{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:E5FI6XGQUNSJEJ4OEQCKPIWMH7","short_pith_number":"pith:E5FI6XGQ","canonical_record":{"source":{"id":"1602.07330","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-23T21:57:45Z","cross_cats_sorted":[],"title_canon_sha256":"117557e1478ed764330d350a876eae5d40e3b86446e1d84750a3f713884af00b","abstract_canon_sha256":"37d88cd75d9dfc739cdcc39094af7ace352587da32ac8c16b046d2bf01911dce"},"schema_version":"1.0"},"canonical_sha256":"274a8f5cd0a36492278e2404a7a2cc3fe079532e0073a278b141033767dbc87b","source":{"kind":"arxiv","id":"1602.07330","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:E5FI6XGQUNSJEJ4OEQCKPIWMH7","target":"record","payload":{"canonical_record":{"source":{"id":"1602.07330","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-23T21:57:45Z","cross_cats_sorted":[],"title_canon_sha256":"117557e1478ed764330d350a876eae5d40e3b86446e1d84750a3f713884af00b","abstract_canon_sha256":"37d88cd75d9dfc739cdcc39094af7ace352587da32ac8c16b046d2bf01911dce"},"schema_version":"1.0"},"canonical_sha256":"274a8f5cd0a36492278e2404a7a2cc3fe079532e0073a278b141033767dbc87b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:08.281608Z","signature_b64":"umcKAi1fq8VcE66bk88LOEJyng5SIvnRwcxspFtX4rXfynaC1pYLEADbuqyd14ngh8WxCYnQyzIIRspiUCbMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"274a8f5cd0a36492278e2404a7a2cc3fe079532e0073a278b141033767dbc87b","last_reissued_at":"2026-05-18T00:41:08.281109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:08.281109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.07330","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P3SaCSBNIXTS7UEebKEoVIuXxvFnhUpW8LoXyWDX7tMSJaKnwcPgvXGLyTZxrElTOJlsVsO+0QjOllqxJfYvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:11:11.840711Z"},"content_sha256":"e182131d3075afc9779245dcf2f4e78cbdbfdbec19d43f417caf62d0af841688","schema_version":"1.0","event_id":"sha256:e182131d3075afc9779245dcf2f4e78cbdbfdbec19d43f417caf62d0af841688"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:E5FI6XGQUNSJEJ4OEQCKPIWMH7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Hilbert's 17th problem in low degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Olivier Benoist","submitted_at":"2016-02-23T21:57:45Z","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 $d=2n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07330","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3SytEGpL6hrA4Epoun1Ij9P+5dmbp5FVsFjeB3vP2lF6whK2le8Tv6fwa2SOZgO3TH+jdpYGdtQkm28q4p77AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:11:11.841392Z"},"content_sha256":"5690bb6e0f2f4b060bba3e6221c506927115ce74741d318778bf9d38105971fa","schema_version":"1.0","event_id":"sha256:5690bb6e0f2f4b060bba3e6221c506927115ce74741d318778bf9d38105971fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E5FI6XGQUNSJEJ4OEQCKPIWMH7/bundle.json","state_url":"https://pith.science/pith/E5FI6XGQUNSJEJ4OEQCKPIWMH7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E5FI6XGQUNSJEJ4OEQCKPIWMH7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T23:11:11Z","links":{"resolver":"https://pith.science/pith/E5FI6XGQUNSJEJ4OEQCKPIWMH7","bundle":"https://pith.science/pith/E5FI6XGQUNSJEJ4OEQCKPIWMH7/bundle.json","state":"https://pith.science/pith/E5FI6XGQUNSJEJ4OEQCKPIWMH7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E5FI6XGQUNSJEJ4OEQCKPIWMH7/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4d2bGwJfHVV4DB+hKTrikJbKLveV55LkS+9rQG40VA8D7FsnpQ8xI8TcdJdh3ijBGLei75F06gEkdDWWnmQODA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:11:11.844997Z","bundle_sha256":"070e0ea1e02e0e6948a7349c918aadcc99d2a9a5012c43a31d614bca16c544b1"}}