{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PZPWYGN4LPPTC5ILN7M7GG77C7","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":"118af01780dfd27b442f5f5387d886a8084bcdd8b90c78926cb9b05897c5cfa9","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-01T18:13:14Z","title_canon_sha256":"57963c2addd22711d46053acaec48343999770c2520a8cab6e2c44c63a22719e"},"schema_version":"1.0","source":{"id":"1504.00931","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00931","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00931v1","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00931","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"pith_short_12","alias_value":"PZPWYGN4LPPT","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PZPWYGN4LPPTC5IL","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PZPWYGN4","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:de36587f30784b29359780ff06736230c659595ef8c3d8e38e9e04c015691b67","target":"graph","created_at":"2026-05-18T02:19:35Z","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":"The real radical ideal of a system of polynomials with finitely many complex roots is generated by a system of real polynomials having only real roots and free of multiplicities. It is a central object in computational real algebraic geometry and important as a preconditioner for numerical solvers. Lasserre and co-workers have shown that the real radical ideal of real polynomial systems with finitely many real solutions can be determined by a combination of semi-definite programming (SDP) and geometric involution techniques. A conjectured extension of such methods to positive dimensional polyn","authors_text":"Fei Wang, Greg Reid, Henry Wolkowicz, Wenyuan Wu","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-01T18:13:14Z","title":"Facial Reduction and SDP Methods for Systems of Polynomial Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00931","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":"sha256:7897c3ebe7fc955d8360cae4a4848c89668f9e4c3537cf3d213f0c1564cf2fa4","target":"record","created_at":"2026-05-18T02:19:35Z","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":"118af01780dfd27b442f5f5387d886a8084bcdd8b90c78926cb9b05897c5cfa9","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-01T18:13:14Z","title_canon_sha256":"57963c2addd22711d46053acaec48343999770c2520a8cab6e2c44c63a22719e"},"schema_version":"1.0","source":{"id":"1504.00931","kind":"arxiv","version":1}},"canonical_sha256":"7e5f6c19bc5bdf31750b6fd9f31bff17f894251daa42ae0a9338252084ad0875","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e5f6c19bc5bdf31750b6fd9f31bff17f894251daa42ae0a9338252084ad0875","first_computed_at":"2026-05-18T02:19:35.524594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:35.524594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BxN8u/wg2+m/R8MwKJLof3B1pkdLA71j4ZRcptYRAA8Imyi/edGnEfxd3BVzotYF/EUvLhhnPr9ZD/adSo+sBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:35.525274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00931","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7897c3ebe7fc955d8360cae4a4848c89668f9e4c3537cf3d213f0c1564cf2fa4","sha256:de36587f30784b29359780ff06736230c659595ef8c3d8e38e9e04c015691b67"],"state_sha256":"dce60c7a5c75d63fb02fb14c29f4855fe2b9f07d4ac17f889f0830799120ba94"}