{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IRAQORNLQODZ4R6YJSDWJM6F6P","short_pith_number":"pith:IRAQORNL","canonical_record":{"source":{"id":"1604.03787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-13T14:15:50Z","cross_cats_sorted":[],"title_canon_sha256":"1e5a5a4a612b41e25af9c55dee4b8017f6c50eef69901df0d56da313dca5f984","abstract_canon_sha256":"47816fd0cf176ecd981bf9b09ab3bf44c2661bce82881cfaee61268e3dda5303"},"schema_version":"1.0"},"canonical_sha256":"44410745ab83879e47d84c8764b3c5f3fdcca627a774c51516255e2981acada4","source":{"kind":"arxiv","id":"1604.03787","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03787","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03787v1","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03787","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"pith_short_12","alias_value":"IRAQORNLQODZ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IRAQORNLQODZ4R6Y","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IRAQORNL","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IRAQORNLQODZ4R6YJSDWJM6F6P","target":"record","payload":{"canonical_record":{"source":{"id":"1604.03787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-13T14:15:50Z","cross_cats_sorted":[],"title_canon_sha256":"1e5a5a4a612b41e25af9c55dee4b8017f6c50eef69901df0d56da313dca5f984","abstract_canon_sha256":"47816fd0cf176ecd981bf9b09ab3bf44c2661bce82881cfaee61268e3dda5303"},"schema_version":"1.0"},"canonical_sha256":"44410745ab83879e47d84c8764b3c5f3fdcca627a774c51516255e2981acada4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:11.067342Z","signature_b64":"UwUuVxjsnvDWKEAjVDu+nnCcpeFnlMI0e12kfXW13/A+xQtxTpFyzxi4hwnMRmfl3tOPACN3il3kBbcARWV7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44410745ab83879e47d84c8764b3c5f3fdcca627a774c51516255e2981acada4","last_reissued_at":"2026-05-18T01:17:11.066533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:11.066533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.03787","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":"2026-05-18T01:17:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5Ykf0LdMUxJeu3xLv5jIQjsmqcQdj3gfG4XnChzId2fPoymJH+vxs669jIOExww7cclCl8wXBeiF94ssgVnDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:14:05.398290Z"},"content_sha256":"c6411bd77448895e00d13fbab797e920e1e06d9104bdbb8a4307e1f3e338a862","schema_version":"1.0","event_id":"sha256:c6411bd77448895e00d13fbab797e920e1e06d9104bdbb8a4307e1f3e338a862"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IRAQORNLQODZ4R6YJSDWJM6F6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A $(p,q)$-Analogue of Poly-Euler Polynomials and Some Related Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jos\\'e L. Ram\\'irez, Takao Komatsu, V\\'ictor F. Sirvent","submitted_at":"2016-04-13T14:15:50Z","abstract_excerpt":"In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give several combinatorial identities and properties of these new polynomials. Moreover, we show some relations with the $(p,q)$-poly-Bernoulli polynomials and $(p,q)$-poly-Cauchy polynomials. The $(p,q)$-analogues generalize the well-known concept of the $q$-analogue."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03787","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":"2026-05-18T01:17:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zq3EDDLc9ZxfU6EFWvX3p2sIOAj/FK4Kg5DSsBkXfRTIZaDTNLZJPwykI6FDmL2YOf7AztMHKW/bGXNv1kAPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:14:05.398672Z"},"content_sha256":"ff6410c96e418e17c308222047086e18c40d3482fa395afb4616f96c836ba679","schema_version":"1.0","event_id":"sha256:ff6410c96e418e17c308222047086e18c40d3482fa395afb4616f96c836ba679"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IRAQORNLQODZ4R6YJSDWJM6F6P/bundle.json","state_url":"https://pith.science/pith/IRAQORNLQODZ4R6YJSDWJM6F6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IRAQORNLQODZ4R6YJSDWJM6F6P/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":"2026-05-26T18:14:05Z","links":{"resolver":"https://pith.science/pith/IRAQORNLQODZ4R6YJSDWJM6F6P","bundle":"https://pith.science/pith/IRAQORNLQODZ4R6YJSDWJM6F6P/bundle.json","state":"https://pith.science/pith/IRAQORNLQODZ4R6YJSDWJM6F6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IRAQORNLQODZ4R6YJSDWJM6F6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IRAQORNLQODZ4R6YJSDWJM6F6P","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":"47816fd0cf176ecd981bf9b09ab3bf44c2661bce82881cfaee61268e3dda5303","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-13T14:15:50Z","title_canon_sha256":"1e5a5a4a612b41e25af9c55dee4b8017f6c50eef69901df0d56da313dca5f984"},"schema_version":"1.0","source":{"id":"1604.03787","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03787","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03787v1","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03787","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"pith_short_12","alias_value":"IRAQORNLQODZ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IRAQORNLQODZ4R6Y","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IRAQORNL","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:ff6410c96e418e17c308222047086e18c40d3482fa395afb4616f96c836ba679","target":"graph","created_at":"2026-05-18T01:17:11Z","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 present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give several combinatorial identities and properties of these new polynomials. Moreover, we show some relations with the $(p,q)$-poly-Bernoulli polynomials and $(p,q)$-poly-Cauchy polynomials. The $(p,q)$-analogues generalize the well-known concept of the $q$-analogue.","authors_text":"Jos\\'e L. Ram\\'irez, Takao Komatsu, V\\'ictor F. Sirvent","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-13T14:15:50Z","title":"A $(p,q)$-Analogue of Poly-Euler Polynomials and Some Related Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03787","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:c6411bd77448895e00d13fbab797e920e1e06d9104bdbb8a4307e1f3e338a862","target":"record","created_at":"2026-05-18T01:17:11Z","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":"47816fd0cf176ecd981bf9b09ab3bf44c2661bce82881cfaee61268e3dda5303","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-13T14:15:50Z","title_canon_sha256":"1e5a5a4a612b41e25af9c55dee4b8017f6c50eef69901df0d56da313dca5f984"},"schema_version":"1.0","source":{"id":"1604.03787","kind":"arxiv","version":1}},"canonical_sha256":"44410745ab83879e47d84c8764b3c5f3fdcca627a774c51516255e2981acada4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44410745ab83879e47d84c8764b3c5f3fdcca627a774c51516255e2981acada4","first_computed_at":"2026-05-18T01:17:11.066533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:11.066533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UwUuVxjsnvDWKEAjVDu+nnCcpeFnlMI0e12kfXW13/A+xQtxTpFyzxi4hwnMRmfl3tOPACN3il3kBbcARWV7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:11.067342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03787","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6411bd77448895e00d13fbab797e920e1e06d9104bdbb8a4307e1f3e338a862","sha256:ff6410c96e418e17c308222047086e18c40d3482fa395afb4616f96c836ba679"],"state_sha256":"3b16d768a41910e9ed7445d74087f33bd56e7fb671d5e02332b90d463079be58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UxnMw0H44Pkx+H3BoSV8kN+lz7nY7ISZXnOfMRPzOoFSpSbARnOqorYfNV5z/Nl8lnmD69pNzt4f7uICmHwhAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:14:05.401526Z","bundle_sha256":"0eb9e5e8a71cb3476ce34abf80d1583eb8c3b203a55690ec92ed9cc9400235a5"}}