{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CWXA6FWG7ENDNN26VROLSWNAZ2","short_pith_number":"pith:CWXA6FWG","schema_version":"1.0","canonical_sha256":"15ae0f16c6f91a36b75eac5cb959a0ce88ce353292dd78e0453b5abbe1fd28bc","source":{"kind":"arxiv","id":"1507.00494","version":2},"attestation_state":"computed","paper":{"title":"Nonnegative Trigonometric Polynomials and Sturms Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Man Kam Kwong","submitted_at":"2015-07-02T09:51:35Z","abstract_excerpt":"In an earlier article [3], we presented an algorithm that can be used to rigorously check whether a specific cosine or sine polynomial is nonnegative in a given interval or not. The algorithm proves to be an indispensable tool in establishing some recent results on nonnegative trigonometric polynomials. See, for example, [2], [4] and [5]. It continues to play an essential role in several ongoing projects. The algorithm, however, cannot handle general trigonometric polynomials that involve both cosine and sine terms. Some ad hoc methods to deal with such polynomials have been suggested in [3], "},"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":"1507.00494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-02T09:51:35Z","cross_cats_sorted":[],"title_canon_sha256":"345f1bd66b00ee442b267ca0c5f80e77bc89953df6715afa9debb689ac4dbd85","abstract_canon_sha256":"608aa649f0835ba20865e62003c18d5a7fd843c6b35e4b549c772f0a2cd84538"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:22.843544Z","signature_b64":"TNJ1pwocSdrGwzdDc8xZsME8SRpRVDg8NW227Frrf09nWawoh64pjzu5qKADZDlRRUOqYa8ncNQI7cy19MbdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15ae0f16c6f91a36b75eac5cb959a0ce88ce353292dd78e0453b5abbe1fd28bc","last_reissued_at":"2026-05-18T01:37:22.842859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:22.842859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonnegative Trigonometric Polynomials and Sturms Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Man Kam Kwong","submitted_at":"2015-07-02T09:51:35Z","abstract_excerpt":"In an earlier article [3], we presented an algorithm that can be used to rigorously check whether a specific cosine or sine polynomial is nonnegative in a given interval or not. The algorithm proves to be an indispensable tool in establishing some recent results on nonnegative trigonometric polynomials. See, for example, [2], [4] and [5]. It continues to play an essential role in several ongoing projects. The algorithm, however, cannot handle general trigonometric polynomials that involve both cosine and sine terms. Some ad hoc methods to deal with such polynomials have been suggested in [3], "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00494","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":"1507.00494","created_at":"2026-05-18T01:37:22.842958+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.00494v2","created_at":"2026-05-18T01:37:22.842958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00494","created_at":"2026-05-18T01:37:22.842958+00:00"},{"alias_kind":"pith_short_12","alias_value":"CWXA6FWG7END","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CWXA6FWG7ENDNN26","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CWXA6FWG","created_at":"2026-05-18T12:29:17.054201+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/CWXA6FWG7ENDNN26VROLSWNAZ2","json":"https://pith.science/pith/CWXA6FWG7ENDNN26VROLSWNAZ2.json","graph_json":"https://pith.science/api/pith-number/CWXA6FWG7ENDNN26VROLSWNAZ2/graph.json","events_json":"https://pith.science/api/pith-number/CWXA6FWG7ENDNN26VROLSWNAZ2/events.json","paper":"https://pith.science/paper/CWXA6FWG"},"agent_actions":{"view_html":"https://pith.science/pith/CWXA6FWG7ENDNN26VROLSWNAZ2","download_json":"https://pith.science/pith/CWXA6FWG7ENDNN26VROLSWNAZ2.json","view_paper":"https://pith.science/paper/CWXA6FWG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.00494&json=true","fetch_graph":"https://pith.science/api/pith-number/CWXA6FWG7ENDNN26VROLSWNAZ2/graph.json","fetch_events":"https://pith.science/api/pith-number/CWXA6FWG7ENDNN26VROLSWNAZ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CWXA6FWG7ENDNN26VROLSWNAZ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CWXA6FWG7ENDNN26VROLSWNAZ2/action/storage_attestation","attest_author":"https://pith.science/pith/CWXA6FWG7ENDNN26VROLSWNAZ2/action/author_attestation","sign_citation":"https://pith.science/pith/CWXA6FWG7ENDNN26VROLSWNAZ2/action/citation_signature","submit_replication":"https://pith.science/pith/CWXA6FWG7ENDNN26VROLSWNAZ2/action/replication_record"}},"created_at":"2026-05-18T01:37:22.842958+00:00","updated_at":"2026-05-18T01:37:22.842958+00:00"}