{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CVM26TFU6DDWADH4ZD6KMNOQ2K","short_pith_number":"pith:CVM26TFU","canonical_record":{"source":{"id":"1709.02229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-07T13:40:46Z","cross_cats_sorted":[],"title_canon_sha256":"a050c10f364929da522157cd29ccbe8d0aaa15534e99021d90447d26565a28a4","abstract_canon_sha256":"cf5d112a12dfcf016dfc2b9c9f5d8286825a28b6014fdc14818a68cade1ab5b5"},"schema_version":"1.0"},"canonical_sha256":"1559af4cb4f0c7600cfcc8fca635d0d286b06fd5a71d84afcb673ac6db47ddb6","source":{"kind":"arxiv","id":"1709.02229","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02229","created_at":"2026-05-18T00:34:41Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02229v2","created_at":"2026-05-18T00:34:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02229","created_at":"2026-05-18T00:34:41Z"},{"alias_kind":"pith_short_12","alias_value":"CVM26TFU6DDW","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CVM26TFU6DDWADH4","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CVM26TFU","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CVM26TFU6DDWADH4ZD6KMNOQ2K","target":"record","payload":{"canonical_record":{"source":{"id":"1709.02229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-07T13:40:46Z","cross_cats_sorted":[],"title_canon_sha256":"a050c10f364929da522157cd29ccbe8d0aaa15534e99021d90447d26565a28a4","abstract_canon_sha256":"cf5d112a12dfcf016dfc2b9c9f5d8286825a28b6014fdc14818a68cade1ab5b5"},"schema_version":"1.0"},"canonical_sha256":"1559af4cb4f0c7600cfcc8fca635d0d286b06fd5a71d84afcb673ac6db47ddb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:41.225461Z","signature_b64":"vbhUr6CZx1L01NT5bmmHCrpGPL+3KrY3Vn5Bk414cDkh1yAAAlQLXo4sIAqZ89CRGdWASzNibLYYcqlty8R/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1559af4cb4f0c7600cfcc8fca635d0d286b06fd5a71d84afcb673ac6db47ddb6","last_reissued_at":"2026-05-18T00:34:41.224715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:41.224715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.02229","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":"2026-05-18T00:34:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SD0QAEf3+vTqrTKJQnCaJz1fQqk3T6o/AM6lffVIucYSGfkIK3Hs3njcjOdAimwo7UOnmgVC6R9bvAjLdlLwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:31:20.273911Z"},"content_sha256":"bd3b72ad46b8d7c73f28af754e3d12871ea09e2d4504ccb595bf805e10680a69","schema_version":"1.0","event_id":"sha256:bd3b72ad46b8d7c73f28af754e3d12871ea09e2d4504ccb595bf805e10680a69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CVM26TFU6DDWADH4ZD6KMNOQ2K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riordan arrays and generalized Euler polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"E. Burlachenko","submitted_at":"2017-09-07T13:40:46Z","abstract_excerpt":"Generalization of the Euler polynomials ${{A}_{n}}\\left( x \\right)={{\\left( 1-x \\right)}^{n+1}}\\sum\\nolimits_{m=0}^{\\infty }{{{m}^{n}}{{x}^{m}}}$ are the polynomials ${{\\alpha }_{n}}\\left( x \\right)={{\\left( 1-x \\right)}^{n+1}}\\sum\\nolimits_{m=0}^{\\infty }{{{u}_{n}}}\\left( m \\right){{x}^{m}}$, where ${{u}_{n}}\\left( x \\right)$ is the polynomial of degree $n$. These polynomials appear in various fields of mathematics, which causes a variety of methods for their study. In present paper we will consider generalized Euler polynomials as an attribute of the theory of Riordan arrays. From this point"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02229","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":"2026-05-18T00:34:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65SAT9srCxjQtoPUX5m7cjLvx548jMq4mwCDIAX9StQ++Bv7LqHF1ldZKWVD0FZATzBiS8LBux7x976Y+dqfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:31:20.274529Z"},"content_sha256":"47ea2f792e1142644dcba4af1ff0f0aa60e3ae4729bd4f1d199cc2f2d45f1044","schema_version":"1.0","event_id":"sha256:47ea2f792e1142644dcba4af1ff0f0aa60e3ae4729bd4f1d199cc2f2d45f1044"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CVM26TFU6DDWADH4ZD6KMNOQ2K/bundle.json","state_url":"https://pith.science/pith/CVM26TFU6DDWADH4ZD6KMNOQ2K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CVM26TFU6DDWADH4ZD6KMNOQ2K/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":"2026-06-02T19:31:20Z","links":{"resolver":"https://pith.science/pith/CVM26TFU6DDWADH4ZD6KMNOQ2K","bundle":"https://pith.science/pith/CVM26TFU6DDWADH4ZD6KMNOQ2K/bundle.json","state":"https://pith.science/pith/CVM26TFU6DDWADH4ZD6KMNOQ2K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CVM26TFU6DDWADH4ZD6KMNOQ2K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CVM26TFU6DDWADH4ZD6KMNOQ2K","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":"cf5d112a12dfcf016dfc2b9c9f5d8286825a28b6014fdc14818a68cade1ab5b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-07T13:40:46Z","title_canon_sha256":"a050c10f364929da522157cd29ccbe8d0aaa15534e99021d90447d26565a28a4"},"schema_version":"1.0","source":{"id":"1709.02229","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02229","created_at":"2026-05-18T00:34:41Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02229v2","created_at":"2026-05-18T00:34:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02229","created_at":"2026-05-18T00:34:41Z"},{"alias_kind":"pith_short_12","alias_value":"CVM26TFU6DDW","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CVM26TFU6DDWADH4","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CVM26TFU","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:47ea2f792e1142644dcba4af1ff0f0aa60e3ae4729bd4f1d199cc2f2d45f1044","target":"graph","created_at":"2026-05-18T00:34:41Z","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":"Generalization of the Euler polynomials ${{A}_{n}}\\left( x \\right)={{\\left( 1-x \\right)}^{n+1}}\\sum\\nolimits_{m=0}^{\\infty }{{{m}^{n}}{{x}^{m}}}$ are the polynomials ${{\\alpha }_{n}}\\left( x \\right)={{\\left( 1-x \\right)}^{n+1}}\\sum\\nolimits_{m=0}^{\\infty }{{{u}_{n}}}\\left( m \\right){{x}^{m}}$, where ${{u}_{n}}\\left( x \\right)$ is the polynomial of degree $n$. These polynomials appear in various fields of mathematics, which causes a variety of methods for their study. In present paper we will consider generalized Euler polynomials as an attribute of the theory of Riordan arrays. From this point","authors_text":"E. Burlachenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-07T13:40:46Z","title":"Riordan arrays and generalized Euler polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02229","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:bd3b72ad46b8d7c73f28af754e3d12871ea09e2d4504ccb595bf805e10680a69","target":"record","created_at":"2026-05-18T00:34:41Z","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":"cf5d112a12dfcf016dfc2b9c9f5d8286825a28b6014fdc14818a68cade1ab5b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-07T13:40:46Z","title_canon_sha256":"a050c10f364929da522157cd29ccbe8d0aaa15534e99021d90447d26565a28a4"},"schema_version":"1.0","source":{"id":"1709.02229","kind":"arxiv","version":2}},"canonical_sha256":"1559af4cb4f0c7600cfcc8fca635d0d286b06fd5a71d84afcb673ac6db47ddb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1559af4cb4f0c7600cfcc8fca635d0d286b06fd5a71d84afcb673ac6db47ddb6","first_computed_at":"2026-05-18T00:34:41.224715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:41.224715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vbhUr6CZx1L01NT5bmmHCrpGPL+3KrY3Vn5Bk414cDkh1yAAAlQLXo4sIAqZ89CRGdWASzNibLYYcqlty8R/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:41.225461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.02229","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd3b72ad46b8d7c73f28af754e3d12871ea09e2d4504ccb595bf805e10680a69","sha256:47ea2f792e1142644dcba4af1ff0f0aa60e3ae4729bd4f1d199cc2f2d45f1044"],"state_sha256":"8a00760044f1c42b928368b0a459a88fa4307bcb2e23fbbd024aa4afd237f157"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AyGTig6P21BTbYT2QMTcXxrDBL4PSZWBDDI1oP66jdTWvMzBz5CpTR2iFs6gV/606Kq1tMDfvDSLnuhKfDt/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:31:20.277087Z","bundle_sha256":"f77f69d713b397dd8c5ecff3c54d71ce6851f667405fb7f4f23be85ffd09aee9"}}