{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:5VWKLHRYXZ5MPNQAXIUBQGD6ZH","short_pith_number":"pith:5VWKLHRY","canonical_record":{"source":{"id":"0903.1996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-03-11T15:30:59Z","cross_cats_sorted":[],"title_canon_sha256":"3b9ae060bd58fef46e4693006514ba94ab52b2ce4823886ac5802af40ab5d43c","abstract_canon_sha256":"f04e990f90f012dff126a35fa9eba129566db07b223b3dc606a662bf5319b8ec"},"schema_version":"1.0"},"canonical_sha256":"ed6ca59e38be7ac7b600ba2818187ec9d722a36e6df2721a5ef42aa7fd3ea0fd","source":{"kind":"arxiv","id":"0903.1996","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1996","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1996v1","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1996","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"5VWKLHRYXZ5M","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5VWKLHRYXZ5MPNQA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5VWKLHRY","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:5VWKLHRYXZ5MPNQAXIUBQGD6ZH","target":"record","payload":{"canonical_record":{"source":{"id":"0903.1996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-03-11T15:30:59Z","cross_cats_sorted":[],"title_canon_sha256":"3b9ae060bd58fef46e4693006514ba94ab52b2ce4823886ac5802af40ab5d43c","abstract_canon_sha256":"f04e990f90f012dff126a35fa9eba129566db07b223b3dc606a662bf5319b8ec"},"schema_version":"1.0"},"canonical_sha256":"ed6ca59e38be7ac7b600ba2818187ec9d722a36e6df2721a5ef42aa7fd3ea0fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:26.766934Z","signature_b64":"qsUI6HzP3pQBeEh8JlNfWX27aT2MBf/YALLlTKQXdq9D/ZywZNTIIUbnabPiHtDiwKwXUqx1bsZ8HpydNG8lBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed6ca59e38be7ac7b600ba2818187ec9d722a36e6df2721a5ef42aa7fd3ea0fd","last_reissued_at":"2026-05-18T03:35:26.766409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:26.766409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.1996","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+HP+YVolE5vb2jD9Ve+ROKRn4osoTrr59dumQc5vqTdoxBYjmLH4MUqRn06bhYILIEjd9ByX77VcyFh+WqYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:46:21.381401Z"},"content_sha256":"c1b37a12fb614120c4f57b45cd3d11622148d3b2e1208d4221fb9f6fa698655d","schema_version":"1.0","event_id":"sha256:c1b37a12fb614120c4f57b45cd3d11622148d3b2e1208d4221fb9f6fa698655d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:5VWKLHRYXZ5MPNQAXIUBQGD6ZH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Refinements of lower bounds for polygamma 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":"2009-03-11T15:30:59Z","abstract_excerpt":"In the paper, some lower bounds for polygamma functions are refined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1996","kind":"arxiv","version":1},"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":"2026-05-18T03:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZEKuA0vCCU2hBFaJ5CZVjF/LcH6C3mDzPHlmUGN6KlKVXnzT2vIGtfkUNBhsJ6iX/Ngqy8belb1HNScs6feAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:46:21.382030Z"},"content_sha256":"f20c82d072e50419270ce099fc46ba6bc8208def3198cb1e2a344cb0da62d098","schema_version":"1.0","event_id":"sha256:f20c82d072e50419270ce099fc46ba6bc8208def3198cb1e2a344cb0da62d098"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5VWKLHRYXZ5MPNQAXIUBQGD6ZH/bundle.json","state_url":"https://pith.science/pith/5VWKLHRYXZ5MPNQAXIUBQGD6ZH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5VWKLHRYXZ5MPNQAXIUBQGD6ZH/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":"2026-05-28T15:46:21Z","links":{"resolver":"https://pith.science/pith/5VWKLHRYXZ5MPNQAXIUBQGD6ZH","bundle":"https://pith.science/pith/5VWKLHRYXZ5MPNQAXIUBQGD6ZH/bundle.json","state":"https://pith.science/pith/5VWKLHRYXZ5MPNQAXIUBQGD6ZH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5VWKLHRYXZ5MPNQAXIUBQGD6ZH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5VWKLHRYXZ5MPNQAXIUBQGD6ZH","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":"f04e990f90f012dff126a35fa9eba129566db07b223b3dc606a662bf5319b8ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-03-11T15:30:59Z","title_canon_sha256":"3b9ae060bd58fef46e4693006514ba94ab52b2ce4823886ac5802af40ab5d43c"},"schema_version":"1.0","source":{"id":"0903.1996","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1996","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1996v1","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1996","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"5VWKLHRYXZ5M","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5VWKLHRYXZ5MPNQA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5VWKLHRY","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:f20c82d072e50419270ce099fc46ba6bc8208def3198cb1e2a344cb0da62d098","target":"graph","created_at":"2026-05-18T03:35:26Z","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, some lower bounds for polygamma functions are refined.","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":"2009-03-11T15:30:59Z","title":"Refinements of lower bounds for polygamma functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1996","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:c1b37a12fb614120c4f57b45cd3d11622148d3b2e1208d4221fb9f6fa698655d","target":"record","created_at":"2026-05-18T03:35:26Z","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":"f04e990f90f012dff126a35fa9eba129566db07b223b3dc606a662bf5319b8ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-03-11T15:30:59Z","title_canon_sha256":"3b9ae060bd58fef46e4693006514ba94ab52b2ce4823886ac5802af40ab5d43c"},"schema_version":"1.0","source":{"id":"0903.1996","kind":"arxiv","version":1}},"canonical_sha256":"ed6ca59e38be7ac7b600ba2818187ec9d722a36e6df2721a5ef42aa7fd3ea0fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed6ca59e38be7ac7b600ba2818187ec9d722a36e6df2721a5ef42aa7fd3ea0fd","first_computed_at":"2026-05-18T03:35:26.766409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:26.766409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qsUI6HzP3pQBeEh8JlNfWX27aT2MBf/YALLlTKQXdq9D/ZywZNTIIUbnabPiHtDiwKwXUqx1bsZ8HpydNG8lBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:26.766934Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.1996","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1b37a12fb614120c4f57b45cd3d11622148d3b2e1208d4221fb9f6fa698655d","sha256:f20c82d072e50419270ce099fc46ba6bc8208def3198cb1e2a344cb0da62d098"],"state_sha256":"7314f636fb912056032a5098eed6709f61a3617229e28b93a2c02b8dccee301d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FQyhxpHeM5WL8+Yne0IqfmJCOjA088qB3Tc4fZ7nfjrOsyA80RObtUG72XbDG5hEf1dRQt8QZZlDDpgeQI3nCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:46:21.385118Z","bundle_sha256":"346689b8baf9f70073221f64bb105bce101edf7175b9f6f2c88291ac4ea80158"}}