{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E5FI6XGQUNSJEJ4OEQCKPIWMH7","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":"37d88cd75d9dfc739cdcc39094af7ace352587da32ac8c16b046d2bf01911dce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-23T21:57:45Z","title_canon_sha256":"117557e1478ed764330d350a876eae5d40e3b86446e1d84750a3f713884af00b"},"schema_version":"1.0","source":{"id":"1602.07330","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07330","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07330v2","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07330","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"E5FI6XGQUNSJ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E5FI6XGQUNSJEJ4O","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E5FI6XGQ","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:5690bb6e0f2f4b060bba3e6221c506927115ce74741d318778bf9d38105971fa","target":"graph","created_at":"2026-05-18T00:41:08Z","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":"Artin solved Hilbert's 17th problem, proving that a real polynomial in $n$ variables that is positive semidefinite is a sum of squares of rational functions, and Pfister showed that only $2^n$ squares are needed. In this paper, we investigate situations where Pfister's theorem may be improved. We show that a real polynomial of degree $d$ in $n$ variables that is positive semidefinite is a sum of $2^n-1$ squares of rational functions if $d\\leq 2n-2$. If $n$ is even, or equal to $3$ or $5$, this result also holds for $d=2n$.","authors_text":"Olivier Benoist","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-23T21:57:45Z","title":"On Hilbert's 17th problem in low degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07330","kind":"arxiv","version":2},"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:e182131d3075afc9779245dcf2f4e78cbdbfdbec19d43f417caf62d0af841688","target":"record","created_at":"2026-05-18T00:41:08Z","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":"37d88cd75d9dfc739cdcc39094af7ace352587da32ac8c16b046d2bf01911dce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-23T21:57:45Z","title_canon_sha256":"117557e1478ed764330d350a876eae5d40e3b86446e1d84750a3f713884af00b"},"schema_version":"1.0","source":{"id":"1602.07330","kind":"arxiv","version":2}},"canonical_sha256":"274a8f5cd0a36492278e2404a7a2cc3fe079532e0073a278b141033767dbc87b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"274a8f5cd0a36492278e2404a7a2cc3fe079532e0073a278b141033767dbc87b","first_computed_at":"2026-05-18T00:41:08.281109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:08.281109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"umcKAi1fq8VcE66bk88LOEJyng5SIvnRwcxspFtX4rXfynaC1pYLEADbuqyd14ngh8WxCYnQyzIIRspiUCbMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:08.281608Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07330","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e182131d3075afc9779245dcf2f4e78cbdbfdbec19d43f417caf62d0af841688","sha256:5690bb6e0f2f4b060bba3e6221c506927115ce74741d318778bf9d38105971fa"],"state_sha256":"9ab08a71e3f0ca2af2f3a398e0c4c0882e735d7f2de862be0e41a03813e3530a"}