{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PNIXO6CRMP22SZGVDLR5OSVCQ5","short_pith_number":"pith:PNIXO6CR","schema_version":"1.0","canonical_sha256":"7b5177785163f5a964d51ae3d74aa2874efbba43b4105c2220cb9fd4556cbf2b","source":{"kind":"arxiv","id":"1307.5110","version":1},"attestation_state":"computed","paper":{"title":"On the positive and negative inertia of weighted graphs","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Feifei Song, Shuchao Li","submitted_at":"2013-07-19T01:10:42Z","abstract_excerpt":"The number of the positive, negative and zero eigenvalues in the spectrum of the (edge)-weighted graph $G$ are called positive inertia index, negative inertia index and nullity of the weighted graph $G$, and denoted by $i_+(G)$, $i_-(G)$, $i_0(G)$, respectively. In this paper, the positive and negative inertia index of weighted trees, weighted unicyclic graphs and weighted bicyclic graphs are discussed, the methods of calculating them are obtained."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.5110","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2013-07-19T01:10:42Z","cross_cats_sorted":[],"title_canon_sha256":"fdf2bb636445e0e7198472dec31e1dc0e9b88ca3b220814af6fd40b72974c115","abstract_canon_sha256":"4bac109f314cc5b1c0737493a320eccacd6ed0ca841488cc82f2a686d283f1d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:05.665891Z","signature_b64":"Bfpb0OKJlz8VqCOgPYEqC/GVmN/0xQjoL9mAjkug4UZCeopIfXAb7cri4W4NBE14sAlqIF6gJ5LCckk5HM7rDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b5177785163f5a964d51ae3d74aa2874efbba43b4105c2220cb9fd4556cbf2b","last_reissued_at":"2026-05-18T03:18:05.665272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:05.665272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the positive and negative inertia of weighted graphs","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Feifei Song, Shuchao Li","submitted_at":"2013-07-19T01:10:42Z","abstract_excerpt":"The number of the positive, negative and zero eigenvalues in the spectrum of the (edge)-weighted graph $G$ are called positive inertia index, negative inertia index and nullity of the weighted graph $G$, and denoted by $i_+(G)$, $i_-(G)$, $i_0(G)$, respectively. In this paper, the positive and negative inertia index of weighted trees, weighted unicyclic graphs and weighted bicyclic graphs are discussed, the methods of calculating them are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5110","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.5110","created_at":"2026-05-18T03:18:05.665371+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.5110v1","created_at":"2026-05-18T03:18:05.665371+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5110","created_at":"2026-05-18T03:18:05.665371+00:00"},{"alias_kind":"pith_short_12","alias_value":"PNIXO6CRMP22","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PNIXO6CRMP22SZGV","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PNIXO6CR","created_at":"2026-05-18T12:27:54.935989+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PNIXO6CRMP22SZGVDLR5OSVCQ5","json":"https://pith.science/pith/PNIXO6CRMP22SZGVDLR5OSVCQ5.json","graph_json":"https://pith.science/api/pith-number/PNIXO6CRMP22SZGVDLR5OSVCQ5/graph.json","events_json":"https://pith.science/api/pith-number/PNIXO6CRMP22SZGVDLR5OSVCQ5/events.json","paper":"https://pith.science/paper/PNIXO6CR"},"agent_actions":{"view_html":"https://pith.science/pith/PNIXO6CRMP22SZGVDLR5OSVCQ5","download_json":"https://pith.science/pith/PNIXO6CRMP22SZGVDLR5OSVCQ5.json","view_paper":"https://pith.science/paper/PNIXO6CR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.5110&json=true","fetch_graph":"https://pith.science/api/pith-number/PNIXO6CRMP22SZGVDLR5OSVCQ5/graph.json","fetch_events":"https://pith.science/api/pith-number/PNIXO6CRMP22SZGVDLR5OSVCQ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PNIXO6CRMP22SZGVDLR5OSVCQ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PNIXO6CRMP22SZGVDLR5OSVCQ5/action/storage_attestation","attest_author":"https://pith.science/pith/PNIXO6CRMP22SZGVDLR5OSVCQ5/action/author_attestation","sign_citation":"https://pith.science/pith/PNIXO6CRMP22SZGVDLR5OSVCQ5/action/citation_signature","submit_replication":"https://pith.science/pith/PNIXO6CRMP22SZGVDLR5OSVCQ5/action/replication_record"}},"created_at":"2026-05-18T03:18:05.665371+00:00","updated_at":"2026-05-18T03:18:05.665371+00:00"}