{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HSIVYQTHJOKM3EPYLQIERAK44N","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":"18a8a6bc3b65fdf3ebf119b7b7d4886809b56798763b6e06dc221264740537dc","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2017-12-15T13:25:50Z","title_canon_sha256":"cc822722cdfb3d8f37dbacc2f9ca87fecd1b03a9a5f687925b2439428e5fd563"},"schema_version":"1.0","source":{"id":"1712.05662","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05662","created_at":"2026-05-18T00:15:52Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05662v2","created_at":"2026-05-18T00:15:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05662","created_at":"2026-05-18T00:15:52Z"},{"alias_kind":"pith_short_12","alias_value":"HSIVYQTHJOKM","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HSIVYQTHJOKM3EPY","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HSIVYQTH","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:eef7c5b1e6ea11f79efb977cc381bdf2a103dcd6a792d7d878214a99fd2d907d","target":"graph","created_at":"2026-05-18T00:15:52Z","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":"We generalize the bounds on the inverses of diagonally dominant matrices obtained in [16] from scalar to block tridiagonal matrices. Our derivations are based on a generalization of the classical condition of block diagonal dominance of matrices given by Feingold and Varga in [11]. Based on this generalization, which was recently presented in [3], we also derive a variant of the Gershgorin Circle Theorem for general block matrices which can provide tighter spectral inclusion regions than those obtained by Feingold and Varga.","authors_text":"Carlos Echeverr\\'ia, J\\\"org Liesen, Reinhard Nabben","cross_cats":["math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2017-12-15T13:25:50Z","title":"Block diagonal dominance of matrices revisited: bounds for the norms of inverses and eigenvalue inclusion sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05662","kind":"arxiv","version":2},"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":"sha256:0125fe0fedb9c3ac5bca74fc33ee95b4eea75e841aa9841b59e4c23926c75ad8","target":"record","created_at":"2026-05-18T00:15:52Z","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":"18a8a6bc3b65fdf3ebf119b7b7d4886809b56798763b6e06dc221264740537dc","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2017-12-15T13:25:50Z","title_canon_sha256":"cc822722cdfb3d8f37dbacc2f9ca87fecd1b03a9a5f687925b2439428e5fd563"},"schema_version":"1.0","source":{"id":"1712.05662","kind":"arxiv","version":2}},"canonical_sha256":"3c915c42674b94cd91f85c1048815ce347070177738c3de2c9d2f5b10bab3e05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c915c42674b94cd91f85c1048815ce347070177738c3de2c9d2f5b10bab3e05","first_computed_at":"2026-05-18T00:15:52.117524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:52.117524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lML3tacVHyklquP4FqdnOcKt/c6exq+8T+1S9IfIs5KEL5l660JyckEQw6CTXr87TUJYxdckyliVQtd4lXRkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:52.118157Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05662","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0125fe0fedb9c3ac5bca74fc33ee95b4eea75e841aa9841b59e4c23926c75ad8","sha256:eef7c5b1e6ea11f79efb977cc381bdf2a103dcd6a792d7d878214a99fd2d907d"],"state_sha256":"e5e7e93e7aed792fb1ab624c4f2fbac67833fa6316c6c4453a994b64ac3e8708"}