{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RIG3OU545O2K7RIW6M6FX5A6ER","short_pith_number":"pith:RIG3OU54","schema_version":"1.0","canonical_sha256":"8a0db753bcebb4afc516f33c5bf41e246117e91fe0a1fc1b39926827d4f45b8b","source":{"kind":"arxiv","id":"1508.01793","version":2},"attestation_state":"computed","paper":{"title":"On a conjecture of Chen-Guo-Wang","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Bo Ning, Yu Zheng","submitted_at":"2015-08-03T02:00:43Z","abstract_excerpt":"Towards confirming Sun's conjecture on the strict log-concavity of combinatorial sequence involving the n$th$ Bernoulli number, Chen, Guo and Wang proposed a conjecture about the log-concavity of the function $\\theta(x)=\\sqrt[x]{2\\zeta(x)\\Gamma(x+1)}$ for $x\\in (6,\\infty)$, where $\\zeta(x)$ is the Riemann zeta function and $\\Gamma(x)$ is the Gamma function. In this paper, we first prove this conjecture along the spirit of Zhu's previous work. Second, we extend Chen et al.'s conjecture in the sense of almost infinite log-monotonicity of combinatorial sequences, which was also introduced by Chen"},"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":"1508.01793","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-03T02:00:43Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cdf5d97762acccf565633bdaa1d89a0c31b8f306f9144902506c1e124f39a4ad","abstract_canon_sha256":"12345f31507d303031961695df3ec4aa809562afa6d28a8df85deb3be3196eea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:43.800255Z","signature_b64":"wysjBNR9UYhZoKu/uxVCr++aaSWeJLw719+/obXnMgTD8Is+jx82dblC+fgnQMDr02boL03YlkBrGV9OsGW3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a0db753bcebb4afc516f33c5bf41e246117e91fe0a1fc1b39926827d4f45b8b","last_reissued_at":"2026-05-18T01:11:43.799930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:43.799930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a conjecture of Chen-Guo-Wang","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Bo Ning, Yu Zheng","submitted_at":"2015-08-03T02:00:43Z","abstract_excerpt":"Towards confirming Sun's conjecture on the strict log-concavity of combinatorial sequence involving the n$th$ Bernoulli number, Chen, Guo and Wang proposed a conjecture about the log-concavity of the function $\\theta(x)=\\sqrt[x]{2\\zeta(x)\\Gamma(x+1)}$ for $x\\in (6,\\infty)$, where $\\zeta(x)$ is the Riemann zeta function and $\\Gamma(x)$ is the Gamma function. In this paper, we first prove this conjecture along the spirit of Zhu's previous work. Second, we extend Chen et al.'s conjecture in the sense of almost infinite log-monotonicity of combinatorial sequences, which was also introduced by Chen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01793","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":"1508.01793","created_at":"2026-05-18T01:11:43.799982+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.01793v2","created_at":"2026-05-18T01:11:43.799982+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01793","created_at":"2026-05-18T01:11:43.799982+00:00"},{"alias_kind":"pith_short_12","alias_value":"RIG3OU545O2K","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RIG3OU545O2K7RIW","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RIG3OU54","created_at":"2026-05-18T12:29:39.896362+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/RIG3OU545O2K7RIW6M6FX5A6ER","json":"https://pith.science/pith/RIG3OU545O2K7RIW6M6FX5A6ER.json","graph_json":"https://pith.science/api/pith-number/RIG3OU545O2K7RIW6M6FX5A6ER/graph.json","events_json":"https://pith.science/api/pith-number/RIG3OU545O2K7RIW6M6FX5A6ER/events.json","paper":"https://pith.science/paper/RIG3OU54"},"agent_actions":{"view_html":"https://pith.science/pith/RIG3OU545O2K7RIW6M6FX5A6ER","download_json":"https://pith.science/pith/RIG3OU545O2K7RIW6M6FX5A6ER.json","view_paper":"https://pith.science/paper/RIG3OU54","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.01793&json=true","fetch_graph":"https://pith.science/api/pith-number/RIG3OU545O2K7RIW6M6FX5A6ER/graph.json","fetch_events":"https://pith.science/api/pith-number/RIG3OU545O2K7RIW6M6FX5A6ER/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RIG3OU545O2K7RIW6M6FX5A6ER/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RIG3OU545O2K7RIW6M6FX5A6ER/action/storage_attestation","attest_author":"https://pith.science/pith/RIG3OU545O2K7RIW6M6FX5A6ER/action/author_attestation","sign_citation":"https://pith.science/pith/RIG3OU545O2K7RIW6M6FX5A6ER/action/citation_signature","submit_replication":"https://pith.science/pith/RIG3OU545O2K7RIW6M6FX5A6ER/action/replication_record"}},"created_at":"2026-05-18T01:11:43.799982+00:00","updated_at":"2026-05-18T01:11:43.799982+00:00"}