{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RPSQE6G64VXJXVNSHPWWVW77OI","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":"4a2e0fa140f32de57def89a78818a5ee3f3b6ef5998da2734ad940b18b52c396","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-03T19:01:11Z","title_canon_sha256":"bfa685f7e8e735926836850121f3660a4067f352ed0c8e30c9e8c766010e4d82"},"schema_version":"1.0","source":{"id":"1402.0462","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0462","created_at":"2026-05-18T01:29:21Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0462v3","created_at":"2026-05-18T01:29:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0462","created_at":"2026-05-18T01:29:21Z"},{"alias_kind":"pith_short_12","alias_value":"RPSQE6G64VXJ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RPSQE6G64VXJXVNS","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RPSQE6G6","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:2112f29a2ec4231d0c1ef35b5ee8bee133b2e2927dc02200830df0259681a028","target":"graph","created_at":"2026-05-18T01:29:21Z","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":"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 ","authors_text":"Sadik Iliman, Timo de Wolff","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-03T19:01:11Z","title":"Amoebas, Nonnegative Polynomials and Sums of Squares Supported on Circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0462","kind":"arxiv","version":3},"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:fedd02dcec38b56a6b8f2a460541cb897d5c7ed8a26eb09fe13b403612cfa711","target":"record","created_at":"2026-05-18T01:29:21Z","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":"4a2e0fa140f32de57def89a78818a5ee3f3b6ef5998da2734ad940b18b52c396","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-03T19:01:11Z","title_canon_sha256":"bfa685f7e8e735926836850121f3660a4067f352ed0c8e30c9e8c766010e4d82"},"schema_version":"1.0","source":{"id":"1402.0462","kind":"arxiv","version":3}},"canonical_sha256":"8be50278dee56e9bd5b23bed6adbff7202f637def60b8d8f06087c06ecd965bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8be50278dee56e9bd5b23bed6adbff7202f637def60b8d8f06087c06ecd965bd","first_computed_at":"2026-05-18T01:29:21.896946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:21.896946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nWGjX2FJ8k4HV3O3LBhru6RQ3bkQBE66Q0R+yUbmO+Dz1iqX6KpxMlqLpu4yLvwB7IgbO//LydcF4wHRhFPJAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:21.897516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0462","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fedd02dcec38b56a6b8f2a460541cb897d5c7ed8a26eb09fe13b403612cfa711","sha256:2112f29a2ec4231d0c1ef35b5ee8bee133b2e2927dc02200830df0259681a028"],"state_sha256":"979a5e34178631efd918a289ee1c56ad259bbe74f870012b8caf2b16a66d7c34"}