{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:QA4M57MFP3ABIHXHMD2OVBRDIV","short_pith_number":"pith:QA4M57MF","schema_version":"1.0","canonical_sha256":"8038cefd857ec0141ee760f4ea862345417c03fa3bfeba92197826d6cd318a80","source":{"kind":"arxiv","id":"2307.02983","version":1},"attestation_state":"computed","paper":{"title":"Analytic results on the massive three-loop form factors: quarkonic contributions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-ph","authors_text":"Abilio De Freitas, Carsten Schneider, Johannes Bl\\\"umlein, Narayan Rana, Peter Marquard","submitted_at":"2023-07-06T13:35:24Z","abstract_excerpt":"The quarkonic contributions to the three-loop heavy-quark form factors for vector, axial-vector, scalar and pseudoscalar currents are described by closed form difference equations for the expansion coefficients in the limit of small virtualities $q^2/m^2$. A part of the contributions can be solved analytically and expressed in terms of harmonic and cyclotomic harmonic polylogarithms and square-root valued iterated integrals. Other contributions obey equations which are not first-order factorizable. For them still infinite series expansions around the singularities of the form factors can be ob"},"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":"2307.02983","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2023-07-06T13:35:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c81b4b610a76d72b17635207ae130383b6a3892651ba534422980237a85b74d1","abstract_canon_sha256":"de44f43974a280a3b50fdf1c295453588847eac7088ff9dc977351638a6f3e71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:28:26.632235Z","signature_b64":"7iLfrSA4g/A1aWaXpTZtKV3eiinY3lBUzVb2j/VEQaDSLPL0OA5sxDbpPVEMyaEqrJ/5lMc57WGFjMIf9zwHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8038cefd857ec0141ee760f4ea862345417c03fa3bfeba92197826d6cd318a80","last_reissued_at":"2026-07-05T06:28:26.631703Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:28:26.631703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic results on the massive three-loop form factors: quarkonic contributions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-ph","authors_text":"Abilio De Freitas, Carsten Schneider, Johannes Bl\\\"umlein, Narayan Rana, Peter Marquard","submitted_at":"2023-07-06T13:35:24Z","abstract_excerpt":"The quarkonic contributions to the three-loop heavy-quark form factors for vector, axial-vector, scalar and pseudoscalar currents are described by closed form difference equations for the expansion coefficients in the limit of small virtualities $q^2/m^2$. A part of the contributions can be solved analytically and expressed in terms of harmonic and cyclotomic harmonic polylogarithms and square-root valued iterated integrals. Other contributions obey equations which are not first-order factorizable. For them still infinite series expansions around the singularities of the form factors can be ob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.02983","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.02983/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2307.02983","created_at":"2026-07-05T06:28:26.631779+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.02983v1","created_at":"2026-07-05T06:28:26.631779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.02983","created_at":"2026-07-05T06:28:26.631779+00:00"},{"alias_kind":"pith_short_12","alias_value":"QA4M57MFP3AB","created_at":"2026-07-05T06:28:26.631779+00:00"},{"alias_kind":"pith_short_16","alias_value":"QA4M57MFP3ABIHXH","created_at":"2026-07-05T06:28:26.631779+00:00"},{"alias_kind":"pith_short_8","alias_value":"QA4M57MF","created_at":"2026-07-05T06:28:26.631779+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.02859","citing_title":"The Fate of Ultra-Collinear Modes in On-Shell Massive Sudakov Form Factors","ref_index":29,"is_internal_anchor":false},{"citing_arxiv_id":"2604.14741","citing_title":"The OPE Approach to Renormalization: Operator Mixing","ref_index":49,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QA4M57MFP3ABIHXHMD2OVBRDIV","json":"https://pith.science/pith/QA4M57MFP3ABIHXHMD2OVBRDIV.json","graph_json":"https://pith.science/api/pith-number/QA4M57MFP3ABIHXHMD2OVBRDIV/graph.json","events_json":"https://pith.science/api/pith-number/QA4M57MFP3ABIHXHMD2OVBRDIV/events.json","paper":"https://pith.science/paper/QA4M57MF"},"agent_actions":{"view_html":"https://pith.science/pith/QA4M57MFP3ABIHXHMD2OVBRDIV","download_json":"https://pith.science/pith/QA4M57MFP3ABIHXHMD2OVBRDIV.json","view_paper":"https://pith.science/paper/QA4M57MF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.02983&json=true","fetch_graph":"https://pith.science/api/pith-number/QA4M57MFP3ABIHXHMD2OVBRDIV/graph.json","fetch_events":"https://pith.science/api/pith-number/QA4M57MFP3ABIHXHMD2OVBRDIV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QA4M57MFP3ABIHXHMD2OVBRDIV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QA4M57MFP3ABIHXHMD2OVBRDIV/action/storage_attestation","attest_author":"https://pith.science/pith/QA4M57MFP3ABIHXHMD2OVBRDIV/action/author_attestation","sign_citation":"https://pith.science/pith/QA4M57MFP3ABIHXHMD2OVBRDIV/action/citation_signature","submit_replication":"https://pith.science/pith/QA4M57MFP3ABIHXHMD2OVBRDIV/action/replication_record"}},"created_at":"2026-07-05T06:28:26.631779+00:00","updated_at":"2026-07-05T06:28:26.631779+00:00"}