{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JV2MZSR5CBOALAIWAL2744YBVU","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":"873f34df04783d0ba0cb2aace65576091435b3dcc267a2f68c5f7e7c60b29558","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-25T01:20:42Z","title_canon_sha256":"b6d9164b913dd6e8ecaf4fe9cd01724c9e9a55b6b6efc80f59915231079c0260"},"schema_version":"1.0","source":{"id":"1101.4698","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4698","created_at":"2026-05-18T01:11:44Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4698v1","created_at":"2026-05-18T01:11:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4698","created_at":"2026-05-18T01:11:44Z"},{"alias_kind":"pith_short_12","alias_value":"JV2MZSR5CBOA","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JV2MZSR5CBOALAIW","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JV2MZSR5","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:853be4079392c45b72b98d8921916ca5b379261c123a11885a5523029e8e62ff","target":"graph","created_at":"2026-05-18T01:11:44Z","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":"In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.","authors_text":"Bai-Ni Guo, Feng Qi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-25T01:20:42Z","title":"An inequality involving the gamma and digamma functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4698","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:edb765311464c46fef98ed9b4a0fbf5d6a8fdde01db4e24a848e052dc8c4e158","target":"record","created_at":"2026-05-18T01:11:44Z","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":"873f34df04783d0ba0cb2aace65576091435b3dcc267a2f68c5f7e7c60b29558","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-25T01:20:42Z","title_canon_sha256":"b6d9164b913dd6e8ecaf4fe9cd01724c9e9a55b6b6efc80f59915231079c0260"},"schema_version":"1.0","source":{"id":"1101.4698","kind":"arxiv","version":1}},"canonical_sha256":"4d74ccca3d105c05811602f5fe7301ad0dcff4c48382c3e24fa690f620ecb4a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d74ccca3d105c05811602f5fe7301ad0dcff4c48382c3e24fa690f620ecb4a6","first_computed_at":"2026-05-18T01:11:44.086620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:44.086620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i/n23ZzztxeDMiAcONBYf1DXkMmTfzma/K4uKZ/tPQj4EINXIXgDi7kF2nOs2zqyZUKTVkZOZ2Xl5LVKEOm/Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:44.086952Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4698","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edb765311464c46fef98ed9b4a0fbf5d6a8fdde01db4e24a848e052dc8c4e158","sha256:853be4079392c45b72b98d8921916ca5b379261c123a11885a5523029e8e62ff"],"state_sha256":"23875c9c2629dfd947fcd8728061a47b28edacd2ba761972be263f1d27499de1"}