{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:6L6QRECS3BG65SGEVTDOOKSU3J","short_pith_number":"pith:6L6QRECS","schema_version":"1.0","canonical_sha256":"f2fd089052d84deec8c4acc6e72a54da7f52bf9e403d4bee9a59a81150209f07","source":{"kind":"arxiv","id":"1904.12455","version":1},"attestation_state":"computed","paper":{"title":"On Hyperbolic Polynomials and Four-term Recurrence with Linear Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Richard Adams","submitted_at":"2019-04-29T05:50:47Z","abstract_excerpt":"For any real numbers $a,\\ b$, and $c$, we form the sequence of polynomials $\\{P_n(z)\\}_{n=0}^\\infty$ satisfying the four-term recurrence \\[ P_n(z)+azP_{n-1}(z)+bP_{n-2}(z)+czP_{n-3}(z)=0,\\ n\\in\\mathbb{N}, \\] with the initial conditions $P_0(z)=1$ and $P_{-n}(z)=0$. We find necessary and sufficient conditions on $a,\\ b$, and $c$ under which the zeros of $P_n(z)$ are real for all $n$, and provide an explicit real interval on which $\\displaystyle\\bigcup_{n=0}^\\infty\\mathcal{Z}(P_n)$ is dense, where $\\mathcal{Z}(P_n)$ is the set of zeros of $P_n(z)$."},"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":"1904.12455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-29T05:50:47Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"9893fb6fccc520a2ec732b567034ec62b9ccae6e9f367ae6f78cbdae73b35e40","abstract_canon_sha256":"d423edf2944023d01216d9b90bfd16a79bcef79e2560f357d49ef5bde1116ddc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:35.130185Z","signature_b64":"dil+TmuYM3gMNwpzvHecW92kukiaDGGFjZU0b4dVu4eS4Wqjuy+1l/qYy2Qt9kMHV4PI+R1JExlCERkzFaYcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2fd089052d84deec8c4acc6e72a54da7f52bf9e403d4bee9a59a81150209f07","last_reissued_at":"2026-05-17T23:47:35.129768Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:35.129768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Hyperbolic Polynomials and Four-term Recurrence with Linear Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Richard Adams","submitted_at":"2019-04-29T05:50:47Z","abstract_excerpt":"For any real numbers $a,\\ b$, and $c$, we form the sequence of polynomials $\\{P_n(z)\\}_{n=0}^\\infty$ satisfying the four-term recurrence \\[ P_n(z)+azP_{n-1}(z)+bP_{n-2}(z)+czP_{n-3}(z)=0,\\ n\\in\\mathbb{N}, \\] with the initial conditions $P_0(z)=1$ and $P_{-n}(z)=0$. We find necessary and sufficient conditions on $a,\\ b$, and $c$ under which the zeros of $P_n(z)$ are real for all $n$, and provide an explicit real interval on which $\\displaystyle\\bigcup_{n=0}^\\infty\\mathcal{Z}(P_n)$ is dense, where $\\mathcal{Z}(P_n)$ is the set of zeros of $P_n(z)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12455","kind":"arxiv","version":1},"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":"1904.12455","created_at":"2026-05-17T23:47:35.129833+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.12455v1","created_at":"2026-05-17T23:47:35.129833+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12455","created_at":"2026-05-17T23:47:35.129833+00:00"},{"alias_kind":"pith_short_12","alias_value":"6L6QRECS3BG6","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"6L6QRECS3BG65SGE","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"6L6QRECS","created_at":"2026-05-18T12:33:10.108867+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/6L6QRECS3BG65SGEVTDOOKSU3J","json":"https://pith.science/pith/6L6QRECS3BG65SGEVTDOOKSU3J.json","graph_json":"https://pith.science/api/pith-number/6L6QRECS3BG65SGEVTDOOKSU3J/graph.json","events_json":"https://pith.science/api/pith-number/6L6QRECS3BG65SGEVTDOOKSU3J/events.json","paper":"https://pith.science/paper/6L6QRECS"},"agent_actions":{"view_html":"https://pith.science/pith/6L6QRECS3BG65SGEVTDOOKSU3J","download_json":"https://pith.science/pith/6L6QRECS3BG65SGEVTDOOKSU3J.json","view_paper":"https://pith.science/paper/6L6QRECS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.12455&json=true","fetch_graph":"https://pith.science/api/pith-number/6L6QRECS3BG65SGEVTDOOKSU3J/graph.json","fetch_events":"https://pith.science/api/pith-number/6L6QRECS3BG65SGEVTDOOKSU3J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6L6QRECS3BG65SGEVTDOOKSU3J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6L6QRECS3BG65SGEVTDOOKSU3J/action/storage_attestation","attest_author":"https://pith.science/pith/6L6QRECS3BG65SGEVTDOOKSU3J/action/author_attestation","sign_citation":"https://pith.science/pith/6L6QRECS3BG65SGEVTDOOKSU3J/action/citation_signature","submit_replication":"https://pith.science/pith/6L6QRECS3BG65SGEVTDOOKSU3J/action/replication_record"}},"created_at":"2026-05-17T23:47:35.129833+00:00","updated_at":"2026-05-17T23:47:35.129833+00:00"}