target":"graph","created_at":"2026-05-18T03:28:31Z","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":"Let $S(G^\\sigma)$ be the skew-adjacency matrix of an oriented graph $G^\\sigma$. The skew energy of $G^\\sigma$ is defined as the sum of all singular values of its skew-adjacency matrix $S(G^\\sigma)$. In this paper, we first deduce an integral formula for the skew energy of an oriented graph. Then we determine all oriented graphs with minimal skew energy among all connected oriented graphs on $n$ vertices with $m \\ (n\\le m < 2(n-2))$ arcs, which is an analogy to the conjecture for the energy of undirected graphs proposed by Caporossi {\\it et al.} [G. Caporossi, D. Cvetkovi$\\acute{c}$, I. Gutman,","authors_text":"Guanghui Xu, Shicai Gong, Xueliang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-09T05:42:20Z","title":"On oriented graphs with minimal skew energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2458","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:b0195d377fa01560c1b2a5a538c30ef7891c582f93e464c546945dff5fdc2a9b","target":"record","created_at":"2026-05-18T03:28:31Z","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":"5910c3d43d3946ee8559ecd1440dd35a004929d7614189c83022c022f9e3c492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-09T05:42:20Z","title_canon_sha256":"748930fdc982879633c8b022bf8dc45af1ef745a0dd4a4d276ea54c20df222b9"},"schema_version":"1.0","source":{"id":"1304.2458","kind":"arxiv","version":1}},"canonical_sha256":"cf6ee6471290e0eba440f36aca23cc32dbea659fdd44438428544587933ff505","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf6ee6471290e0eba440f36aca23cc32dbea659fdd44438428544587933ff505","first_computed_at":"2026-05-18T03:28:31.956035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:31.956035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ue755gnDMbsX+XY1ND1e9JnLFvXTiY0A4+4ZzJEbaxS5aChoM75w3L8gL3nWr/LWkFdMAtcClpAM4zymXFUODA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:31.956756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2458","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0195d377fa01560c1b2a5a538c30ef7891c582f93e464c546945dff5fdc2a9b","sha256:4ea96c45b0b0dd1f670b441b242234033778dc7fcf9e0a3cc3f4ffe34652ae1c"],"state_sha256":"36da8a39cec4e123e0fe558a302241353884f40020a41c9322f207558730c0f6"}