{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JTNMZMLTI4MIMIPF5HF4PVVMB7","short_pith_number":"pith:JTNMZMLT","schema_version":"1.0","canonical_sha256":"4cdaccb17347188621e5e9cbc7d6ac0fcb7d57a2cffb833c3bbb28bb31cef111","source":{"kind":"arxiv","id":"1609.04477","version":1},"attestation_state":"computed","paper":{"title":"Eigenvalue location in cographs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David P. Jacobs, Fernando C. Tura, Vilmar Trevisan","submitted_at":"2016-09-15T00:12:56Z","abstract_excerpt":"We give an $O(n)$ time and space algorithm for constructing a diagonal matrix congruent to A+xI, where A is the adjacency matrix of a cograph and $x\\in \\mathbb{R}$. Applications include determining the number of eigenvalues of a cograph's adjacency matrix that lie in any interval, obtaining a formula for the inertia of a cograph, and exhibiting infinitely many pairs of equienergetic cographs with integer energy."},"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":"1609.04477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-15T00:12:56Z","cross_cats_sorted":[],"title_canon_sha256":"3fc0d7cf4e212e339191c7e3d308215223028a2bb1bb66ae445fecb3cdfc9e50","abstract_canon_sha256":"0f7adcc86190906653c1caa6ad3341ac010900c5662f782e521853e61a3acdba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:20.631049Z","signature_b64":"A+Hq8qxRW2AFF4W+7LNq5CxaRD1gUFM63cb1RR2DeEbmb3+qUun7hZcp2B66Kch99veUXeC4LTBFKJbawvjIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cdaccb17347188621e5e9cbc7d6ac0fcb7d57a2cffb833c3bbb28bb31cef111","last_reissued_at":"2026-05-18T00:47:20.630403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:20.630403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eigenvalue location in cographs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David P. Jacobs, Fernando C. Tura, Vilmar Trevisan","submitted_at":"2016-09-15T00:12:56Z","abstract_excerpt":"We give an $O(n)$ time and space algorithm for constructing a diagonal matrix congruent to A+xI, where A is the adjacency matrix of a cograph and $x\\in \\mathbb{R}$. Applications include determining the number of eigenvalues of a cograph's adjacency matrix that lie in any interval, obtaining a formula for the inertia of a cograph, and exhibiting infinitely many pairs of equienergetic cographs with integer energy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04477","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":"1609.04477","created_at":"2026-05-18T00:47:20.630513+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.04477v1","created_at":"2026-05-18T00:47:20.630513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04477","created_at":"2026-05-18T00:47:20.630513+00:00"},{"alias_kind":"pith_short_12","alias_value":"JTNMZMLTI4MI","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JTNMZMLTI4MIMIPF","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JTNMZMLT","created_at":"2026-05-18T12:30:25.849896+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/JTNMZMLTI4MIMIPF5HF4PVVMB7","json":"https://pith.science/pith/JTNMZMLTI4MIMIPF5HF4PVVMB7.json","graph_json":"https://pith.science/api/pith-number/JTNMZMLTI4MIMIPF5HF4PVVMB7/graph.json","events_json":"https://pith.science/api/pith-number/JTNMZMLTI4MIMIPF5HF4PVVMB7/events.json","paper":"https://pith.science/paper/JTNMZMLT"},"agent_actions":{"view_html":"https://pith.science/pith/JTNMZMLTI4MIMIPF5HF4PVVMB7","download_json":"https://pith.science/pith/JTNMZMLTI4MIMIPF5HF4PVVMB7.json","view_paper":"https://pith.science/paper/JTNMZMLT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.04477&json=true","fetch_graph":"https://pith.science/api/pith-number/JTNMZMLTI4MIMIPF5HF4PVVMB7/graph.json","fetch_events":"https://pith.science/api/pith-number/JTNMZMLTI4MIMIPF5HF4PVVMB7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JTNMZMLTI4MIMIPF5HF4PVVMB7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JTNMZMLTI4MIMIPF5HF4PVVMB7/action/storage_attestation","attest_author":"https://pith.science/pith/JTNMZMLTI4MIMIPF5HF4PVVMB7/action/author_attestation","sign_citation":"https://pith.science/pith/JTNMZMLTI4MIMIPF5HF4PVVMB7/action/citation_signature","submit_replication":"https://pith.science/pith/JTNMZMLTI4MIMIPF5HF4PVVMB7/action/replication_record"}},"created_at":"2026-05-18T00:47:20.630513+00:00","updated_at":"2026-05-18T00:47:20.630513+00:00"}