{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:IS2L4X5XRJCGSCQDENF225KMBM","short_pith_number":"pith:IS2L4X5X","schema_version":"1.0","canonical_sha256":"44b4be5fb78a44690a03234bad754c0b1d1b89647af6749292c540566ae0b5ac","source":{"kind":"arxiv","id":"1407.1822","version":1},"attestation_state":"computed","paper":{"title":"Iterated Binomial Sums and their Associated Iterated Integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"C.G. Raab, C. Schneider, J. Ablinger, J. Bl\\\"umlein","submitted_at":"2014-07-03T12:23:35Z","abstract_excerpt":"We consider finite iterated generalized harmonic sums weighted by the binomial $\\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting at 3-loop order in the coupling constant and extends the classes of the nested harmonic, generalized harmonic and cyclotomic sums. The binomially weighted sums are associated by the Mellin transform to iterated integrals over square-root valued alphabets. The values of the sums for $N \\rightarrow \\infty$ and the iterated integrals at $x=1$ lea"},"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":"1407.1822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-07-03T12:23:35Z","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"title_canon_sha256":"e4fb52e112be6a4626bc4f10384b07ee082d9625c7e20f654ff259035e6ee050","abstract_canon_sha256":"b2cd926f72fec700c9248707f75f1e8f4a37d49f347b34148d8dbd349d085bd0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:41.245081Z","signature_b64":"2w5++8gnqqzrrze88RkemK832Q0jtPZUsrmy+RInfdAj2bMGQwPW9yGE6JVHOwYKhJhX7XUSXFElvEa3DlhGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44b4be5fb78a44690a03234bad754c0b1d1b89647af6749292c540566ae0b5ac","last_reissued_at":"2026-05-18T01:42:41.244559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:41.244559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Iterated Binomial Sums and their Associated Iterated Integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"C.G. Raab, C. Schneider, J. Ablinger, J. Bl\\\"umlein","submitted_at":"2014-07-03T12:23:35Z","abstract_excerpt":"We consider finite iterated generalized harmonic sums weighted by the binomial $\\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting at 3-loop order in the coupling constant and extends the classes of the nested harmonic, generalized harmonic and cyclotomic sums. The binomially weighted sums are associated by the Mellin transform to iterated integrals over square-root valued alphabets. The values of the sums for $N \\rightarrow \\infty$ and the iterated integrals at $x=1$ lea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1822","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.1822","created_at":"2026-05-18T01:42:41.244651+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.1822v1","created_at":"2026-05-18T01:42:41.244651+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1822","created_at":"2026-05-18T01:42:41.244651+00:00"},{"alias_kind":"pith_short_12","alias_value":"IS2L4X5XRJCG","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"IS2L4X5XRJCGSCQD","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"IS2L4X5X","created_at":"2026-05-18T12:28:33.132498+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.15751","citing_title":"The photon-energy spectrum in $B\\to X_s\\gamma$ to N$^3$LO: light-fermion and large-$N_{\\rm c}$ corrections","ref_index":72,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IS2L4X5XRJCGSCQDENF225KMBM","json":"https://pith.science/pith/IS2L4X5XRJCGSCQDENF225KMBM.json","graph_json":"https://pith.science/api/pith-number/IS2L4X5XRJCGSCQDENF225KMBM/graph.json","events_json":"https://pith.science/api/pith-number/IS2L4X5XRJCGSCQDENF225KMBM/events.json","paper":"https://pith.science/paper/IS2L4X5X"},"agent_actions":{"view_html":"https://pith.science/pith/IS2L4X5XRJCGSCQDENF225KMBM","download_json":"https://pith.science/pith/IS2L4X5XRJCGSCQDENF225KMBM.json","view_paper":"https://pith.science/paper/IS2L4X5X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.1822&json=true","fetch_graph":"https://pith.science/api/pith-number/IS2L4X5XRJCGSCQDENF225KMBM/graph.json","fetch_events":"https://pith.science/api/pith-number/IS2L4X5XRJCGSCQDENF225KMBM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IS2L4X5XRJCGSCQDENF225KMBM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IS2L4X5XRJCGSCQDENF225KMBM/action/storage_attestation","attest_author":"https://pith.science/pith/IS2L4X5XRJCGSCQDENF225KMBM/action/author_attestation","sign_citation":"https://pith.science/pith/IS2L4X5XRJCGSCQDENF225KMBM/action/citation_signature","submit_replication":"https://pith.science/pith/IS2L4X5XRJCGSCQDENF225KMBM/action/replication_record"}},"created_at":"2026-05-18T01:42:41.244651+00:00","updated_at":"2026-05-18T01:42:41.244651+00:00"}