{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2R36G4MLK2EJ66GYIVEAR4BIA2","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":"f20c0d6d6efddcbd8c66106e3321a9f29f77998409f795ab96e11df17d9dbea4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-27T03:23:49Z","title_canon_sha256":"e9a8b952a4533ea0ec195790a6cfae3c86bac8871c8756ec6d182bdae04a2b84"},"schema_version":"1.0","source":{"id":"1208.5285","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5285","created_at":"2026-05-18T03:46:59Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5285v1","created_at":"2026-05-18T03:46:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5285","created_at":"2026-05-18T03:46:59Z"},{"alias_kind":"pith_short_12","alias_value":"2R36G4MLK2EJ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2R36G4MLK2EJ66GY","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2R36G4ML","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:44120f34df5021ecf6bc3ac93ede0faafbfbc8e30443405fe4ad161e7ab49f43","target":"graph","created_at":"2026-05-18T03:46:59Z","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 is a pair $(G,\\Sigma)$, where $G=(V,E)$ is a graph (in which parallel edges are permitted, but loops are not) with $V={1,...,n}$ and $\\Sigma\\subseteq E$. By $S(G,\\Sigma)$ we denote the set of all symmetric $V\\times V$ matrices $A=[a_{i,j}]$ with $a_{i,j}<0$ if $i$ and $j$ are connected by only even edges, $a_{i,j}>0$ if $i$ and $j$ are connected by only odd edges, $a_{i,j}\\in \\mathbb{R}$ if $i$ and $j$ are connected by both even and odd edges, $a_{i,j}=0$ if $i\\not=j$ and $i$ and $j$ are non-adjacent, and $a_{i,i} \\in \\mathbb{R}$ for all vertices $i$. The stable inertia set of a","authors_text":"Frank J. Hall, Hein van der Holst, Marina Arav, Zhongshan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-27T03:23:49Z","title":"The inertia set of a signed graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5285","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":"sha256:624948fd246d8bcfd9d986d9e66a146d7bd06ed7a4f67afcdda4f727a81876a5","target":"record","created_at":"2026-05-18T03:46:59Z","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":"f20c0d6d6efddcbd8c66106e3321a9f29f77998409f795ab96e11df17d9dbea4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-27T03:23:49Z","title_canon_sha256":"e9a8b952a4533ea0ec195790a6cfae3c86bac8871c8756ec6d182bdae04a2b84"},"schema_version":"1.0","source":{"id":"1208.5285","kind":"arxiv","version":1}},"canonical_sha256":"d477e3718b56889f78d8454808f02806b85fdae697a2ae20f284b2749e64ae70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d477e3718b56889f78d8454808f02806b85fdae697a2ae20f284b2749e64ae70","first_computed_at":"2026-05-18T03:46:59.872717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:59.872717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XFCZBjA+y+Vuk3iTW2xKnK6hxdznmoVQ2wr2OFDw1fCivQPTL0nCoTi1yQOn7bS5ksfwsMireMwkzAdwTG0CBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:59.873412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5285","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:624948fd246d8bcfd9d986d9e66a146d7bd06ed7a4f67afcdda4f727a81876a5","sha256:44120f34df5021ecf6bc3ac93ede0faafbfbc8e30443405fe4ad161e7ab49f43"],"state_sha256":"ae8e9d00fabdb7d3e3598b8380f73041e2e4e2aae982a9ac1c485816bb2cd374"}