{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2ARDEGN3XTEIMSB25DLGASXYJ7","short_pith_number":"pith:2ARDEGN3","schema_version":"1.0","canonical_sha256":"d0223219bbbcc886483ae8d6604af84fe455a06db97decfa8f84baf9c66be030","source":{"kind":"arxiv","id":"1011.6057","version":2},"attestation_state":"computed","paper":{"title":"Computing Linear Matrix Representations of Helton-Vinnikov Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.OC"],"primary_cat":"math.AG","authors_text":"Bernd Sturmfels, Cynthia Vinzant, Daniel Plaumann","submitted_at":"2010-11-28T16:06:52Z","abstract_excerpt":"Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We study three approaches to this problem: an algebraic approach via solving polynomial equations, a geometric approach via contact curves, and an analytic approach via theta functions. These are explained, compared, and tested experimentally for low degree instances."},"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":"1011.6057","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-11-28T16:06:52Z","cross_cats_sorted":["cs.CG","math.OC"],"title_canon_sha256":"1273cfee7beabcfea776b5201ef41e913d599fb337e033b48cafc0a434632715","abstract_canon_sha256":"65456e266e31b616a3294cfcd8e0fdba90f7e9d62b7ab12e413a27a1262ea4db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:55.298535Z","signature_b64":"fM7mFgqVbeHXYXG2eTXii7rWMb9zFrZx4s7E2C1MX5/U0fXexNijJXe8Y5Uu6gk/fj7D9h85n6lVN8kumW+6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0223219bbbcc886483ae8d6604af84fe455a06db97decfa8f84baf9c66be030","last_reissued_at":"2026-05-18T03:05:55.298077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:55.298077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing Linear Matrix Representations of Helton-Vinnikov Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.OC"],"primary_cat":"math.AG","authors_text":"Bernd Sturmfels, Cynthia Vinzant, Daniel Plaumann","submitted_at":"2010-11-28T16:06:52Z","abstract_excerpt":"Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We study three approaches to this problem: an algebraic approach via solving polynomial equations, a geometric approach via contact curves, and an analytic approach via theta functions. These are explained, compared, and tested experimentally for low degree instances."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6057","kind":"arxiv","version":2},"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":"1011.6057","created_at":"2026-05-18T03:05:55.298143+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.6057v2","created_at":"2026-05-18T03:05:55.298143+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6057","created_at":"2026-05-18T03:05:55.298143+00:00"},{"alias_kind":"pith_short_12","alias_value":"2ARDEGN3XTEI","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2ARDEGN3XTEIMSB2","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2ARDEGN3","created_at":"2026-05-18T12:26:03.138858+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/2ARDEGN3XTEIMSB25DLGASXYJ7","json":"https://pith.science/pith/2ARDEGN3XTEIMSB25DLGASXYJ7.json","graph_json":"https://pith.science/api/pith-number/2ARDEGN3XTEIMSB25DLGASXYJ7/graph.json","events_json":"https://pith.science/api/pith-number/2ARDEGN3XTEIMSB25DLGASXYJ7/events.json","paper":"https://pith.science/paper/2ARDEGN3"},"agent_actions":{"view_html":"https://pith.science/pith/2ARDEGN3XTEIMSB25DLGASXYJ7","download_json":"https://pith.science/pith/2ARDEGN3XTEIMSB25DLGASXYJ7.json","view_paper":"https://pith.science/paper/2ARDEGN3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.6057&json=true","fetch_graph":"https://pith.science/api/pith-number/2ARDEGN3XTEIMSB25DLGASXYJ7/graph.json","fetch_events":"https://pith.science/api/pith-number/2ARDEGN3XTEIMSB25DLGASXYJ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2ARDEGN3XTEIMSB25DLGASXYJ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2ARDEGN3XTEIMSB25DLGASXYJ7/action/storage_attestation","attest_author":"https://pith.science/pith/2ARDEGN3XTEIMSB25DLGASXYJ7/action/author_attestation","sign_citation":"https://pith.science/pith/2ARDEGN3XTEIMSB25DLGASXYJ7/action/citation_signature","submit_replication":"https://pith.science/pith/2ARDEGN3XTEIMSB25DLGASXYJ7/action/replication_record"}},"created_at":"2026-05-18T03:05:55.298143+00:00","updated_at":"2026-05-18T03:05:55.298143+00:00"}