{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6CSFKX2UXWBGN2DTLRG6XCLDHA","short_pith_number":"pith:6CSFKX2U","schema_version":"1.0","canonical_sha256":"f0a4555f54bd8266e8735c4deb89633824408248c90f3efde35e31640033af32","source":{"kind":"arxiv","id":"1502.00955","version":1},"attestation_state":"computed","paper":{"title":"Continuous Selections of the Inverse Numerical Range Map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Brian Lins, Parth Parihar","submitted_at":"2015-02-03T18:50:53Z","abstract_excerpt":"For a complex $n$-by-$n$ matrix $A$, the numerical range $F(A)$ is the range of the map $f_A(x) = x^*A x$ acting on the unit sphere in $\\C^n$. We ask whether the multivalued inverse numerical range map $f_A^{-1}$ has a continuous single-valued selection defined on all or part of $F(A)$. We show that for a large class of matrices, $f_A^{-1}$ does have a continuous selection on $F(A)$. For other matrices, $f_A^{-1}$ has a continuous selection defined everywhere on $F(A)$ except in the vicinity of a finite number of exceptional points on the boundary of $F(A)$."},"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":"1502.00955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-03T18:50:53Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"e7133400d1e43109f4a9d81be38a14e06700c8bc22c91786120d0b10f4478d36","abstract_canon_sha256":"895600aac714483908113c77ed586d81f8a938f29ff5f0483142eac952808db9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:59.146204Z","signature_b64":"kU4u8t/JKXQZR+pZTQtSOXRDyLw2CEgZwWimieKBiWnRQxyiLy+zHDFge3Gjhe23M1OCpkmDt65af8tCVgTpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0a4555f54bd8266e8735c4deb89633824408248c90f3efde35e31640033af32","last_reissued_at":"2026-05-18T02:27:59.145680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:59.145680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuous Selections of the Inverse Numerical Range Map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Brian Lins, Parth Parihar","submitted_at":"2015-02-03T18:50:53Z","abstract_excerpt":"For a complex $n$-by-$n$ matrix $A$, the numerical range $F(A)$ is the range of the map $f_A(x) = x^*A x$ acting on the unit sphere in $\\C^n$. We ask whether the multivalued inverse numerical range map $f_A^{-1}$ has a continuous single-valued selection defined on all or part of $F(A)$. We show that for a large class of matrices, $f_A^{-1}$ does have a continuous selection on $F(A)$. For other matrices, $f_A^{-1}$ has a continuous selection defined everywhere on $F(A)$ except in the vicinity of a finite number of exceptional points on the boundary of $F(A)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00955","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":"1502.00955","created_at":"2026-05-18T02:27:59.145766+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.00955v1","created_at":"2026-05-18T02:27:59.145766+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00955","created_at":"2026-05-18T02:27:59.145766+00:00"},{"alias_kind":"pith_short_12","alias_value":"6CSFKX2UXWBG","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6CSFKX2UXWBGN2DT","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6CSFKX2U","created_at":"2026-05-18T12:29:07.941421+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/6CSFKX2UXWBGN2DTLRG6XCLDHA","json":"https://pith.science/pith/6CSFKX2UXWBGN2DTLRG6XCLDHA.json","graph_json":"https://pith.science/api/pith-number/6CSFKX2UXWBGN2DTLRG6XCLDHA/graph.json","events_json":"https://pith.science/api/pith-number/6CSFKX2UXWBGN2DTLRG6XCLDHA/events.json","paper":"https://pith.science/paper/6CSFKX2U"},"agent_actions":{"view_html":"https://pith.science/pith/6CSFKX2UXWBGN2DTLRG6XCLDHA","download_json":"https://pith.science/pith/6CSFKX2UXWBGN2DTLRG6XCLDHA.json","view_paper":"https://pith.science/paper/6CSFKX2U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.00955&json=true","fetch_graph":"https://pith.science/api/pith-number/6CSFKX2UXWBGN2DTLRG6XCLDHA/graph.json","fetch_events":"https://pith.science/api/pith-number/6CSFKX2UXWBGN2DTLRG6XCLDHA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6CSFKX2UXWBGN2DTLRG6XCLDHA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6CSFKX2UXWBGN2DTLRG6XCLDHA/action/storage_attestation","attest_author":"https://pith.science/pith/6CSFKX2UXWBGN2DTLRG6XCLDHA/action/author_attestation","sign_citation":"https://pith.science/pith/6CSFKX2UXWBGN2DTLRG6XCLDHA/action/citation_signature","submit_replication":"https://pith.science/pith/6CSFKX2UXWBGN2DTLRG6XCLDHA/action/replication_record"}},"created_at":"2026-05-18T02:27:59.145766+00:00","updated_at":"2026-05-18T02:27:59.145766+00:00"}