{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B","short_pith_number":"pith:4WYLLRJ7","schema_version":"1.0","canonical_sha256":"e5b0b5c53fcff3d54336e4342a9b62d84beffe86f7bf6a745dbebaa3cd956832","source":{"kind":"arxiv","id":"1704.07931","version":2},"attestation_state":"computed","paper":{"title":"Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Claude Duhr, Einan Gardi, Ruth Britto, Samuel Abreu","submitted_at":"2017-04-25T23:34:17Z","abstract_excerpt":"We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent expansion in the dimensional regulator are multiple polylogarithms (MPLs). Our main result is the conjecture that this diagrammatic coaction reproduces the combinatorics of the coaction on MPLs order by order in the Laurent expansion. We show that our conjecture holds in a broad range of nontrivial one-loop integrals. We then explore its consequences for the stud"},"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":"1704.07931","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-04-25T23:34:17Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"310a38e03b26f0df5d81507a0d340f1ee0df62723b3186267a47a35bf10ee490","abstract_canon_sha256":"f20697e1f9398d07c1890b523ec11b718a5f9799d1227c55a5804bb4e4ab7602"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:37.738560Z","signature_b64":"BmjwNmizQyGCjq5uaqc81FKZwlf0XJPxfUFDrMIyz06TH+GxCGbXYlPjx6col3s5KsJiqUN8aSPbpQTgLGkOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5b0b5c53fcff3d54336e4342a9b62d84beffe86f7bf6a745dbebaa3cd956832","last_reissued_at":"2026-05-18T00:24:37.737957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:37.737957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Claude Duhr, Einan Gardi, Ruth Britto, Samuel Abreu","submitted_at":"2017-04-25T23:34:17Z","abstract_excerpt":"We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent expansion in the dimensional regulator are multiple polylogarithms (MPLs). Our main result is the conjecture that this diagrammatic coaction reproduces the combinatorics of the coaction on MPLs order by order in the Laurent expansion. We show that our conjecture holds in a broad range of nontrivial one-loop integrals. We then explore its consequences for the stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07931","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":"1704.07931","created_at":"2026-05-18T00:24:37.738042+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.07931v2","created_at":"2026-05-18T00:24:37.738042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07931","created_at":"2026-05-18T00:24:37.738042+00:00"},{"alias_kind":"pith_short_12","alias_value":"4WYLLRJ7Z7Z5","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"4WYLLRJ7Z7Z5KQZW","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"4WYLLRJ7","created_at":"2026-05-18T12:31:00.734936+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2503.02096","citing_title":"Deriving motivic coactions and single-valued maps at genus zero from zeta generators","ref_index":47,"is_internal_anchor":true},{"citing_arxiv_id":"2508.02800","citing_title":"Towards Motivic Coactions at Genus One from Zeta Generators","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B","json":"https://pith.science/pith/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B.json","graph_json":"https://pith.science/api/pith-number/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B/graph.json","events_json":"https://pith.science/api/pith-number/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B/events.json","paper":"https://pith.science/paper/4WYLLRJ7"},"agent_actions":{"view_html":"https://pith.science/pith/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B","download_json":"https://pith.science/pith/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B.json","view_paper":"https://pith.science/paper/4WYLLRJ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.07931&json=true","fetch_graph":"https://pith.science/api/pith-number/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B/graph.json","fetch_events":"https://pith.science/api/pith-number/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B/action/storage_attestation","attest_author":"https://pith.science/pith/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B/action/author_attestation","sign_citation":"https://pith.science/pith/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B/action/citation_signature","submit_replication":"https://pith.science/pith/4WYLLRJ7Z7Z5KQZW4Q2CVG3C3B/action/replication_record"}},"created_at":"2026-05-18T00:24:37.738042+00:00","updated_at":"2026-05-18T00:24:37.738042+00:00"}