{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VHOT3KBJQINI2GDK2BWV4RQZTL","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":"29370d34149936ab3f7ccfe2e16b8c7ce0a9833d69ffa1c2886eba3ff440478f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-26T21:01:04Z","title_canon_sha256":"d793d77605cfb4ddfe6c179e4c7113223695fd17d27150fff24140aafe2952f7"},"schema_version":"1.0","source":{"id":"1801.08972","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08972","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08972v1","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08972","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"VHOT3KBJQINI","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VHOT3KBJQINI2GDK","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VHOT3KBJ","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:3d89b73213a5c7125a4f97d89375aee1622a1ccbe26e508a711b3585dfb5cddc","target":"graph","created_at":"2026-05-18T00:24:58Z","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":"Motivated by the linear time algorithm that locates the eigenvalues of a cograph G [10], we investigate the multiplicity of eigenvalue for \\lambda \\neq -1,0. For cographs with balanced cotrees we determine explicitly the highest value for the multiplicity.The energy of a graph is defined as the sum of absolute values of the eigenvalues. A graph G on n vertices is said to be borderenergetic if its energy equals the energy of the complete graph Kn. We present families of non-cospectral and borderenergetic cographs.","authors_text":"Fernando Tura, Luiz Emilio Allem","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-26T21:01:04Z","title":"Multiplicity of eigenvalues of cographs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08972","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":"sha256:7631ec7ec68c72673796835dba13858b62697c287461d1176b2d35078905dd45","target":"record","created_at":"2026-05-18T00:24:58Z","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":"29370d34149936ab3f7ccfe2e16b8c7ce0a9833d69ffa1c2886eba3ff440478f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-26T21:01:04Z","title_canon_sha256":"d793d77605cfb4ddfe6c179e4c7113223695fd17d27150fff24140aafe2952f7"},"schema_version":"1.0","source":{"id":"1801.08972","kind":"arxiv","version":1}},"canonical_sha256":"a9dd3da829821a8d186ad06d5e46199adea27b7a9ac9089a8ffa06f014e9b364","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9dd3da829821a8d186ad06d5e46199adea27b7a9ac9089a8ffa06f014e9b364","first_computed_at":"2026-05-18T00:24:58.981475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:58.981475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qW2tdds+hSXVi4b1/blcLS/pRE1sf6kAKUpaOFEO44KCMHhW7FB0kFoUwmyGgTTfaR72Zq660g4qub+m0HEfAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:58.982070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08972","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7631ec7ec68c72673796835dba13858b62697c287461d1176b2d35078905dd45","sha256:3d89b73213a5c7125a4f97d89375aee1622a1ccbe26e508a711b3585dfb5cddc"],"state_sha256":"17ef66377ebd47dd5f0b945cdd16bdbaf15837dcc33f2d465b0ee462da7b3ac2"}