{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:64IEIQ5UF4JSBWMHW27KQFRQGL","short_pith_number":"pith:64IEIQ5U","schema_version":"1.0","canonical_sha256":"f7104443b42f1320d987b6bea8163032ffeea2da896b81b1468a26b31694d514","source":{"kind":"arxiv","id":"1606.04387","version":2},"attestation_state":"computed","paper":{"title":"Low-Rank Sum-of-Squares Representations on Varieties of Minimal Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AG","authors_text":"Cynthia Vinzant, Daniel Plaumann, Grigoriy Blekherman, Rainer Sinn","submitted_at":"2016-06-14T14:24:15Z","abstract_excerpt":"A celebrated result by Hilbert says that every real nonnegative ternary quartic is a sum of three squares. We show more generally that every nonnegative quadratic form on a real projective variety $X$ of minimal degree is a sum of $\\dim(X)+1$ squares of linear forms. This strengthens one direction of a recent result due to Blekherman, Smith, and Velasco. Our upper bound is the best possible, and it implies the existence of low-rank factorizations of positive semidefinite bivariate matrix polynomials and representations of biforms as sums of few squares. We determine the number of equivalence c"},"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":"1606.04387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-14T14:24:15Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"1e038393b33f8d3c17af70e48988f58c189c71c0653de0a1db92997d14567610","abstract_canon_sha256":"afba05654ff17cd9bef8dc7f6ecd1bb85fff5c966ba83a98fa3c7c38b2c9b5c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:32.456756Z","signature_b64":"HY9RCIe/oV/ApgXh5fhrWfAujWDlkE7BJccfNWOrdzaiDeauilF8RuGHA2BqK3Kh4vT/gMMfBJwgjwBUg/PxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7104443b42f1320d987b6bea8163032ffeea2da896b81b1468a26b31694d514","last_reissued_at":"2026-05-18T00:49:32.456106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:32.456106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low-Rank Sum-of-Squares Representations on Varieties of Minimal Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AG","authors_text":"Cynthia Vinzant, Daniel Plaumann, Grigoriy Blekherman, Rainer Sinn","submitted_at":"2016-06-14T14:24:15Z","abstract_excerpt":"A celebrated result by Hilbert says that every real nonnegative ternary quartic is a sum of three squares. We show more generally that every nonnegative quadratic form on a real projective variety $X$ of minimal degree is a sum of $\\dim(X)+1$ squares of linear forms. This strengthens one direction of a recent result due to Blekherman, Smith, and Velasco. Our upper bound is the best possible, and it implies the existence of low-rank factorizations of positive semidefinite bivariate matrix polynomials and representations of biforms as sums of few squares. We determine the number of equivalence c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04387","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":"1606.04387","created_at":"2026-05-18T00:49:32.456193+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.04387v2","created_at":"2026-05-18T00:49:32.456193+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04387","created_at":"2026-05-18T00:49:32.456193+00:00"},{"alias_kind":"pith_short_12","alias_value":"64IEIQ5UF4JS","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"64IEIQ5UF4JSBWMH","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"64IEIQ5U","created_at":"2026-05-18T12:30:01.593930+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/64IEIQ5UF4JSBWMHW27KQFRQGL","json":"https://pith.science/pith/64IEIQ5UF4JSBWMHW27KQFRQGL.json","graph_json":"https://pith.science/api/pith-number/64IEIQ5UF4JSBWMHW27KQFRQGL/graph.json","events_json":"https://pith.science/api/pith-number/64IEIQ5UF4JSBWMHW27KQFRQGL/events.json","paper":"https://pith.science/paper/64IEIQ5U"},"agent_actions":{"view_html":"https://pith.science/pith/64IEIQ5UF4JSBWMHW27KQFRQGL","download_json":"https://pith.science/pith/64IEIQ5UF4JSBWMHW27KQFRQGL.json","view_paper":"https://pith.science/paper/64IEIQ5U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.04387&json=true","fetch_graph":"https://pith.science/api/pith-number/64IEIQ5UF4JSBWMHW27KQFRQGL/graph.json","fetch_events":"https://pith.science/api/pith-number/64IEIQ5UF4JSBWMHW27KQFRQGL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/64IEIQ5UF4JSBWMHW27KQFRQGL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/64IEIQ5UF4JSBWMHW27KQFRQGL/action/storage_attestation","attest_author":"https://pith.science/pith/64IEIQ5UF4JSBWMHW27KQFRQGL/action/author_attestation","sign_citation":"https://pith.science/pith/64IEIQ5UF4JSBWMHW27KQFRQGL/action/citation_signature","submit_replication":"https://pith.science/pith/64IEIQ5UF4JSBWMHW27KQFRQGL/action/replication_record"}},"created_at":"2026-05-18T00:49:32.456193+00:00","updated_at":"2026-05-18T00:49:32.456193+00:00"}