{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4HUS2MUYAG4VDROIRWJXJJ4OLY","short_pith_number":"pith:4HUS2MUY","canonical_record":{"source":{"id":"2506.17260","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T13:35:43Z","cross_cats_sorted":[],"title_canon_sha256":"9ddc9ab68d86eba2cf6e2c93c3c85ed5473c86cb7819d2d6e8837811430b263d","abstract_canon_sha256":"e7c201b2e72aac1a9a2102d5f86bf8da2d11361e73a33217085d6bee23b51b8a"},"schema_version":"1.0"},"canonical_sha256":"e1e92d329801b951c5c88d9374a78e5e33b238be60dc53e02e6c74c190b6cb6f","source":{"kind":"arxiv","id":"2506.17260","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.17260","created_at":"2026-07-05T11:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"2506.17260v4","created_at":"2026-07-05T11:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.17260","created_at":"2026-07-05T11:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"4HUS2MUYAG4V","created_at":"2026-07-05T11:38:30Z"},{"alias_kind":"pith_short_16","alias_value":"4HUS2MUYAG4VDROI","created_at":"2026-07-05T11:38:30Z"},{"alias_kind":"pith_short_8","alias_value":"4HUS2MUY","created_at":"2026-07-05T11:38:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4HUS2MUYAG4VDROIRWJXJJ4OLY","target":"record","payload":{"canonical_record":{"source":{"id":"2506.17260","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T13:35:43Z","cross_cats_sorted":[],"title_canon_sha256":"9ddc9ab68d86eba2cf6e2c93c3c85ed5473c86cb7819d2d6e8837811430b263d","abstract_canon_sha256":"e7c201b2e72aac1a9a2102d5f86bf8da2d11361e73a33217085d6bee23b51b8a"},"schema_version":"1.0"},"canonical_sha256":"e1e92d329801b951c5c88d9374a78e5e33b238be60dc53e02e6c74c190b6cb6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:30.435089Z","signature_b64":"JYUGuXRWHXK4W4TPSi8PI8C31jbcvmc0z9HcXoVX4qnMYznJ9nG6bM4HS4RlYhoLK5sgIUN8D+cStFrYc5auCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1e92d329801b951c5c88d9374a78e5e33b238be60dc53e02e6c74c190b6cb6f","last_reissued_at":"2026-07-05T11:38:30.434562Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:30.434562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.17260","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:38:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Reutfi6PutwuBEoHDXvVjaHVchvN2piv0S0r+Gk+KoOE+CJOrEFtCeXPQgcPmwGSekpO7pubOMjH4iIx4FpNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T08:22:41.293916Z"},"content_sha256":"a890cee7d802a44a1fa559a0a4fa527bc93d9c635a76dfe9d3a3033a2f2c3b20","schema_version":"1.0","event_id":"sha256:a890cee7d802a44a1fa559a0a4fa527bc93d9c635a76dfe9d3a3033a2f2c3b20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4HUS2MUYAG4VDROIRWJXJJ4OLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Postive Semidefinite and Sum of Squares Biquadratic Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chunfeng Cui, Liqun Qi, Yi Xu","submitted_at":"2025-06-09T13:35:43Z","abstract_excerpt":"Hilbert proved in 1888 that a positive semi-definite (PSD) homogeneous quartic polynomial of three variables always can be expressed as the sum of squares (SOS) of three quadratic polynomials, and a psd homogeneous quartic polynomial of four variables may not be sos. Only after 87 years, in 1975, Choi gave the explicit expression of such a psd-not-sos (PNS) homogeneous quartic polynomial of four variables. An $m \\times n$ biquadratic polynomial is a homogeneous quartic polynomial of $m+n$ variables. In this paper, we show that an $m \\times n$ biquadratic polynomial can be expressed as a tripar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17260","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.17260/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:38:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"st0bmEZB+mccFEJJghpbCxilIOuPH+5C7gPf6+xkMdAO2UpvojEcXlrougBhTrxX7CMDxyqwg/JHzN76WftRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T08:22:41.294398Z"},"content_sha256":"de1ebc4f909528b497b404087328d7e12cc5ece94e6d5d1bd514b347e7de829a","schema_version":"1.0","event_id":"sha256:de1ebc4f909528b497b404087328d7e12cc5ece94e6d5d1bd514b347e7de829a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4HUS2MUYAG4VDROIRWJXJJ4OLY/bundle.json","state_url":"https://pith.science/pith/4HUS2MUYAG4VDROIRWJXJJ4OLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4HUS2MUYAG4VDROIRWJXJJ4OLY/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":"2026-08-09T08:22:41Z","links":{"resolver":"https://pith.science/pith/4HUS2MUYAG4VDROIRWJXJJ4OLY","bundle":"https://pith.science/pith/4HUS2MUYAG4VDROIRWJXJJ4OLY/bundle.json","state":"https://pith.science/pith/4HUS2MUYAG4VDROIRWJXJJ4OLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4HUS2MUYAG4VDROIRWJXJJ4OLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4HUS2MUYAG4VDROIRWJXJJ4OLY","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":"e7c201b2e72aac1a9a2102d5f86bf8da2d11361e73a33217085d6bee23b51b8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T13:35:43Z","title_canon_sha256":"9ddc9ab68d86eba2cf6e2c93c3c85ed5473c86cb7819d2d6e8837811430b263d"},"schema_version":"1.0","source":{"id":"2506.17260","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.17260","created_at":"2026-07-05T11:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"2506.17260v4","created_at":"2026-07-05T11:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.17260","created_at":"2026-07-05T11:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"4HUS2MUYAG4V","created_at":"2026-07-05T11:38:30Z"},{"alias_kind":"pith_short_16","alias_value":"4HUS2MUYAG4VDROI","created_at":"2026-07-05T11:38:30Z"},{"alias_kind":"pith_short_8","alias_value":"4HUS2MUY","created_at":"2026-07-05T11:38:30Z"}],"graph_snapshots":[{"event_id":"sha256:de1ebc4f909528b497b404087328d7e12cc5ece94e6d5d1bd514b347e7de829a","target":"graph","created_at":"2026-07-05T11:38:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.17260/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Hilbert proved in 1888 that a positive semi-definite (PSD) homogeneous quartic polynomial of three variables always can be expressed as the sum of squares (SOS) of three quadratic polynomials, and a psd homogeneous quartic polynomial of four variables may not be sos. Only after 87 years, in 1975, Choi gave the explicit expression of such a psd-not-sos (PNS) homogeneous quartic polynomial of four variables. An $m \\times n$ biquadratic polynomial is a homogeneous quartic polynomial of $m+n$ variables. In this paper, we show that an $m \\times n$ biquadratic polynomial can be expressed as a tripar","authors_text":"Chunfeng Cui, Liqun Qi, Yi Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T13:35:43Z","title":"Postive Semidefinite and Sum of Squares Biquadratic Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17260","kind":"arxiv","version":4},"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:a890cee7d802a44a1fa559a0a4fa527bc93d9c635a76dfe9d3a3033a2f2c3b20","target":"record","created_at":"2026-07-05T11:38:30Z","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":"e7c201b2e72aac1a9a2102d5f86bf8da2d11361e73a33217085d6bee23b51b8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T13:35:43Z","title_canon_sha256":"9ddc9ab68d86eba2cf6e2c93c3c85ed5473c86cb7819d2d6e8837811430b263d"},"schema_version":"1.0","source":{"id":"2506.17260","kind":"arxiv","version":4}},"canonical_sha256":"e1e92d329801b951c5c88d9374a78e5e33b238be60dc53e02e6c74c190b6cb6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1e92d329801b951c5c88d9374a78e5e33b238be60dc53e02e6c74c190b6cb6f","first_computed_at":"2026-07-05T11:38:30.434562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:30.434562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JYUGuXRWHXK4W4TPSi8PI8C31jbcvmc0z9HcXoVX4qnMYznJ9nG6bM4HS4RlYhoLK5sgIUN8D+cStFrYc5auCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:30.435089Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.17260","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a890cee7d802a44a1fa559a0a4fa527bc93d9c635a76dfe9d3a3033a2f2c3b20","sha256:de1ebc4f909528b497b404087328d7e12cc5ece94e6d5d1bd514b347e7de829a"],"state_sha256":"816cd2622e6dcdb095bc3bad548f192db2df65b3012d14627502b5cf5c48f697"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z4BfcH1JmtW3goehr9yNa5RYm/ehX5omAWbq5sRitvFM5KrAq6d+drExPrX/aBNTADIT9IU8VxuzN1Mmh1yhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T08:22:41.297638Z","bundle_sha256":"273d038f25b45e431356ecbe71be049ae476b7be69740a5b8dcc25ae89f0b492"}}