{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QAZRWOL5ZMLJMAADJWPBDG7LP3","short_pith_number":"pith:QAZRWOL5","schema_version":"1.0","canonical_sha256":"80331b397dcb169600034d9e119beb7eec1f2403baab526dcb08e104998de604","source":{"kind":"arxiv","id":"1607.06010","version":2},"attestation_state":"computed","paper":{"title":"A Positivstellensatz for Sums of Nonnegative Circuit Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AG","authors_text":"Mareike Dressler, Sadik Iliman, Timo de Wolff","submitted_at":"2016-07-20T16:24:24Z","abstract_excerpt":"Recently, the second and the third author developed sums of nonnegative circuit polynomials (SONC) as a new certificate of nonnegativity for real polynomials, which is independent of sums of squares.\n  In this article we show that the SONC cone is full-dimensional in the cone of nonnegative polynomials. We establish a Positivstellensatz which guarantees that every polynomial which is positive on a given compact, semi-algebraic set can be represented by the constraints of the set and SONC polynomials. Based on this Positivstellensatz we provide a hierarchy of lower bounds converging against the"},"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":"1607.06010","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-20T16:24:24Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"0d1594c30cf0ca4543567e135c54ac0c86f168ec4981cfb6372151f86b748ebb","abstract_canon_sha256":"8fd87c53bd830bce8962b6de39539a6481d89568b34ac4b5430d53bb38526b00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:32.809839Z","signature_b64":"rt71o7OVu7GTC4sFC5wGoXu7RfEKWw+j8jFdLUNNYQFSP0rprazI3an6beU2HNGDsXW5XK6u+FFKpohUtrNaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80331b397dcb169600034d9e119beb7eec1f2403baab526dcb08e104998de604","last_reissued_at":"2026-05-18T00:48:32.809338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:32.809338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Positivstellensatz for Sums of Nonnegative Circuit Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AG","authors_text":"Mareike Dressler, Sadik Iliman, Timo de Wolff","submitted_at":"2016-07-20T16:24:24Z","abstract_excerpt":"Recently, the second and the third author developed sums of nonnegative circuit polynomials (SONC) as a new certificate of nonnegativity for real polynomials, which is independent of sums of squares.\n  In this article we show that the SONC cone is full-dimensional in the cone of nonnegative polynomials. We establish a Positivstellensatz which guarantees that every polynomial which is positive on a given compact, semi-algebraic set can be represented by the constraints of the set and SONC polynomials. Based on this Positivstellensatz we provide a hierarchy of lower bounds converging against the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06010","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":"1607.06010","created_at":"2026-05-18T00:48:32.809414+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.06010v2","created_at":"2026-05-18T00:48:32.809414+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06010","created_at":"2026-05-18T00:48:32.809414+00:00"},{"alias_kind":"pith_short_12","alias_value":"QAZRWOL5ZMLJ","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QAZRWOL5ZMLJMAAD","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QAZRWOL5","created_at":"2026-05-18T12:30:39.010887+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/QAZRWOL5ZMLJMAADJWPBDG7LP3","json":"https://pith.science/pith/QAZRWOL5ZMLJMAADJWPBDG7LP3.json","graph_json":"https://pith.science/api/pith-number/QAZRWOL5ZMLJMAADJWPBDG7LP3/graph.json","events_json":"https://pith.science/api/pith-number/QAZRWOL5ZMLJMAADJWPBDG7LP3/events.json","paper":"https://pith.science/paper/QAZRWOL5"},"agent_actions":{"view_html":"https://pith.science/pith/QAZRWOL5ZMLJMAADJWPBDG7LP3","download_json":"https://pith.science/pith/QAZRWOL5ZMLJMAADJWPBDG7LP3.json","view_paper":"https://pith.science/paper/QAZRWOL5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.06010&json=true","fetch_graph":"https://pith.science/api/pith-number/QAZRWOL5ZMLJMAADJWPBDG7LP3/graph.json","fetch_events":"https://pith.science/api/pith-number/QAZRWOL5ZMLJMAADJWPBDG7LP3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QAZRWOL5ZMLJMAADJWPBDG7LP3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QAZRWOL5ZMLJMAADJWPBDG7LP3/action/storage_attestation","attest_author":"https://pith.science/pith/QAZRWOL5ZMLJMAADJWPBDG7LP3/action/author_attestation","sign_citation":"https://pith.science/pith/QAZRWOL5ZMLJMAADJWPBDG7LP3/action/citation_signature","submit_replication":"https://pith.science/pith/QAZRWOL5ZMLJMAADJWPBDG7LP3/action/replication_record"}},"created_at":"2026-05-18T00:48:32.809414+00:00","updated_at":"2026-05-18T00:48:32.809414+00:00"}