{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TN4B3U6HLZLV3ZVDVH3NIUXGC7","short_pith_number":"pith:TN4B3U6H","canonical_record":{"source":{"id":"1601.02094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-09T10:43:59Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"85a1df2b5c72127176640c61eb0644e5a44dc5de0e20d5729b5dae6f0f1fe3f5","abstract_canon_sha256":"39823b81f8015fd2cfc5cb0e40472b3daa071dca6aaafc0688c4801dfb8e08c6"},"schema_version":"1.0"},"canonical_sha256":"9b781dd3c75e575de6a3a9f6d452e617d85aae60bd2b334c4ff025425ecaf361","source":{"kind":"arxiv","id":"1601.02094","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02094","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02094v2","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02094","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"pith_short_12","alias_value":"TN4B3U6HLZLV","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TN4B3U6HLZLV3ZVD","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TN4B3U6H","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TN4B3U6HLZLV3ZVDVH3NIUXGC7","target":"record","payload":{"canonical_record":{"source":{"id":"1601.02094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-09T10:43:59Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"85a1df2b5c72127176640c61eb0644e5a44dc5de0e20d5729b5dae6f0f1fe3f5","abstract_canon_sha256":"39823b81f8015fd2cfc5cb0e40472b3daa071dca6aaafc0688c4801dfb8e08c6"},"schema_version":"1.0"},"canonical_sha256":"9b781dd3c75e575de6a3a9f6d452e617d85aae60bd2b334c4ff025425ecaf361","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:28.827616Z","signature_b64":"GEqXjBKGbjg98N/tPhRdxYDfBShQ3dY6rAVMVt8GE9FXKcN6n+y28NWtqgOHZdjZdqfR8tKKWEPypboLagMfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b781dd3c75e575de6a3a9f6d452e617d85aae60bd2b334c4ff025425ecaf361","last_reissued_at":"2026-05-18T01:01:28.827178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:28.827178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.02094","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":"2026-05-18T01:01:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZmLkWn+QiSGXeUhC2g/odil95Z3+wbraPKFRdP+cP2fnMLiXuqGnonCQDaxboFEMY89tsYlRh2Jic4xTWVclAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T06:12:37.380751Z"},"content_sha256":"a305fb90dab413a3c8d00a504c755adad0cecb90fcc592c35e846920573308a6","schema_version":"1.0","event_id":"sha256:a305fb90dab413a3c8d00a504c755adad0cecb90fcc592c35e846920573308a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TN4B3U6HLZLV3ZVDVH3NIUXGC7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New properties of the Lerch's transcendent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"A. K. Kohara, E. M. Ferreira, J. Sesma","submitted_at":"2016-01-09T10:43:59Z","abstract_excerpt":"A new representation of the Lerch's transcendent Phi(z,s,a), valid for positive integer s=n=1,2,... and for z and a belonging to certain regions of the complex plane, is presented. It allows to write an equation relating Phi(z,n,a) and Phi(1/z,n,1-a), which provides an expansion of Phi(z,n,a) as a power series of 1/z, convergent for |z|>1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02094","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":"2026-05-18T01:01:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EhvUyw2gXZCKtZ5toVT2YUd4afxYVJQgSoxNHLQ4MxtA+MEDnpAINlzdkCiWcRLcKNfJJ0TxiOG8qVfui1kfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T06:12:37.381093Z"},"content_sha256":"fc0b98a5ae0e2de30ec3fbeb8dc86da8299d6b2296ed8a6a26ac0c820ac2b7ce","schema_version":"1.0","event_id":"sha256:fc0b98a5ae0e2de30ec3fbeb8dc86da8299d6b2296ed8a6a26ac0c820ac2b7ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TN4B3U6HLZLV3ZVDVH3NIUXGC7/bundle.json","state_url":"https://pith.science/pith/TN4B3U6HLZLV3ZVDVH3NIUXGC7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TN4B3U6HLZLV3ZVDVH3NIUXGC7/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":"2026-06-28T06:12:37Z","links":{"resolver":"https://pith.science/pith/TN4B3U6HLZLV3ZVDVH3NIUXGC7","bundle":"https://pith.science/pith/TN4B3U6HLZLV3ZVDVH3NIUXGC7/bundle.json","state":"https://pith.science/pith/TN4B3U6HLZLV3ZVDVH3NIUXGC7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TN4B3U6HLZLV3ZVDVH3NIUXGC7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TN4B3U6HLZLV3ZVDVH3NIUXGC7","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":"39823b81f8015fd2cfc5cb0e40472b3daa071dca6aaafc0688c4801dfb8e08c6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-09T10:43:59Z","title_canon_sha256":"85a1df2b5c72127176640c61eb0644e5a44dc5de0e20d5729b5dae6f0f1fe3f5"},"schema_version":"1.0","source":{"id":"1601.02094","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02094","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02094v2","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02094","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"pith_short_12","alias_value":"TN4B3U6HLZLV","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TN4B3U6HLZLV3ZVD","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TN4B3U6H","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:fc0b98a5ae0e2de30ec3fbeb8dc86da8299d6b2296ed8a6a26ac0c820ac2b7ce","target":"graph","created_at":"2026-05-18T01:01:28Z","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":"A new representation of the Lerch's transcendent Phi(z,s,a), valid for positive integer s=n=1,2,... and for z and a belonging to certain regions of the complex plane, is presented. It allows to write an equation relating Phi(z,n,a) and Phi(1/z,n,1-a), which provides an expansion of Phi(z,n,a) as a power series of 1/z, convergent for |z|>1.","authors_text":"A. K. Kohara, E. M. Ferreira, J. Sesma","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-09T10:43:59Z","title":"New properties of the Lerch's transcendent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02094","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:a305fb90dab413a3c8d00a504c755adad0cecb90fcc592c35e846920573308a6","target":"record","created_at":"2026-05-18T01:01:28Z","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":"39823b81f8015fd2cfc5cb0e40472b3daa071dca6aaafc0688c4801dfb8e08c6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-09T10:43:59Z","title_canon_sha256":"85a1df2b5c72127176640c61eb0644e5a44dc5de0e20d5729b5dae6f0f1fe3f5"},"schema_version":"1.0","source":{"id":"1601.02094","kind":"arxiv","version":2}},"canonical_sha256":"9b781dd3c75e575de6a3a9f6d452e617d85aae60bd2b334c4ff025425ecaf361","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b781dd3c75e575de6a3a9f6d452e617d85aae60bd2b334c4ff025425ecaf361","first_computed_at":"2026-05-18T01:01:28.827178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:28.827178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GEqXjBKGbjg98N/tPhRdxYDfBShQ3dY6rAVMVt8GE9FXKcN6n+y28NWtqgOHZdjZdqfR8tKKWEPypboLagMfDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:28.827616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02094","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a305fb90dab413a3c8d00a504c755adad0cecb90fcc592c35e846920573308a6","sha256:fc0b98a5ae0e2de30ec3fbeb8dc86da8299d6b2296ed8a6a26ac0c820ac2b7ce"],"state_sha256":"8adb6335797d55f1688715ed9a530dfe1976d56b5b91385978caa9433767f7a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+k+HJxD1qBLXdL0xK3+zONLKBSfm41eDknGkXN6uuBL8MqRHUZWiVvdPJ7/7DTt7Ihty2HezAdUCUy6TsgoUBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T06:12:37.383011Z","bundle_sha256":"5ac818ca7a37cd056832da42e66a843efa4f877f1806e93435eb030abc587c0a"}}