{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:LAWGHXIJYXKI3GCIPHVC3BYW27","short_pith_number":"pith:LAWGHXIJ","schema_version":"1.0","canonical_sha256":"582c63dd09c5d48d984879ea2d8716d7d9f568fa0d9a68170b07dcdd7236609d","source":{"kind":"arxiv","id":"2207.12893","version":2},"attestation_state":"computed","paper":{"title":"The three-loop equal-mass banana integral in $\\varepsilon$-factorised form with meromorphic modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Sebastian P\\\"ogel, Stefan Weinzierl, Xing Wang","submitted_at":"2022-07-26T13:42:59Z","abstract_excerpt":"We show that the differential equation for the three-loop equal-mass banana integral can be cast into an $\\varepsilon$-factorised form with entries constructed from (meromorphic) modular forms and one special function, which can be given as an iterated integral of meromorphic modular forms. The $\\varepsilon$-factorised form of the differential equation allows for a systematic solution to any order in the dimensional regularisation parameter $\\varepsilon$. The alphabet of the iterated integrals contains six letters."},"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":"2207.12893","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-07-26T13:42:59Z","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"title_canon_sha256":"a5aae8b699665092b6a77571eff4fb5d989a983e4b2ce04c680e94149af54caa","abstract_canon_sha256":"4aa108d0d8b99fbbabf40cb08d9e250523eb9c22a43df0bb12d3c397a87ef24a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:01:27.639083Z","signature_b64":"hIfrwm5wx3A0iE3rpw6ky2Z2HkMSKKIeszVDdhkEEjn5Ccj3pfnYwuVtgtZzYc1sFfAKJCN7sC2K9HsivrBVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"582c63dd09c5d48d984879ea2d8716d7d9f568fa0d9a68170b07dcdd7236609d","last_reissued_at":"2026-07-05T05:01:27.638664Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:01:27.638664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The three-loop equal-mass banana integral in $\\varepsilon$-factorised form with meromorphic modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Sebastian P\\\"ogel, Stefan Weinzierl, Xing Wang","submitted_at":"2022-07-26T13:42:59Z","abstract_excerpt":"We show that the differential equation for the three-loop equal-mass banana integral can be cast into an $\\varepsilon$-factorised form with entries constructed from (meromorphic) modular forms and one special function, which can be given as an iterated integral of meromorphic modular forms. The $\\varepsilon$-factorised form of the differential equation allows for a systematic solution to any order in the dimensional regularisation parameter $\\varepsilon$. The alphabet of the iterated integrals contains six letters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.12893","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.12893/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":"2207.12893","created_at":"2026-07-05T05:01:27.638724+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.12893v2","created_at":"2026-07-05T05:01:27.638724+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.12893","created_at":"2026-07-05T05:01:27.638724+00:00"},{"alias_kind":"pith_short_12","alias_value":"LAWGHXIJYXKI","created_at":"2026-07-05T05:01:27.638724+00:00"},{"alias_kind":"pith_short_16","alias_value":"LAWGHXIJYXKI3GCI","created_at":"2026-07-05T05:01:27.638724+00:00"},{"alias_kind":"pith_short_8","alias_value":"LAWGHXIJ","created_at":"2026-07-05T05:01:27.638724+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":8,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2607.00187","citing_title":"From geometry to phenomenology","ref_index":64,"is_internal_anchor":false},{"citing_arxiv_id":"2606.02744","citing_title":"IterInt: Evaluating iterated integrals via differential equations","ref_index":39,"is_internal_anchor":false},{"citing_arxiv_id":"2512.10518","citing_title":"Fano and Reflexive Polytopes from Feynman Integrals","ref_index":83,"is_internal_anchor":false},{"citing_arxiv_id":"2508.02800","citing_title":"Towards Motivic Coactions at Genus One from Zeta Generators","ref_index":84,"is_internal_anchor":false},{"citing_arxiv_id":"2511.15381","citing_title":"New algorithms for Feynman integral reduction and $\\varepsilon$-factorised differential equations","ref_index":57,"is_internal_anchor":false},{"citing_arxiv_id":"2604.25270","citing_title":"Integrand Analysis, Leading Singularities and Canonical Bases beyond Polylogarithms","ref_index":25,"is_internal_anchor":false},{"citing_arxiv_id":"2604.09129","citing_title":"Picard-Fuchs Equations of Twisted Differential forms associated to Feynman Integrals","ref_index":73,"is_internal_anchor":false},{"citing_arxiv_id":"2604.08332","citing_title":"Discrete symmetries of Feynman integrals","ref_index":59,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LAWGHXIJYXKI3GCIPHVC3BYW27","json":"https://pith.science/pith/LAWGHXIJYXKI3GCIPHVC3BYW27.json","graph_json":"https://pith.science/api/pith-number/LAWGHXIJYXKI3GCIPHVC3BYW27/graph.json","events_json":"https://pith.science/api/pith-number/LAWGHXIJYXKI3GCIPHVC3BYW27/events.json","paper":"https://pith.science/paper/LAWGHXIJ"},"agent_actions":{"view_html":"https://pith.science/pith/LAWGHXIJYXKI3GCIPHVC3BYW27","download_json":"https://pith.science/pith/LAWGHXIJYXKI3GCIPHVC3BYW27.json","view_paper":"https://pith.science/paper/LAWGHXIJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.12893&json=true","fetch_graph":"https://pith.science/api/pith-number/LAWGHXIJYXKI3GCIPHVC3BYW27/graph.json","fetch_events":"https://pith.science/api/pith-number/LAWGHXIJYXKI3GCIPHVC3BYW27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LAWGHXIJYXKI3GCIPHVC3BYW27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LAWGHXIJYXKI3GCIPHVC3BYW27/action/storage_attestation","attest_author":"https://pith.science/pith/LAWGHXIJYXKI3GCIPHVC3BYW27/action/author_attestation","sign_citation":"https://pith.science/pith/LAWGHXIJYXKI3GCIPHVC3BYW27/action/citation_signature","submit_replication":"https://pith.science/pith/LAWGHXIJYXKI3GCIPHVC3BYW27/action/replication_record"}},"created_at":"2026-07-05T05:01:27.638724+00:00","updated_at":"2026-07-05T05:01:27.638724+00:00"}