{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NZYXWIZASSYPTBMUN6PMXGNNYI","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":"a1cb9709c0d21e13b8e1ba0e9218449e41918f0b350ec0e8e0f789848c64c368","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-12-28T01:16:07Z","title_canon_sha256":"9bc246aeae40017acad0d3930e1dc455ae9813f883f8c495aa1f777e163dc3ef"},"schema_version":"1.0","source":{"id":"2001.02061","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.02061","created_at":"2026-07-05T09:44:02Z"},{"alias_kind":"arxiv_version","alias_value":"2001.02061v3","created_at":"2026-07-05T09:44:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.02061","created_at":"2026-07-05T09:44:02Z"},{"alias_kind":"pith_short_12","alias_value":"NZYXWIZASSYP","created_at":"2026-07-05T09:44:02Z"},{"alias_kind":"pith_short_16","alias_value":"NZYXWIZASSYPTBMU","created_at":"2026-07-05T09:44:02Z"},{"alias_kind":"pith_short_8","alias_value":"NZYXWIZA","created_at":"2026-07-05T09:44:02Z"}],"graph_snapshots":[{"event_id":"sha256:d604edcb1e2f73f17550372d82f1239853589c9f919a3d704265b718273c1066","target":"graph","created_at":"2026-07-05T09:44:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2001.02061/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Scaled Relative Graph (SRG) is a geometric tool that maps the action of a multi-valued nonlinear operator onto the 2D plane, used to analyze the convergence of a wide range of iterative methods. As the SRG includes the spectrum for linear operators, we can view the SRG as a generalization of the spectrum to multi-valued nonlinear operators. In this work, we further study the SRG of linear operators and characterize the SRG of block-diagonal and normal matrices.","authors_text":"Ernest K. Ryu, Wotao Yin, Xinmeng Huang","cross_cats":["cs.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-12-28T01:16:07Z","title":"Scaled Relative Graph of Normal Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.02061","kind":"arxiv","version":3},"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":"sha256:1191f3b3706fcbea9efcf4ec7721845b9c3b5157522d38afb0404e39d48e0102","target":"record","created_at":"2026-07-05T09:44:02Z","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":"a1cb9709c0d21e13b8e1ba0e9218449e41918f0b350ec0e8e0f789848c64c368","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-12-28T01:16:07Z","title_canon_sha256":"9bc246aeae40017acad0d3930e1dc455ae9813f883f8c495aa1f777e163dc3ef"},"schema_version":"1.0","source":{"id":"2001.02061","kind":"arxiv","version":3}},"canonical_sha256":"6e717b232094b0f985946f9ecb99adc2273b886ce6eef4bedf5f4ee080449c5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e717b232094b0f985946f9ecb99adc2273b886ce6eef4bedf5f4ee080449c5a","first_computed_at":"2026-07-05T09:44:02.876373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:44:02.876373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+kqdv392EtmE8e3cKyoEEH9gkXfJtJgGaBVhZpLySx3DlaK7N1N2OJ18PR7tdtUFNSSECsnvyloeShseZvdxDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:44:02.877089Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.02061","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1191f3b3706fcbea9efcf4ec7721845b9c3b5157522d38afb0404e39d48e0102","sha256:d604edcb1e2f73f17550372d82f1239853589c9f919a3d704265b718273c1066"],"state_sha256":"449165263755007e4fd7f3f6b8cdc64b7a77887f94b77d62ae6b437a62d28b75"}