{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZCN6X4PAP4MR5MUYNE6TPHS3TM","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":"00c499f8864ff3569924cd0ee5579b4ad2587ed010575bb66d9b88d95c1013a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-12T17:31:29Z","title_canon_sha256":"d53733583eb332961d40bf0d9b7f543d7d622795f78db7f99e419f9376fe3c59"},"schema_version":"1.0","source":{"id":"1905.04751","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04751","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04751v1","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04751","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZCN6X4PAP4MR","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZCN6X4PAP4MR5MUY","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZCN6X4PA","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:8511b1429b92f489ca1823f166a3ac23bc0d127844a6d86a029391d1d582fcbc","target":"graph","created_at":"2026-05-17T23:46:23Z","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":"Hilbert's ternary quartic theorem states that every nonnegative degree 4 homogeneous polynomial in three variables can be written as a sum of three squares of homogeneous quadratic polynomials. We give a linear-algebraic approach to Hilbert's theorem by showing that a structured cone of positive semidefinite matrices is generated by rank 1 elements.","authors_text":"Anatolii Grinshpan, Hugo J. Woerdeman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-12T17:31:29Z","title":"A Linear-algebraic Proof of Hilbert's Ternary Quartic Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04751","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":"sha256:74b391fa3f65a3d82a34ddd00137ab7b80ab0743b04ae57dc2c02b93fdedbeab","target":"record","created_at":"2026-05-17T23:46:23Z","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":"00c499f8864ff3569924cd0ee5579b4ad2587ed010575bb66d9b88d95c1013a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-12T17:31:29Z","title_canon_sha256":"d53733583eb332961d40bf0d9b7f543d7d622795f78db7f99e419f9376fe3c59"},"schema_version":"1.0","source":{"id":"1905.04751","kind":"arxiv","version":1}},"canonical_sha256":"c89bebf1e07f191eb298693d379e5b9b07c4e000afa0dc9eac2c5484532f720a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c89bebf1e07f191eb298693d379e5b9b07c4e000afa0dc9eac2c5484532f720a","first_computed_at":"2026-05-17T23:46:23.657761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:23.657761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1d4CzxWAx3r33VBBa19UEjY89F8ignayjZmmkxOtOOXVUY9Qw6Nnlo0FDJNBd7Ccri5d7zyZhzs6rHGa4igkDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:23.658414Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.04751","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74b391fa3f65a3d82a34ddd00137ab7b80ab0743b04ae57dc2c02b93fdedbeab","sha256:8511b1429b92f489ca1823f166a3ac23bc0d127844a6d86a029391d1d582fcbc"],"state_sha256":"48069fa8765ac9e07d2ffbc48ad3559b73e33b2c9c761377fd8158feaa85a772"}