{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:WY4WDKCDL26IY5D3Q4KSFOLXKM","short_pith_number":"pith:WY4WDKCD","schema_version":"1.0","canonical_sha256":"b63961a8435ebc8c747b871522b977532101739ad72a28345fcb938eac52e6f3","source":{"kind":"arxiv","id":"math/0609528","version":2},"attestation_state":"computed","paper":{"title":"Semidefinite Characterization and Computation of Real Radical Ideals","license":"","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AG","authors_text":"J.B. Lasserre, M. Laurent, P. Rostalski","submitted_at":"2006-09-19T14:32:06Z","abstract_excerpt":"For an ideal $I\\subseteq\\mathbb{R}[x]$ given by a set of generators, a new semidefinite characterization of its real radical $I(V_\\mathbb{R}(I))$ is presented, provided it is zero-dimensional (even if $I$ is not). Moreover we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety $V_\\mathbb{R}(I)$ as well as a set of generators of the real radical ideal. The latter is obtained in the form of a border or Gr\\\"obner basis. The algorithm is based on moment relaxations and, in contrast to other existing"},"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":"math/0609528","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-09-19T14:32:06Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"44d99037404c6f6a54631afb7abde7c3a329e6e8deca6f44ec34383f533bcf37","abstract_canon_sha256":"1b2cb931b82ba46497f37d0565418c896a87e1bbe6f1ee0dffce70fbcf21e854"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:33.148011Z","signature_b64":"ibPmT2eTzI5dzK+WNyXRwpR4WBwcD/DSNaOIesx+u4SwOpuzztD3gLCJZ9p0SX65Tdhw60WegN7oLGHGYqovBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b63961a8435ebc8c747b871522b977532101739ad72a28345fcb938eac52e6f3","last_reissued_at":"2026-05-18T00:00:33.147456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:33.147456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semidefinite Characterization and Computation of Real Radical Ideals","license":"","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AG","authors_text":"J.B. Lasserre, M. Laurent, P. Rostalski","submitted_at":"2006-09-19T14:32:06Z","abstract_excerpt":"For an ideal $I\\subseteq\\mathbb{R}[x]$ given by a set of generators, a new semidefinite characterization of its real radical $I(V_\\mathbb{R}(I))$ is presented, provided it is zero-dimensional (even if $I$ is not). Moreover we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety $V_\\mathbb{R}(I)$ as well as a set of generators of the real radical ideal. The latter is obtained in the form of a border or Gr\\\"obner basis. The algorithm is based on moment relaxations and, in contrast to other existing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609528","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":"math/0609528","created_at":"2026-05-18T00:00:33.147544+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0609528v2","created_at":"2026-05-18T00:00:33.147544+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609528","created_at":"2026-05-18T00:00:33.147544+00:00"},{"alias_kind":"pith_short_12","alias_value":"WY4WDKCDL26I","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"WY4WDKCDL26IY5D3","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"WY4WDKCD","created_at":"2026-05-18T12:25:54.717736+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/WY4WDKCDL26IY5D3Q4KSFOLXKM","json":"https://pith.science/pith/WY4WDKCDL26IY5D3Q4KSFOLXKM.json","graph_json":"https://pith.science/api/pith-number/WY4WDKCDL26IY5D3Q4KSFOLXKM/graph.json","events_json":"https://pith.science/api/pith-number/WY4WDKCDL26IY5D3Q4KSFOLXKM/events.json","paper":"https://pith.science/paper/WY4WDKCD"},"agent_actions":{"view_html":"https://pith.science/pith/WY4WDKCDL26IY5D3Q4KSFOLXKM","download_json":"https://pith.science/pith/WY4WDKCDL26IY5D3Q4KSFOLXKM.json","view_paper":"https://pith.science/paper/WY4WDKCD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0609528&json=true","fetch_graph":"https://pith.science/api/pith-number/WY4WDKCDL26IY5D3Q4KSFOLXKM/graph.json","fetch_events":"https://pith.science/api/pith-number/WY4WDKCDL26IY5D3Q4KSFOLXKM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WY4WDKCDL26IY5D3Q4KSFOLXKM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WY4WDKCDL26IY5D3Q4KSFOLXKM/action/storage_attestation","attest_author":"https://pith.science/pith/WY4WDKCDL26IY5D3Q4KSFOLXKM/action/author_attestation","sign_citation":"https://pith.science/pith/WY4WDKCDL26IY5D3Q4KSFOLXKM/action/citation_signature","submit_replication":"https://pith.science/pith/WY4WDKCDL26IY5D3Q4KSFOLXKM/action/replication_record"}},"created_at":"2026-05-18T00:00:33.147544+00:00","updated_at":"2026-05-18T00:00:33.147544+00:00"}