{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CGMXKASO555XJQ7E3BASRBN3RN","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":"0fa10d281e6324c0133bd7fc33a6d79cbefd20ea6f5fd26be0356ea533546300","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-12T03:38:38Z","title_canon_sha256":"ab2ea9fb59a83979c7df70fa72715b471fe12f784246016126957bf1600650d0"},"schema_version":"1.0","source":{"id":"1303.2770","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2770","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2770v1","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2770","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"CGMXKASO555X","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CGMXKASO555XJQ7E","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CGMXKASO","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:830a901efab7f91d7320d47b24468f5dc4d40d7cdb21eae9784e25adc7425cfc","target":"graph","created_at":"2026-05-18T01:02:14Z","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":"These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The emphasis is on the way signed graphs arise naturally from geometry, especially from the geometry of the classical root systems. Most of the properties I discuss generalize those of unsigned graphs, but the constructions and proofs are often more complicated. My aim is a coherent presentation of the subject, with a few illustrative proofs and adequate references. H","authors_text":"Thomas Zaslavsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-12T03:38:38Z","title":"Signed Graphs and Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2770","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":"sha256:29947d119298cd38973303e3d695dafd18f214d7b51597327ffd3bba0af0793b","target":"record","created_at":"2026-05-18T01:02:14Z","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":"0fa10d281e6324c0133bd7fc33a6d79cbefd20ea6f5fd26be0356ea533546300","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-12T03:38:38Z","title_canon_sha256":"ab2ea9fb59a83979c7df70fa72715b471fe12f784246016126957bf1600650d0"},"schema_version":"1.0","source":{"id":"1303.2770","kind":"arxiv","version":1}},"canonical_sha256":"119975024eef7b74c3e4d8412885bb8b6f2b6741a7a43998cc302203eb78d163","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"119975024eef7b74c3e4d8412885bb8b6f2b6741a7a43998cc302203eb78d163","first_computed_at":"2026-05-18T01:02:14.416210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:14.416210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BBMJfmtIKqSMJZgWqbPFe47sXS9YCyMYFt2Ksg1sYGbVt81KVBflkK4zlEIP9J3eG/qJa8pLU00rpTHmNw6YBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:14.417136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.2770","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29947d119298cd38973303e3d695dafd18f214d7b51597327ffd3bba0af0793b","sha256:830a901efab7f91d7320d47b24468f5dc4d40d7cdb21eae9784e25adc7425cfc"],"state_sha256":"ef8e457278431c2f12ec9ff2b17a2c74903fa494b3b9e5e9bffc7359c85c333b"}