{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HHMOKHXUYPUUJ54Z2PYJ7AHSTT","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":"b3eb05c443cefb9e09e7a8479a9480fa5933276b00af58e769560b00dc81817c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-25T14:43:03Z","title_canon_sha256":"8a614432386ae35fb7ecb1ed54edf8957a3de13827234c6cbc95c4f2e9025902"},"schema_version":"1.0","source":{"id":"1505.06650","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06650","created_at":"2026-05-18T02:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06650v2","created_at":"2026-05-18T02:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06650","created_at":"2026-05-18T02:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"HHMOKHXUYPUU","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HHMOKHXUYPUUJ54Z","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HHMOKHXU","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:0326bb23d8b3e9cd98d2ab77fc1012dad02ecbe3854f38932d12e397b9d293c5","target":"graph","created_at":"2026-05-18T02:03:32Z","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":"Let $\\{P_n\\}_{n\\geq 0}$ denote the Catalan-Larcombe-French sequence, which naturally came up from the series expansion of the complete elliptic integral of the first kind. In this paper, we prove the strict log-concavity of the sequence $\\{\\sqrt[n]{P_n}\\}_{n\\geq 1}$, which was originally conjectured by Sun. We also obtain the strict log-concavity of the sequence $\\{\\sqrt[n]{V_n}\\}_{n\\geq 1}$, where $\\{V_n\\}_{n\\geq 0}$ is the Fennessey-Larcombe-French sequence arising in the series expansion of the complete elliptic integral of the second kind.","authors_text":"James J.Y. Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-25T14:43:03Z","title":"Sun's log-concavity conjecture on the Catalan-Larcombe-French sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06650","kind":"arxiv","version":2},"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":"sha256:9fc557efffeb2e572ab1e4de4cf8d4eadf3e2dd677ffa6fbde30be968a5f7686","target":"record","created_at":"2026-05-18T02:03:32Z","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":"b3eb05c443cefb9e09e7a8479a9480fa5933276b00af58e769560b00dc81817c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-25T14:43:03Z","title_canon_sha256":"8a614432386ae35fb7ecb1ed54edf8957a3de13827234c6cbc95c4f2e9025902"},"schema_version":"1.0","source":{"id":"1505.06650","kind":"arxiv","version":2}},"canonical_sha256":"39d8e51ef4c3e944f799d3f09f80f29ce8376b12c6b2ee82b31cee45b94b9b33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39d8e51ef4c3e944f799d3f09f80f29ce8376b12c6b2ee82b31cee45b94b9b33","first_computed_at":"2026-05-18T02:03:32.033034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:32.033034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pf04eNd68F2yn0sWvRgJVYQXUhNWTAYP7F6F8qm5SRmbPlaakM8Oate+8IP5s1t31NIo2MONRbCIowV5k9bwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:32.033751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06650","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fc557efffeb2e572ab1e4de4cf8d4eadf3e2dd677ffa6fbde30be968a5f7686","sha256:0326bb23d8b3e9cd98d2ab77fc1012dad02ecbe3854f38932d12e397b9d293c5"],"state_sha256":"052361f2631e9e9e5fe224b20797c15217c63793c8a525492fe77dd2dc13a855"}