{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:G4F6UJHWWJV3PVZYZYNBD6QDCX","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":"d8afa1e20d5d891342d81c19fa692fb134de95cf9bbaa08b89edf5e3763fd28b","cross_cats_sorted":["cs.LG","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-03-08T06:20:10Z","title_canon_sha256":"7bfbcc4d38ac56825b661e45d65eba9020c0ad70083f21181b7a150e82451d10"},"schema_version":"1.0","source":{"id":"2003.03731","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.03731","created_at":"2026-07-05T01:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"2003.03731v4","created_at":"2026-07-05T01:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.03731","created_at":"2026-07-05T01:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"G4F6UJHWWJV3","created_at":"2026-07-05T01:45:41Z"},{"alias_kind":"pith_short_16","alias_value":"G4F6UJHWWJV3PVZY","created_at":"2026-07-05T01:45:41Z"},{"alias_kind":"pith_short_8","alias_value":"G4F6UJHW","created_at":"2026-07-05T01:45:41Z"}],"graph_snapshots":[{"event_id":"sha256:53909e95468f0d9fa2319aee32adff54829acb7053efe7b11e590182d06887a1","target":"graph","created_at":"2026-07-05T01:45:41Z","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/2003.03731/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, the conditional SAGE certificate has been proposed as a sufficient condition for signomial positivity over a convex set. In this article, we show that the conditional SAGE certificate is $\\textit{complete}$. That is, for any signomial $f(\\mathbf{x}) = \\sum_{j=1}^{\\ell}c_j \\exp(\\mathbf{A}_j\\mathbf{x})$ defined by rational exponents that is positive over a compact convex set $\\mathcal{X}$, there is $p \\in \\mathbb{Z}_+$ and a specific positive definite function $w(\\mathbf{x})$ such that $w(\\mathbf{x})^p f(\\mathbf{x})$ may be verified by the conditional SAGE certificate. The completeness","authors_text":"Allen Houze Wang, Pascal Poupart, Priyank Jaini, Yaoliang Yu","cross_cats":["cs.LG","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-03-08T06:20:10Z","title":"A Positivstellensatz for Conditional SAGE Signomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.03731","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":"sha256:7190029209c108c628c801493dbc40806327a969f6518ae59ae8da84033a9277","target":"record","created_at":"2026-07-05T01:45:41Z","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":"d8afa1e20d5d891342d81c19fa692fb134de95cf9bbaa08b89edf5e3763fd28b","cross_cats_sorted":["cs.LG","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-03-08T06:20:10Z","title_canon_sha256":"7bfbcc4d38ac56825b661e45d65eba9020c0ad70083f21181b7a150e82451d10"},"schema_version":"1.0","source":{"id":"2003.03731","kind":"arxiv","version":4}},"canonical_sha256":"370bea24f6b26bb7d738ce1a11fa0315dd3b3e56237e00468101fd11ec6490e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"370bea24f6b26bb7d738ce1a11fa0315dd3b3e56237e00468101fd11ec6490e7","first_computed_at":"2026-07-05T01:45:41.862301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:45:41.862301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WDGPbWmIDvzyWDULPQjFKCvRIg7HBbKiqcCL6WMMBoZ4t2aq17LTguBdgRwmnfuH/b7UMgkrQp4jsM/l3EScAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:45:41.862697Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.03731","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7190029209c108c628c801493dbc40806327a969f6518ae59ae8da84033a9277","sha256:53909e95468f0d9fa2319aee32adff54829acb7053efe7b11e590182d06887a1"],"state_sha256":"9f3fa82b13a24c7514d319ea194d680560c5a64c6aaa162d32be2b61ed17a9b7"}