{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FILR2XSKYPMKAYFLL4OYI3IM74","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":"1218f269676d19c0dc5fbe34a328339d246f94889899bf5b949acbca64c23414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-27T13:11:13Z","title_canon_sha256":"b6190a6fb9f76a18020c47fcd8ce9468fd88d290c0542f3c624df2a1b2743e19"},"schema_version":"1.0","source":{"id":"1812.11865","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11865","created_at":"2026-05-17T23:57:10Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11865v1","created_at":"2026-05-17T23:57:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11865","created_at":"2026-05-17T23:57:10Z"},{"alias_kind":"pith_short_12","alias_value":"FILR2XSKYPMK","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FILR2XSKYPMKAYFL","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FILR2XSK","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:3dbcad98e0b0e810964cbd368f4260c3838c2accd756ccac0afacaf0d520f291","target":"graph","created_at":"2026-05-17T23:57:10Z","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 signed graph $\\Gamma(G)$ is a graph with a sign attached to each of its edges, where $G$ is the underlying graph of $\\Gamma(G)$. The energy of a signed graph $\\Gamma(G)$ is the sum of the absolute values of the eigenvalues of the adjacency matrix $A(\\Gamma(G))$ of $\\Gamma(G)$. The random signed graph model $\\mathcal{G}_n(p, q)$ is defined as follows: Let $p, q \\ge 0$ be fixed, $0 \\le p+q \\le 1$. Given a set of $n$ vertices, between each pair of distinct vertices there is either a positive edge with probability $p$ or a negative edge with probability $q$, or else there is no edge with probabi","authors_text":"Shuchao Li, Shujing Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-27T13:11:13Z","title":"The energy of random signed graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11865","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":"sha256:836a184e40a0b3b8f0e5b4cf707e2afae7c450bccdc270b421d5d08f1c6b620a","target":"record","created_at":"2026-05-17T23:57:10Z","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":"1218f269676d19c0dc5fbe34a328339d246f94889899bf5b949acbca64c23414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-27T13:11:13Z","title_canon_sha256":"b6190a6fb9f76a18020c47fcd8ce9468fd88d290c0542f3c624df2a1b2743e19"},"schema_version":"1.0","source":{"id":"1812.11865","kind":"arxiv","version":1}},"canonical_sha256":"2a171d5e4ac3d8a060ab5f1d846d0cff32297cf35af5f9eade2ecf956176a780","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a171d5e4ac3d8a060ab5f1d846d0cff32297cf35af5f9eade2ecf956176a780","first_computed_at":"2026-05-17T23:57:10.917620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:10.917620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"od/W2quqgOrEhh5iuKSofgFXLIJrxyf08PTitH54W4QLaJfrDffQOBxviYWARKmIE5X/D4KpVPBeafWz3XTFAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:10.918097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11865","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:836a184e40a0b3b8f0e5b4cf707e2afae7c450bccdc270b421d5d08f1c6b620a","sha256:3dbcad98e0b0e810964cbd368f4260c3838c2accd756ccac0afacaf0d520f291"],"state_sha256":"5c0dc0232e595e386cb43267df93c0bc42cade5d097a25f3bdd57024e67ebddd"}