{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:U6GZH3V4CFC2LU7VSBQYL4KQ5Q","short_pith_number":"pith:U6GZH3V4","schema_version":"1.0","canonical_sha256":"a78d93eebc1145a5d3f5906185f150ec35b9ad3e6058cbb1e51deb20df8ce7cd","source":{"kind":"arxiv","id":"1205.0305","version":1},"attestation_state":"computed","paper":{"title":"Branden's Conjectures on the Boros-Moll Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Arthur L. B. Yang, Donna Q. J. Dou, William Y. C. Chen","submitted_at":"2012-05-02T02:34:41Z","abstract_excerpt":"We prove two conjectures of Br\\\"{a}nd\\'{e}n on the real-rootedness of polynomials $Q_n(x)$ and $R_n(x)$ which are related to the Boros-Moll polynomials $P_n(x)$. In fact, we show that both $Q_n(x)$ and $R_n(x)$ form Sturm sequences. The first conjecture implies the 2-log-concavity of $P_n(x)$, and the second conjecture implies the 3-log-concavity of $P_n(x)$."},"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":"1205.0305","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-02T02:34:41Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"2d7ceaad7e50ee9dfaaa2004a370598747021bfcf029f5c6f08fbfe78bff3acd","abstract_canon_sha256":"c304d398ce4fac5a1a2601f8030bb45d1f9676461e617be372db80e0f816c38f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:34.825898Z","signature_b64":"rcRnDN882NVsfX57RuI+/mMmBzL5DA5CutHmJmfVMNTLrGPrH6s3MJ27zkUvBPb0igYCJ8cw+nu0Tp6W+jCNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a78d93eebc1145a5d3f5906185f150ec35b9ad3e6058cbb1e51deb20df8ce7cd","last_reissued_at":"2026-05-18T03:56:34.825399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:34.825399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Branden's Conjectures on the Boros-Moll Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Arthur L. B. Yang, Donna Q. J. Dou, William Y. C. Chen","submitted_at":"2012-05-02T02:34:41Z","abstract_excerpt":"We prove two conjectures of Br\\\"{a}nd\\'{e}n on the real-rootedness of polynomials $Q_n(x)$ and $R_n(x)$ which are related to the Boros-Moll polynomials $P_n(x)$. In fact, we show that both $Q_n(x)$ and $R_n(x)$ form Sturm sequences. The first conjecture implies the 2-log-concavity of $P_n(x)$, and the second conjecture implies the 3-log-concavity of $P_n(x)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0305","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":"1205.0305","created_at":"2026-05-18T03:56:34.825477+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.0305v1","created_at":"2026-05-18T03:56:34.825477+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0305","created_at":"2026-05-18T03:56:34.825477+00:00"},{"alias_kind":"pith_short_12","alias_value":"U6GZH3V4CFC2","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"U6GZH3V4CFC2LU7V","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"U6GZH3V4","created_at":"2026-05-18T12:27:23.164592+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/U6GZH3V4CFC2LU7VSBQYL4KQ5Q","json":"https://pith.science/pith/U6GZH3V4CFC2LU7VSBQYL4KQ5Q.json","graph_json":"https://pith.science/api/pith-number/U6GZH3V4CFC2LU7VSBQYL4KQ5Q/graph.json","events_json":"https://pith.science/api/pith-number/U6GZH3V4CFC2LU7VSBQYL4KQ5Q/events.json","paper":"https://pith.science/paper/U6GZH3V4"},"agent_actions":{"view_html":"https://pith.science/pith/U6GZH3V4CFC2LU7VSBQYL4KQ5Q","download_json":"https://pith.science/pith/U6GZH3V4CFC2LU7VSBQYL4KQ5Q.json","view_paper":"https://pith.science/paper/U6GZH3V4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.0305&json=true","fetch_graph":"https://pith.science/api/pith-number/U6GZH3V4CFC2LU7VSBQYL4KQ5Q/graph.json","fetch_events":"https://pith.science/api/pith-number/U6GZH3V4CFC2LU7VSBQYL4KQ5Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U6GZH3V4CFC2LU7VSBQYL4KQ5Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U6GZH3V4CFC2LU7VSBQYL4KQ5Q/action/storage_attestation","attest_author":"https://pith.science/pith/U6GZH3V4CFC2LU7VSBQYL4KQ5Q/action/author_attestation","sign_citation":"https://pith.science/pith/U6GZH3V4CFC2LU7VSBQYL4KQ5Q/action/citation_signature","submit_replication":"https://pith.science/pith/U6GZH3V4CFC2LU7VSBQYL4KQ5Q/action/replication_record"}},"created_at":"2026-05-18T03:56:34.825477+00:00","updated_at":"2026-05-18T03:56:34.825477+00:00"}