{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BY5PHUI3HTSQVTTTHJBNQ2KC25","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":"b9bd1d0cf08900ff295d1d4f2a995d21015862550fd3f824cffe9c3b9e7c64a0","cross_cats_sorted":["math.OA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-02T12:13:44Z","title_canon_sha256":"591df18a4b3a74c25ec363c664ddf6fd522a8eca4aa5aefd168977b7a1c710cf"},"schema_version":"1.0","source":{"id":"1705.00935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00935","created_at":"2026-05-18T00:45:09Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00935v1","created_at":"2026-05-18T00:45:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00935","created_at":"2026-05-18T00:45:09Z"},{"alias_kind":"pith_short_12","alias_value":"BY5PHUI3HTSQ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BY5PHUI3HTSQVTTT","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BY5PHUI3","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:1bab68d6b002bbb41be9a302178e1ad0345b627230151651e420f80f9c7459de","target":"graph","created_at":"2026-05-18T00:45:09Z","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":"Kippenhahn discovered a real algebraic plane curve whose convex hull is the numerical range of a matrix. The correctness of this theorem was called into question when Chien and Nakazato found an example where the spatial analogue fails. They showed that the mentioned plane curve indeed lies inside the numerical range. We prove the easier converse direction of the theorem. Finding higher-dimensional generalizations of Kippenhahn's theorem is a challenge in real algebraic geometry.","authors_text":"Stephan Weis","cross_cats":["math.OA","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-02T12:13:44Z","title":"On a theorem by Kippenhahn"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00935","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":"sha256:18b6d48a12898c2bfcd3060535a3c7be86404b1b1e3ec0f6c770d5dfe22d0cc6","target":"record","created_at":"2026-05-18T00:45:09Z","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":"b9bd1d0cf08900ff295d1d4f2a995d21015862550fd3f824cffe9c3b9e7c64a0","cross_cats_sorted":["math.OA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-02T12:13:44Z","title_canon_sha256":"591df18a4b3a74c25ec363c664ddf6fd522a8eca4aa5aefd168977b7a1c710cf"},"schema_version":"1.0","source":{"id":"1705.00935","kind":"arxiv","version":1}},"canonical_sha256":"0e3af3d11b3ce50ace733a42d86942d744c111650eafcc68fbcfc5cd000bdc45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e3af3d11b3ce50ace733a42d86942d744c111650eafcc68fbcfc5cd000bdc45","first_computed_at":"2026-05-18T00:45:09.330645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:09.330645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SDeOkhs24+WBod0N2WtCyJiGsas5xm6192kbCvtagfjB3Mc66JIXDvrkP1tDkWJof7TGnMf26AYV0JMY0NcsBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:09.331218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18b6d48a12898c2bfcd3060535a3c7be86404b1b1e3ec0f6c770d5dfe22d0cc6","sha256:1bab68d6b002bbb41be9a302178e1ad0345b627230151651e420f80f9c7459de"],"state_sha256":"52e34208d85da44a8b65be5464f5c0556f22bc1317cbf2cbff3646c96854e01e"}