{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WHWE2XDWKBYSUS3NJG76IPNYQA","short_pith_number":"pith:WHWE2XDW","canonical_record":{"source":{"id":"1604.04328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-15T01:27:24Z","cross_cats_sorted":[],"title_canon_sha256":"7ae7db6d586980cb64eb1413c8f29861671d780b6dced964743605d7c89d2595","abstract_canon_sha256":"13807adf9bcf7698caceaa558e19a9bb58905bb01ff9aeac0c44fc0748674898"},"schema_version":"1.0"},"canonical_sha256":"b1ec4d5c7650712a4b6d49bfe43db8802006d7dd37e49105348eb7f510914f2d","source":{"kind":"arxiv","id":"1604.04328","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04328","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04328v1","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04328","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"WHWE2XDWKBYS","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WHWE2XDWKBYSUS3N","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WHWE2XDW","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WHWE2XDWKBYSUS3NJG76IPNYQA","target":"record","payload":{"canonical_record":{"source":{"id":"1604.04328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-15T01:27:24Z","cross_cats_sorted":[],"title_canon_sha256":"7ae7db6d586980cb64eb1413c8f29861671d780b6dced964743605d7c89d2595","abstract_canon_sha256":"13807adf9bcf7698caceaa558e19a9bb58905bb01ff9aeac0c44fc0748674898"},"schema_version":"1.0"},"canonical_sha256":"b1ec4d5c7650712a4b6d49bfe43db8802006d7dd37e49105348eb7f510914f2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:04.492684Z","signature_b64":"ZnraRTaC4+O2UgmEStmoE4dndP8QNNRlc1Lvxb24b/kqRx2hRKBItPQGnuNN3C/KJslKCBVoACwIl1d7rOgUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1ec4d5c7650712a4b6d49bfe43db8802006d7dd37e49105348eb7f510914f2d","last_reissued_at":"2026-05-18T01:17:04.492013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:04.492013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.04328","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":"2026-05-18T01:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZGeO/8c4MPHT23O+6EOy9xnCAoNWttZjV4bLCwURRGFHMVq9dj88bkwxg4szaRnkPAzngD3LEVFjP9GEDZDDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:59:52.967463Z"},"content_sha256":"35e4d8028ae421b68139a7670fcf1f1ce677b5728a28d500e16ee2f5ecc02e3f","schema_version":"1.0","event_id":"sha256:35e4d8028ae421b68139a7670fcf1f1ce677b5728a28d500e16ee2f5ecc02e3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WHWE2XDWKBYSUS3NJG76IPNYQA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear differential equation for Korobov numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dae San Kim, Hyuck In Kwon, Taekyun Kim, Toufik Mansour","submitted_at":"2016-04-15T01:27:24Z","abstract_excerpt":"In this paper, we present nonlinear differential equations for the generating functions for the Korobov numbers and for the Frobenuius-Euler numbers. As an application, we find an explicit expression for the nth derivative of 1/ log(1 + t)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04328","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":"2026-05-18T01:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8XfjZfrGnhZSSMLpbWlRnkgC4cBF926i9iEt2pW4nGFVklgw5wU1bhSuNwL+advKeClUjtcx0ZLo06t8rweyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:59:52.967804Z"},"content_sha256":"206543731e775e1176f5bbe4d88608340bf3c07e4b39e56c1d9abd5bf73a0044","schema_version":"1.0","event_id":"sha256:206543731e775e1176f5bbe4d88608340bf3c07e4b39e56c1d9abd5bf73a0044"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WHWE2XDWKBYSUS3NJG76IPNYQA/bundle.json","state_url":"https://pith.science/pith/WHWE2XDWKBYSUS3NJG76IPNYQA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WHWE2XDWKBYSUS3NJG76IPNYQA/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":"2026-06-01T18:59:52Z","links":{"resolver":"https://pith.science/pith/WHWE2XDWKBYSUS3NJG76IPNYQA","bundle":"https://pith.science/pith/WHWE2XDWKBYSUS3NJG76IPNYQA/bundle.json","state":"https://pith.science/pith/WHWE2XDWKBYSUS3NJG76IPNYQA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WHWE2XDWKBYSUS3NJG76IPNYQA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WHWE2XDWKBYSUS3NJG76IPNYQA","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":"13807adf9bcf7698caceaa558e19a9bb58905bb01ff9aeac0c44fc0748674898","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-15T01:27:24Z","title_canon_sha256":"7ae7db6d586980cb64eb1413c8f29861671d780b6dced964743605d7c89d2595"},"schema_version":"1.0","source":{"id":"1604.04328","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04328","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04328v1","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04328","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"WHWE2XDWKBYS","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WHWE2XDWKBYSUS3N","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WHWE2XDW","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:206543731e775e1176f5bbe4d88608340bf3c07e4b39e56c1d9abd5bf73a0044","target":"graph","created_at":"2026-05-18T01:17:04Z","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 this paper, we present nonlinear differential equations for the generating functions for the Korobov numbers and for the Frobenuius-Euler numbers. As an application, we find an explicit expression for the nth derivative of 1/ log(1 + t).","authors_text":"Dae San Kim, Hyuck In Kwon, Taekyun Kim, Toufik Mansour","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-15T01:27:24Z","title":"Nonlinear differential equation for Korobov numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04328","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":"sha256:35e4d8028ae421b68139a7670fcf1f1ce677b5728a28d500e16ee2f5ecc02e3f","target":"record","created_at":"2026-05-18T01:17:04Z","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":"13807adf9bcf7698caceaa558e19a9bb58905bb01ff9aeac0c44fc0748674898","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-15T01:27:24Z","title_canon_sha256":"7ae7db6d586980cb64eb1413c8f29861671d780b6dced964743605d7c89d2595"},"schema_version":"1.0","source":{"id":"1604.04328","kind":"arxiv","version":1}},"canonical_sha256":"b1ec4d5c7650712a4b6d49bfe43db8802006d7dd37e49105348eb7f510914f2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1ec4d5c7650712a4b6d49bfe43db8802006d7dd37e49105348eb7f510914f2d","first_computed_at":"2026-05-18T01:17:04.492013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:04.492013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZnraRTaC4+O2UgmEStmoE4dndP8QNNRlc1Lvxb24b/kqRx2hRKBItPQGnuNN3C/KJslKCBVoACwIl1d7rOgUDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:04.492684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35e4d8028ae421b68139a7670fcf1f1ce677b5728a28d500e16ee2f5ecc02e3f","sha256:206543731e775e1176f5bbe4d88608340bf3c07e4b39e56c1d9abd5bf73a0044"],"state_sha256":"a0e49a70b871a453673b4bd7b4376cc68829b6f22169cdcf6a45b09774a15157"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FG2llJpygT+dCTjuwB36DpA1634FfNHWXymAUyj4aTybjoOeLrAJU5SvZMfsK7S0fzjWffWaXWHNdtvqB2iUBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:59:52.969986Z","bundle_sha256":"196cb778569ff98c9f022da112017606f600457f667c79d4e61096d471e54df6"}}