{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LPCMNR4FCS4QEVKJPD7RMCEUUF","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":"3fd7cc629aba44d8a95b623a1b0185ab74b58bcdb16835701e31935be6adf66a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-18T15:08:11Z","title_canon_sha256":"0cc84dca811b7ac5167711edc7563b5b4bd9328931f3fbe2cd853ab6a2358ffc"},"schema_version":"1.0","source":{"id":"1409.5328","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5328","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5328v1","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5328","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"LPCMNR4FCS4Q","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LPCMNR4FCS4QEVKJ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LPCMNR4F","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:da00ce1eb9af9e15ba58300ce73b77187c2aee27f5d3aa66b54a49d847050cd4","target":"graph","created_at":"2026-05-18T00:35:55Z","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":"Let $G$ be a graph and let $A(G)$ be adjacency matrix of $G$.The positive inertia index (respectively, the negative inertia index) of $G$, denoted by $p(G)$ (respectively, $n(G)$), is defined to be the number of positive eigenvalues (respectively, negative eigenvalues) of $A(G)$. In this paper, we present the bounds for $p(G)$ and $n(G)$ as follows:\n  $$m(G)-c(G)\\leq p(G)\\leq m(G)+c(G), \\ m(G)-c(G)\\leq n(G)\\leq m(G)+c(G),$$\n  where $m(G)$ and $c(G)$ are respectively the matching number and the cyclomatic number of $G$. Furthermore, we characterize the graphs which attain the upper bounds or th","authors_text":"Long Wang, Yi-Zheng Fan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-18T15:08:11Z","title":"Bounds for the positive or negative inertia index of a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5328","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:d8a03f00ee94b93654c6bf4180f87ae58a28fe3fa2f83f90d12ee4ff67b19888","target":"record","created_at":"2026-05-18T00:35:55Z","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":"3fd7cc629aba44d8a95b623a1b0185ab74b58bcdb16835701e31935be6adf66a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-18T15:08:11Z","title_canon_sha256":"0cc84dca811b7ac5167711edc7563b5b4bd9328931f3fbe2cd853ab6a2358ffc"},"schema_version":"1.0","source":{"id":"1409.5328","kind":"arxiv","version":1}},"canonical_sha256":"5bc4c6c78514b902554978ff160894a169928d4cdbcfa7925d3a339a4bbfa5a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bc4c6c78514b902554978ff160894a169928d4cdbcfa7925d3a339a4bbfa5a2","first_computed_at":"2026-05-18T00:35:55.919647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:55.919647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O7aOW3gR0gGhCos7M7GJHv3JXL7HtKIyj9qsACQuDu3yu73S9cvFFCp1CoWEe20FhZ43bOKJhdGkAzQa1euQDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:55.920058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8a03f00ee94b93654c6bf4180f87ae58a28fe3fa2f83f90d12ee4ff67b19888","sha256:da00ce1eb9af9e15ba58300ce73b77187c2aee27f5d3aa66b54a49d847050cd4"],"state_sha256":"2b5aacd14d20d0b739250e804400bcd3ad0cf398af5b5451b0cc652c6980d283"}