{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:FUKNPI6V7FOYEP5ZPKPEL2PRIU","short_pith_number":"pith:FUKNPI6V","canonical_record":{"source":{"id":"0902.2519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-15T03:43:13Z","cross_cats_sorted":[],"title_canon_sha256":"ef19cb87f2b65ebb999b9a3f9d3037ded7d64b9ac4e47c30a1b014e8fd1f2675","abstract_canon_sha256":"57b442c90f6c5a2e37ca352c20e9d2f610570d22398528cc539265b88c46d319"},"schema_version":"1.0"},"canonical_sha256":"2d14d7a3d5f95d823fb97a9e45e9f1450be4a7e550a13ef1286c535207ae84be","source":{"kind":"arxiv","id":"0902.2519","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2519","created_at":"2026-05-18T03:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2519v2","created_at":"2026-05-18T03:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2519","created_at":"2026-05-18T03:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"FUKNPI6V7FOY","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"FUKNPI6V7FOYEP5Z","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"FUKNPI6V","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:FUKNPI6V7FOYEP5ZPKPEL2PRIU","target":"record","payload":{"canonical_record":{"source":{"id":"0902.2519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-15T03:43:13Z","cross_cats_sorted":[],"title_canon_sha256":"ef19cb87f2b65ebb999b9a3f9d3037ded7d64b9ac4e47c30a1b014e8fd1f2675","abstract_canon_sha256":"57b442c90f6c5a2e37ca352c20e9d2f610570d22398528cc539265b88c46d319"},"schema_version":"1.0"},"canonical_sha256":"2d14d7a3d5f95d823fb97a9e45e9f1450be4a7e550a13ef1286c535207ae84be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:30.917045Z","signature_b64":"p2U4/Rynp5gwG5f2cl3CD7/vGO+uQKNSe3/G9S5cYgl//kH91+KjZm4O3ODHih82RDQ1dk8ztIVr5ap6lue8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d14d7a3d5f95d823fb97a9e45e9f1450be4a7e550a13ef1286c535207ae84be","last_reissued_at":"2026-05-18T03:28:30.916043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:30.916043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.2519","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7KpLf2LPqkMQZB9wen/2tduzyYkXyvxhAAotTCsqRhTCDZnOMC5pBJr7KfBfo81PFkwQfc0Zs+jsczr0eaKWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:10:33.308725Z"},"content_sha256":"9ced90b7ebc3e71dfd20b2bf13268b1f4f841722ef3e0a1324834e8148e7bc75","schema_version":"1.0","event_id":"sha256:9ced90b7ebc3e71dfd20b2bf13268b1f4f841722ef3e0a1324834e8148e7bc75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:FUKNPI6V7FOYEP5ZPKPEL2PRIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proofs for a monotonicity result of a function involving the psi and exponential functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bai-Ni Guo, Feng Qi","submitted_at":"2009-02-15T03:43:13Z","abstract_excerpt":"In the note, two alternative proofs are provided for a monotonicity result that the function $\\psi(x)+\\ln\\bigl(e^{1/x}-1\\bigr)$ is strictly increasing on $(0,\\infty)$, where $\\psi(x)$ is the psi function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2519","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wt2a14eCFAeKjEeAg7GWCOItqIICKVkXxqQH4oTjvOeO8sfCBgUpsH9xFK5fYmu9bDHwZTwTo9s+8Bxt1VStDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:10:33.309070Z"},"content_sha256":"8f5b27727d73fb3a866fc9ccacd00a6d047bb50141b7f20931513889a9b6d994","schema_version":"1.0","event_id":"sha256:8f5b27727d73fb3a866fc9ccacd00a6d047bb50141b7f20931513889a9b6d994"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FUKNPI6V7FOYEP5ZPKPEL2PRIU/bundle.json","state_url":"https://pith.science/pith/FUKNPI6V7FOYEP5ZPKPEL2PRIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FUKNPI6V7FOYEP5ZPKPEL2PRIU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T13:10:33Z","links":{"resolver":"https://pith.science/pith/FUKNPI6V7FOYEP5ZPKPEL2PRIU","bundle":"https://pith.science/pith/FUKNPI6V7FOYEP5ZPKPEL2PRIU/bundle.json","state":"https://pith.science/pith/FUKNPI6V7FOYEP5ZPKPEL2PRIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FUKNPI6V7FOYEP5ZPKPEL2PRIU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:FUKNPI6V7FOYEP5ZPKPEL2PRIU","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":"57b442c90f6c5a2e37ca352c20e9d2f610570d22398528cc539265b88c46d319","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-15T03:43:13Z","title_canon_sha256":"ef19cb87f2b65ebb999b9a3f9d3037ded7d64b9ac4e47c30a1b014e8fd1f2675"},"schema_version":"1.0","source":{"id":"0902.2519","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2519","created_at":"2026-05-18T03:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2519v2","created_at":"2026-05-18T03:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2519","created_at":"2026-05-18T03:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"FUKNPI6V7FOY","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"FUKNPI6V7FOYEP5Z","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"FUKNPI6V","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:8f5b27727d73fb3a866fc9ccacd00a6d047bb50141b7f20931513889a9b6d994","target":"graph","created_at":"2026-05-18T03:28:30Z","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 note, two alternative proofs are provided for a monotonicity result that the function $\\psi(x)+\\ln\\bigl(e^{1/x}-1\\bigr)$ is strictly increasing on $(0,\\infty)$, where $\\psi(x)$ is the psi function.","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":"2009-02-15T03:43:13Z","title":"Proofs for a monotonicity result of a function involving the psi and exponential functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2519","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":"sha256:9ced90b7ebc3e71dfd20b2bf13268b1f4f841722ef3e0a1324834e8148e7bc75","target":"record","created_at":"2026-05-18T03:28:30Z","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":"57b442c90f6c5a2e37ca352c20e9d2f610570d22398528cc539265b88c46d319","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-15T03:43:13Z","title_canon_sha256":"ef19cb87f2b65ebb999b9a3f9d3037ded7d64b9ac4e47c30a1b014e8fd1f2675"},"schema_version":"1.0","source":{"id":"0902.2519","kind":"arxiv","version":2}},"canonical_sha256":"2d14d7a3d5f95d823fb97a9e45e9f1450be4a7e550a13ef1286c535207ae84be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d14d7a3d5f95d823fb97a9e45e9f1450be4a7e550a13ef1286c535207ae84be","first_computed_at":"2026-05-18T03:28:30.916043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:30.916043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p2U4/Rynp5gwG5f2cl3CD7/vGO+uQKNSe3/G9S5cYgl//kH91+KjZm4O3ODHih82RDQ1dk8ztIVr5ap6lue8DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:30.917045Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.2519","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ced90b7ebc3e71dfd20b2bf13268b1f4f841722ef3e0a1324834e8148e7bc75","sha256:8f5b27727d73fb3a866fc9ccacd00a6d047bb50141b7f20931513889a9b6d994"],"state_sha256":"fe82d228f83ab25756ca1099751ee0861f57dd79eba6071da72242bc9d86f103"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lvCMk7KZHnpjcoOASQsIJk15U6RO3WRJgR3Vnl/eD3cjP5wMz0KKwaMDeL5nAu7T9RwzOosc2P3IPnhsP9eXDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:10:33.311129Z","bundle_sha256":"91492896d21b05e9675e67fa118af8a0a4afc20b8b670f70f32a9f09f9c4f39a"}}