{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OLJC4PFLDX4XZMLVXW4KBLC2EB","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":"335c5ee6b0483cede2c6a1f611fde6f0076ccd612c7ee08b4f998966963100aa","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-30T15:45:40Z","title_canon_sha256":"889d4849bec90a58a15f6ec23ee66a13553fbb9f9739da900c56246ae81bf8bf"},"schema_version":"1.0","source":{"id":"1706.10245","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.10245","created_at":"2026-05-18T00:41:09Z"},{"alias_kind":"arxiv_version","alias_value":"1706.10245v1","created_at":"2026-05-18T00:41:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10245","created_at":"2026-05-18T00:41:09Z"},{"alias_kind":"pith_short_12","alias_value":"OLJC4PFLDX4X","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OLJC4PFLDX4XZMLV","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OLJC4PFL","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:c6e15bd2de8931fc4557f83a8c594bcd7e3aa2b9982b81ca674379a6de1674f1","target":"graph","created_at":"2026-05-18T00:41:09Z","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":"The Tur\\'{a}n inequalities and the higher order Tur\\'{a}n inequalities arise in the study of Maclaurin coefficients of an entire function in the Laguerre-P\\'{o}lya class. A real sequence $\\{a_{n}\\}$ is said to satisfy the Tur\\'{a}n inequalities if for $n\\geq 1$, $a_n^2-a_{n-1}a_{n+1}\\geq 0$. It is said to satisfy the higher order Tur\\'{a}n inequalities if for $n\\geq 1$, $4(a_{n}^2-a_{n-1}a_{n+1})(a_{n+1}^2-a_{n}a_{n+2})-(a_{n}a_{n+1}-a_{n-1}a_{n+2})^2\\geq 0$. A sequence satisfying the Tur\\'an inequalities is also called log-concave. For the partition function $p(n)$, DeSalvo and Pak showed tha","authors_text":"Dennis X.Q. Jia, Larry X.W. Wang, William Y.C. Chen","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-30T15:45:40Z","title":"Higher Order Tur\\'an Inequalities for the Partition Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10245","kind":"arxiv","version":1},"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":"sha256:4fcb46946d0427ae515a0510bc347fd9dc71ee4a9a6a3db9865983d04af8df79","target":"record","created_at":"2026-05-18T00:41:09Z","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":"335c5ee6b0483cede2c6a1f611fde6f0076ccd612c7ee08b4f998966963100aa","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-30T15:45:40Z","title_canon_sha256":"889d4849bec90a58a15f6ec23ee66a13553fbb9f9739da900c56246ae81bf8bf"},"schema_version":"1.0","source":{"id":"1706.10245","kind":"arxiv","version":1}},"canonical_sha256":"72d22e3cab1df97cb175bdb8a0ac5a207c2c8cb350507caa5e8d5ca329e92e1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72d22e3cab1df97cb175bdb8a0ac5a207c2c8cb350507caa5e8d5ca329e92e1c","first_computed_at":"2026-05-18T00:41:09.022751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:09.022751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0WO+VD5m2yCyadX/wMexOZNxDW0nGEfpf7YhpHyXjaEsdXuyKG42Ufy2Is5wH6ko4/AneAqPSOySq9GJKv3CDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:09.023371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.10245","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fcb46946d0427ae515a0510bc347fd9dc71ee4a9a6a3db9865983d04af8df79","sha256:c6e15bd2de8931fc4557f83a8c594bcd7e3aa2b9982b81ca674379a6de1674f1"],"state_sha256":"5ad2e481482b4fffd369213271bd19db2d61b92472cbf85db9cf379de9336052"}