{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Y2FFMQ3IQ2I2T6QK3VK2UZQ7XB","short_pith_number":"pith:Y2FFMQ3I","canonical_record":{"source":{"id":"1806.07948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-06T08:54:26Z","cross_cats_sorted":[],"title_canon_sha256":"3ee18a7f447c874a237234f0a821357f4190ea19a650dfa65d76da097940a29c","abstract_canon_sha256":"77e7d2c3e42d9b74a6fca81dd479401ae98764b35e2896a33bc50b5194fa3da5"},"schema_version":"1.0"},"canonical_sha256":"c68a5643688691a9fa0add55aa661fb87a7659e7b067c6bbd7d8066f1fcd07cf","source":{"kind":"arxiv","id":"1806.07948","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07948","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07948v1","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07948","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"pith_short_12","alias_value":"Y2FFMQ3IQ2I2","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Y2FFMQ3IQ2I2T6QK","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Y2FFMQ3I","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Y2FFMQ3IQ2I2T6QK3VK2UZQ7XB","target":"record","payload":{"canonical_record":{"source":{"id":"1806.07948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-06T08:54:26Z","cross_cats_sorted":[],"title_canon_sha256":"3ee18a7f447c874a237234f0a821357f4190ea19a650dfa65d76da097940a29c","abstract_canon_sha256":"77e7d2c3e42d9b74a6fca81dd479401ae98764b35e2896a33bc50b5194fa3da5"},"schema_version":"1.0"},"canonical_sha256":"c68a5643688691a9fa0add55aa661fb87a7659e7b067c6bbd7d8066f1fcd07cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:42.530500Z","signature_b64":"UAx7fk1NYSBmIWhvoDo+SaYaHhDl6ilDSlFTOP8uDbZVKGhGLzlonkjDc/Me0ZmO5g+9lMSkAB9BH4GZW9vQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c68a5643688691a9fa0add55aa661fb87a7659e7b067c6bbd7d8066f1fcd07cf","last_reissued_at":"2026-05-18T00:12:42.529795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:42.529795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.07948","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":"2026-05-18T00:12:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"izDpySlgv7EPoso0jRZ5I3vh1w6PBkGD3ivi34gOUrhdMZ6WreG+qYQMUDfZ31I3RHV4jDPw598wrz9ptj2IDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T00:44:16.496149Z"},"content_sha256":"b77169f4f07c45b8dce61316af6d5e9f0182d1fbf622d297e09165b4ead8b1b1","schema_version":"1.0","event_id":"sha256:b77169f4f07c45b8dce61316af6d5e9f0182d1fbf622d297e09165b4ead8b1b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Y2FFMQ3IQ2I2T6QK3VK2UZQ7XB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic computations of digamma function using some new identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"M.I. Qureshi, Mohd Shadab","submitted_at":"2018-06-06T08:54:26Z","abstract_excerpt":"Motivated by rigorous development in the theory of digamma functions, we have first derived some new identities for the digamma function, and then computed the values of digamma function for the fractional orders using these identities conveniently."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07948","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":"2026-05-18T00:12:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wm1QE3l/Us4M3iaYdE2w6u6AqKFm9B4CqlyLnSs8ajaSuPq4HzzK1NgrsIQz69KX+BFUudiayO5FzdYNol15Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T00:44:16.496710Z"},"content_sha256":"c9995f5185ba63b2537cec3570afd2fd10cc67ad1b0ef122b1f342a6023cd747","schema_version":"1.0","event_id":"sha256:c9995f5185ba63b2537cec3570afd2fd10cc67ad1b0ef122b1f342a6023cd747"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2FFMQ3IQ2I2T6QK3VK2UZQ7XB/bundle.json","state_url":"https://pith.science/pith/Y2FFMQ3IQ2I2T6QK3VK2UZQ7XB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2FFMQ3IQ2I2T6QK3VK2UZQ7XB/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":"2026-06-28T00:44:16Z","links":{"resolver":"https://pith.science/pith/Y2FFMQ3IQ2I2T6QK3VK2UZQ7XB","bundle":"https://pith.science/pith/Y2FFMQ3IQ2I2T6QK3VK2UZQ7XB/bundle.json","state":"https://pith.science/pith/Y2FFMQ3IQ2I2T6QK3VK2UZQ7XB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2FFMQ3IQ2I2T6QK3VK2UZQ7XB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Y2FFMQ3IQ2I2T6QK3VK2UZQ7XB","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":"77e7d2c3e42d9b74a6fca81dd479401ae98764b35e2896a33bc50b5194fa3da5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-06T08:54:26Z","title_canon_sha256":"3ee18a7f447c874a237234f0a821357f4190ea19a650dfa65d76da097940a29c"},"schema_version":"1.0","source":{"id":"1806.07948","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07948","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07948v1","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07948","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"pith_short_12","alias_value":"Y2FFMQ3IQ2I2","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Y2FFMQ3IQ2I2T6QK","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Y2FFMQ3I","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:c9995f5185ba63b2537cec3570afd2fd10cc67ad1b0ef122b1f342a6023cd747","target":"graph","created_at":"2026-05-18T00:12:42Z","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":"Motivated by rigorous development in the theory of digamma functions, we have first derived some new identities for the digamma function, and then computed the values of digamma function for the fractional orders using these identities conveniently.","authors_text":"M.I. Qureshi, Mohd Shadab","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-06T08:54:26Z","title":"Analytic computations of digamma function using some new identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07948","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:b77169f4f07c45b8dce61316af6d5e9f0182d1fbf622d297e09165b4ead8b1b1","target":"record","created_at":"2026-05-18T00:12:42Z","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":"77e7d2c3e42d9b74a6fca81dd479401ae98764b35e2896a33bc50b5194fa3da5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-06T08:54:26Z","title_canon_sha256":"3ee18a7f447c874a237234f0a821357f4190ea19a650dfa65d76da097940a29c"},"schema_version":"1.0","source":{"id":"1806.07948","kind":"arxiv","version":1}},"canonical_sha256":"c68a5643688691a9fa0add55aa661fb87a7659e7b067c6bbd7d8066f1fcd07cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c68a5643688691a9fa0add55aa661fb87a7659e7b067c6bbd7d8066f1fcd07cf","first_computed_at":"2026-05-18T00:12:42.529795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:42.529795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UAx7fk1NYSBmIWhvoDo+SaYaHhDl6ilDSlFTOP8uDbZVKGhGLzlonkjDc/Me0ZmO5g+9lMSkAB9BH4GZW9vQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:42.530500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07948","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b77169f4f07c45b8dce61316af6d5e9f0182d1fbf622d297e09165b4ead8b1b1","sha256:c9995f5185ba63b2537cec3570afd2fd10cc67ad1b0ef122b1f342a6023cd747"],"state_sha256":"1d24e50034c48baeae6e81dc7b479c17fc830b60056eb9ef38a5894070ed1eae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3zrcUyH34ImNj5A5zJcz62np8/QchqPwGzQWPzKaNBgcc6O92wSMKir/cbGKOEMmhVi5+3a7fSsRoB3lVDbODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T00:44:16.498640Z","bundle_sha256":"91429204fdc48a38e92c5e0e0f087014bb0c6d5d81d39820c22ca190358f5c0d"}}