{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:OE55ADM76SJF5MT7WIPQNXXBH6","short_pith_number":"pith:OE55ADM7","schema_version":"1.0","canonical_sha256":"713bd00d9ff4925eb27fb21f06dee13fb88e28df9645041a100b6f4c2b71c692","source":{"kind":"arxiv","id":"1902.11001","version":2},"attestation_state":"computed","paper":{"title":"Discovering and Proving Infinite Pochhammer Sum Identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.NT"],"primary_cat":"math.CO","authors_text":"Jakob Ablinger","submitted_at":"2019-02-28T10:40:48Z","abstract_excerpt":"We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of $\\pi,$ $\\log(2)$ or zeta values. In order to perform these simplifications, we view the series as specializations of generating series. For these generating series, we derive integral representations in terms of root-valued iterated integrals or directly in terms of cyclotomic harmonic polylogarithms. Using substitutions, we express the root-valued iterated integrals as cyclotomic harmonic polylogarithms. Finally, by applying known relations among the cyc"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1902.11001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-28T10:40:48Z","cross_cats_sorted":["cs.SC","math.NT"],"title_canon_sha256":"e02aee5312ceccfe05f843ac4029dd0e12c3958d1a7830451e5221c750f51575","abstract_canon_sha256":"6f5121e6c0810eaddc4a2ab1fe88e61090b91fd08058df2faa167c60050fcc19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:54.882710Z","signature_b64":"FOmudxonlk2LNYYgljPTnKpJCGCyYwQKZrCN3eSW4YuUB/VE7e1yM5cBbqRiLgHbqvVi3xkVdlK+jqM+VmByDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"713bd00d9ff4925eb27fb21f06dee13fb88e28df9645041a100b6f4c2b71c692","last_reissued_at":"2026-05-17T23:48:54.882210Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:54.882210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discovering and Proving Infinite Pochhammer Sum Identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.NT"],"primary_cat":"math.CO","authors_text":"Jakob Ablinger","submitted_at":"2019-02-28T10:40:48Z","abstract_excerpt":"We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of $\\pi,$ $\\log(2)$ or zeta values. In order to perform these simplifications, we view the series as specializations of generating series. For these generating series, we derive integral representations in terms of root-valued iterated integrals or directly in terms of cyclotomic harmonic polylogarithms. Using substitutions, we express the root-valued iterated integrals as cyclotomic harmonic polylogarithms. Finally, by applying known relations among the cyc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.11001","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.11001","created_at":"2026-05-17T23:48:54.882300+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.11001v2","created_at":"2026-05-17T23:48:54.882300+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.11001","created_at":"2026-05-17T23:48:54.882300+00:00"},{"alias_kind":"pith_short_12","alias_value":"OE55ADM76SJF","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"OE55ADM76SJF5MT7","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"OE55ADM7","created_at":"2026-05-18T12:33:24.271573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OE55ADM76SJF5MT7WIPQNXXBH6","json":"https://pith.science/pith/OE55ADM76SJF5MT7WIPQNXXBH6.json","graph_json":"https://pith.science/api/pith-number/OE55ADM76SJF5MT7WIPQNXXBH6/graph.json","events_json":"https://pith.science/api/pith-number/OE55ADM76SJF5MT7WIPQNXXBH6/events.json","paper":"https://pith.science/paper/OE55ADM7"},"agent_actions":{"view_html":"https://pith.science/pith/OE55ADM76SJF5MT7WIPQNXXBH6","download_json":"https://pith.science/pith/OE55ADM76SJF5MT7WIPQNXXBH6.json","view_paper":"https://pith.science/paper/OE55ADM7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.11001&json=true","fetch_graph":"https://pith.science/api/pith-number/OE55ADM76SJF5MT7WIPQNXXBH6/graph.json","fetch_events":"https://pith.science/api/pith-number/OE55ADM76SJF5MT7WIPQNXXBH6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OE55ADM76SJF5MT7WIPQNXXBH6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OE55ADM76SJF5MT7WIPQNXXBH6/action/storage_attestation","attest_author":"https://pith.science/pith/OE55ADM76SJF5MT7WIPQNXXBH6/action/author_attestation","sign_citation":"https://pith.science/pith/OE55ADM76SJF5MT7WIPQNXXBH6/action/citation_signature","submit_replication":"https://pith.science/pith/OE55ADM76SJF5MT7WIPQNXXBH6/action/replication_record"}},"created_at":"2026-05-17T23:48:54.882300+00:00","updated_at":"2026-05-17T23:48:54.882300+00:00"}