{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:RPSQE6G64VXJXVNSHPWWVW77OI","short_pith_number":"pith:RPSQE6G6","schema_version":"1.0","canonical_sha256":"8be50278dee56e9bd5b23bed6adbff7202f637def60b8d8f06087c06ecd965bd","source":{"kind":"arxiv","id":"1402.0462","version":3},"attestation_state":"computed","paper":{"title":"Amoebas, Nonnegative Polynomials and Sums of Squares Supported on Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Sadik Iliman, Timo de Wolff","submitted_at":"2014-02-03T19:01:11Z","abstract_excerpt":"We completely characterize sections of the cones of nonnegative polynomials, convex polynomials and sums of squares with polynomials supported on circuits, a genuine class of sparse polynomials. In particular, nonnegativity is characterized by an invariant, which can be immediately derived from the initial polynomial. Furthermore, nonnegativity of such polynomials $f$ coincides with solidness of the amoeba of $f$, i.e., the Log-absolute-value image of the algebraic variety $\\mathcal{V}(f) \\subset (\\mathbb{C}^*)^n$ of $f$.\n  These results generalize earlier works both in amoeba theory and real "},"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":"1402.0462","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-03T19:01:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bfa685f7e8e735926836850121f3660a4067f352ed0c8e30c9e8c766010e4d82","abstract_canon_sha256":"4a2e0fa140f32de57def89a78818a5ee3f3b6ef5998da2734ad940b18b52c396"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:21.897516Z","signature_b64":"nWGjX2FJ8k4HV3O3LBhru6RQ3bkQBE66Q0R+yUbmO+Dz1iqX6KpxMlqLpu4yLvwB7IgbO//LydcF4wHRhFPJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8be50278dee56e9bd5b23bed6adbff7202f637def60b8d8f06087c06ecd965bd","last_reissued_at":"2026-05-18T01:29:21.896946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:21.896946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Amoebas, Nonnegative Polynomials and Sums of Squares Supported on Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Sadik Iliman, Timo de Wolff","submitted_at":"2014-02-03T19:01:11Z","abstract_excerpt":"We completely characterize sections of the cones of nonnegative polynomials, convex polynomials and sums of squares with polynomials supported on circuits, a genuine class of sparse polynomials. In particular, nonnegativity is characterized by an invariant, which can be immediately derived from the initial polynomial. Furthermore, nonnegativity of such polynomials $f$ coincides with solidness of the amoeba of $f$, i.e., the Log-absolute-value image of the algebraic variety $\\mathcal{V}(f) \\subset (\\mathbb{C}^*)^n$ of $f$.\n  These results generalize earlier works both in amoeba theory and real "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0462","kind":"arxiv","version":3},"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":"1402.0462","created_at":"2026-05-18T01:29:21.897039+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.0462v3","created_at":"2026-05-18T01:29:21.897039+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0462","created_at":"2026-05-18T01:29:21.897039+00:00"},{"alias_kind":"pith_short_12","alias_value":"RPSQE6G64VXJ","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RPSQE6G64VXJXVNS","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RPSQE6G6","created_at":"2026-05-18T12:28:46.137349+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/RPSQE6G64VXJXVNSHPWWVW77OI","json":"https://pith.science/pith/RPSQE6G64VXJXVNSHPWWVW77OI.json","graph_json":"https://pith.science/api/pith-number/RPSQE6G64VXJXVNSHPWWVW77OI/graph.json","events_json":"https://pith.science/api/pith-number/RPSQE6G64VXJXVNSHPWWVW77OI/events.json","paper":"https://pith.science/paper/RPSQE6G6"},"agent_actions":{"view_html":"https://pith.science/pith/RPSQE6G64VXJXVNSHPWWVW77OI","download_json":"https://pith.science/pith/RPSQE6G64VXJXVNSHPWWVW77OI.json","view_paper":"https://pith.science/paper/RPSQE6G6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.0462&json=true","fetch_graph":"https://pith.science/api/pith-number/RPSQE6G64VXJXVNSHPWWVW77OI/graph.json","fetch_events":"https://pith.science/api/pith-number/RPSQE6G64VXJXVNSHPWWVW77OI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RPSQE6G64VXJXVNSHPWWVW77OI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RPSQE6G64VXJXVNSHPWWVW77OI/action/storage_attestation","attest_author":"https://pith.science/pith/RPSQE6G64VXJXVNSHPWWVW77OI/action/author_attestation","sign_citation":"https://pith.science/pith/RPSQE6G64VXJXVNSHPWWVW77OI/action/citation_signature","submit_replication":"https://pith.science/pith/RPSQE6G64VXJXVNSHPWWVW77OI/action/replication_record"}},"created_at":"2026-05-18T01:29:21.897039+00:00","updated_at":"2026-05-18T01:29:21.897039+00:00"}