{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:65KVL6KZQHDFRNDLBES5SGBI6E","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":"ee719f736ed79026d4048fde4ba46c4488e9c1a0bb393eebcd6a48d7314d7518","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-20T05:05:08Z","title_canon_sha256":"c345a18eaf668a0a253661efe58945569bbd3f72bc8cfca0da15dd9d436cd7ec"},"schema_version":"1.0","source":{"id":"1212.4924","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4924","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4924v1","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4924","created_at":"2026-05-18T03:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"65KVL6KZQHDF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"65KVL6KZQHDFRNDL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"65KVL6KZ","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:63ffc507d4f0447203346c5f1c5668aa3fb1176596b8c13e0a7dd1212c608a9a","target":"graph","created_at":"2026-05-18T03:38:04Z","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":"For an ideal I with a positive dimensional real variety, based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Groebner basis of an ideal J generated by the kernel of a truncated moment matrix and nesting between I and its real radical ideal. We provide a certificate consisting of a condition on coranks of moment matrices for terminating the algorithm. For a generic delta-regular coordinate system, we prove that the condition is satisfiable in a large enough order of moment relaxations.","authors_text":"Chu Wang, Lihong Zhi, Yue Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-20T05:05:08Z","title":"A certificate for semidefinite relaxations in computing positive dimensional real varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4924","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":"sha256:544d38f2d879fdd66530197372b8b069af2356861b3246468a31c0fd7c88d534","target":"record","created_at":"2026-05-18T03:38:04Z","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":"ee719f736ed79026d4048fde4ba46c4488e9c1a0bb393eebcd6a48d7314d7518","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-20T05:05:08Z","title_canon_sha256":"c345a18eaf668a0a253661efe58945569bbd3f72bc8cfca0da15dd9d436cd7ec"},"schema_version":"1.0","source":{"id":"1212.4924","kind":"arxiv","version":1}},"canonical_sha256":"f75555f95981c658b46b0925d91828f118254a4c2f991af432a0a653705f1fe6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f75555f95981c658b46b0925d91828f118254a4c2f991af432a0a653705f1fe6","first_computed_at":"2026-05-18T03:38:04.333426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:04.333426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bx5sruy1oQ2HCqeWoBNkUk3J5V6EWbMBSAx0wFRp31NwOjdmFPRdhMgZ8rOEntakctyTDtbr74371mdVNGLeAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:04.333954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4924","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:544d38f2d879fdd66530197372b8b069af2356861b3246468a31c0fd7c88d534","sha256:63ffc507d4f0447203346c5f1c5668aa3fb1176596b8c13e0a7dd1212c608a9a"],"state_sha256":"c2236943a1201083d6d9fd9582890a4dc97894d5eb223ffbb734df3bc80102d8"}