{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NIQ5EYMOAGM5QJFHBUD6G3AHVV","short_pith_number":"pith:NIQ5EYMO","schema_version":"1.0","canonical_sha256":"6a21d2618e0199d824a70d07e36c07ad5b2004402d3836d9af1aaae780858fe2","source":{"kind":"arxiv","id":"1609.07439","version":1},"attestation_state":"computed","paper":{"title":"Gershgorin disks for multiple eigenvalues of non-negative matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CO","authors_text":"Imre B\\'ar\\'any, J\\'ozsef Solymosi","submitted_at":"2016-09-23T17:29:44Z","abstract_excerpt":"Gershgorin's famous circle theorem states that all eigenvalues of a square matrix lie in disks (called Gershgorin disks) around the diagonal elements. Here we show that if the matrix entries are non-negative and an eigenvalue has geometric multiplicity at least two, then this eigenvalue lies in a smaller disk. The proof uses geometric rearrangement inequalities on sums of higher dimensional real vectors which is another new result of this paper."},"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":"1609.07439","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-23T17:29:44Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"8abd86d2813b90b3c2630b777877c6ee5d9d1a3ff2135e035e0a5ae801c305f7","abstract_canon_sha256":"4e823ad677413c6b2f101e2628fa3377fc81e73304bf4ffc12c5b4d9dbe14a7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:00.857396Z","signature_b64":"0HzdA8hnB27cnqeTQL3iTkR8hwrKOYyGuGVjeMSM4Azwl07gWeu4EDgw1JfUaQVq1C8wYwTP3CZqNd/RtuZwCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a21d2618e0199d824a70d07e36c07ad5b2004402d3836d9af1aaae780858fe2","last_reissued_at":"2026-05-18T01:04:00.856748Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:00.856748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gershgorin disks for multiple eigenvalues of non-negative matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CO","authors_text":"Imre B\\'ar\\'any, J\\'ozsef Solymosi","submitted_at":"2016-09-23T17:29:44Z","abstract_excerpt":"Gershgorin's famous circle theorem states that all eigenvalues of a square matrix lie in disks (called Gershgorin disks) around the diagonal elements. Here we show that if the matrix entries are non-negative and an eigenvalue has geometric multiplicity at least two, then this eigenvalue lies in a smaller disk. The proof uses geometric rearrangement inequalities on sums of higher dimensional real vectors which is another new result of this paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07439","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":"1609.07439","created_at":"2026-05-18T01:04:00.856847+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07439v1","created_at":"2026-05-18T01:04:00.856847+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07439","created_at":"2026-05-18T01:04:00.856847+00:00"},{"alias_kind":"pith_short_12","alias_value":"NIQ5EYMOAGM5","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"NIQ5EYMOAGM5QJFH","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"NIQ5EYMO","created_at":"2026-05-18T12:30:32.724797+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/NIQ5EYMOAGM5QJFHBUD6G3AHVV","json":"https://pith.science/pith/NIQ5EYMOAGM5QJFHBUD6G3AHVV.json","graph_json":"https://pith.science/api/pith-number/NIQ5EYMOAGM5QJFHBUD6G3AHVV/graph.json","events_json":"https://pith.science/api/pith-number/NIQ5EYMOAGM5QJFHBUD6G3AHVV/events.json","paper":"https://pith.science/paper/NIQ5EYMO"},"agent_actions":{"view_html":"https://pith.science/pith/NIQ5EYMOAGM5QJFHBUD6G3AHVV","download_json":"https://pith.science/pith/NIQ5EYMOAGM5QJFHBUD6G3AHVV.json","view_paper":"https://pith.science/paper/NIQ5EYMO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07439&json=true","fetch_graph":"https://pith.science/api/pith-number/NIQ5EYMOAGM5QJFHBUD6G3AHVV/graph.json","fetch_events":"https://pith.science/api/pith-number/NIQ5EYMOAGM5QJFHBUD6G3AHVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NIQ5EYMOAGM5QJFHBUD6G3AHVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NIQ5EYMOAGM5QJFHBUD6G3AHVV/action/storage_attestation","attest_author":"https://pith.science/pith/NIQ5EYMOAGM5QJFHBUD6G3AHVV/action/author_attestation","sign_citation":"https://pith.science/pith/NIQ5EYMOAGM5QJFHBUD6G3AHVV/action/citation_signature","submit_replication":"https://pith.science/pith/NIQ5EYMOAGM5QJFHBUD6G3AHVV/action/replication_record"}},"created_at":"2026-05-18T01:04:00.856847+00:00","updated_at":"2026-05-18T01:04:00.856847+00:00"}