{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PCZNOKUV4BTCKY2SAVHVFCRGH7","short_pith_number":"pith:PCZNOKUV","schema_version":"1.0","canonical_sha256":"78b2d72a95e066256352054f528a263ff387717ed7a6f31294502d65caf7f4b7","source":{"kind":"arxiv","id":"2404.04644","version":4},"attestation_state":"computed","paper":{"title":"Solving arbitrary one-loop reduction via generating function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Liang Zhang, Tingfei Li, Yuekai Song","submitted_at":"2024-04-06T14:34:35Z","abstract_excerpt":"Recently, the concept of generating function has been employed in one-loop reduction. For one-loop integrals encompassing arbitrary tensor ranks and higher-pole contributions, the generating function can be decomposed into a tensor part and a higher-pole part. While the tensor component has been thoroughly addressed in recent studies, there remains a lack of satisfactory investigations regarding the higher-pole part. In this work, we completely solve the problem. We first establish the partial differential equations governing the higher-pole generating function. Based on these equations, we de"},"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":"2404.04644","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2024-04-06T14:34:35Z","cross_cats_sorted":[],"title_canon_sha256":"a3a66747abf758db9cad6be64d7b3b688dbbc01b043e91775921315dd0799d7f","abstract_canon_sha256":"daff4667ed476e1387a15b91800e7ec830c1cc540b8fbcdbe5fc1003eecc4832"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:56:50.780251Z","signature_b64":"nl2VakrUW9pvvd5wxTR16oiroQbLfIneSe2hz7Vdva4FPS5JWS8+oErt/lp+qzw461f6+VJrlPUFvI58rEGMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78b2d72a95e066256352054f528a263ff387717ed7a6f31294502d65caf7f4b7","last_reissued_at":"2026-07-05T09:56:50.779755Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:56:50.779755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solving arbitrary one-loop reduction via generating function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Liang Zhang, Tingfei Li, Yuekai Song","submitted_at":"2024-04-06T14:34:35Z","abstract_excerpt":"Recently, the concept of generating function has been employed in one-loop reduction. For one-loop integrals encompassing arbitrary tensor ranks and higher-pole contributions, the generating function can be decomposed into a tensor part and a higher-pole part. While the tensor component has been thoroughly addressed in recent studies, there remains a lack of satisfactory investigations regarding the higher-pole part. In this work, we completely solve the problem. We first establish the partial differential equations governing the higher-pole generating function. Based on these equations, we de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04644","kind":"arxiv","version":4},"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/2404.04644/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":"2404.04644","created_at":"2026-07-05T09:56:50.779814+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.04644v4","created_at":"2026-07-05T09:56:50.779814+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.04644","created_at":"2026-07-05T09:56:50.779814+00:00"},{"alias_kind":"pith_short_12","alias_value":"PCZNOKUV4BTC","created_at":"2026-07-05T09:56:50.779814+00:00"},{"alias_kind":"pith_short_16","alias_value":"PCZNOKUV4BTCKY2S","created_at":"2026-07-05T09:56:50.779814+00:00"},{"alias_kind":"pith_short_8","alias_value":"PCZNOKUV","created_at":"2026-07-05T09:56:50.779814+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.10698","citing_title":"Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding","ref_index":43,"is_internal_anchor":false},{"citing_arxiv_id":"2412.15962","citing_title":"Feynman Integral Reduction without Integration-By-Parts","ref_index":47,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PCZNOKUV4BTCKY2SAVHVFCRGH7","json":"https://pith.science/pith/PCZNOKUV4BTCKY2SAVHVFCRGH7.json","graph_json":"https://pith.science/api/pith-number/PCZNOKUV4BTCKY2SAVHVFCRGH7/graph.json","events_json":"https://pith.science/api/pith-number/PCZNOKUV4BTCKY2SAVHVFCRGH7/events.json","paper":"https://pith.science/paper/PCZNOKUV"},"agent_actions":{"view_html":"https://pith.science/pith/PCZNOKUV4BTCKY2SAVHVFCRGH7","download_json":"https://pith.science/pith/PCZNOKUV4BTCKY2SAVHVFCRGH7.json","view_paper":"https://pith.science/paper/PCZNOKUV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.04644&json=true","fetch_graph":"https://pith.science/api/pith-number/PCZNOKUV4BTCKY2SAVHVFCRGH7/graph.json","fetch_events":"https://pith.science/api/pith-number/PCZNOKUV4BTCKY2SAVHVFCRGH7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PCZNOKUV4BTCKY2SAVHVFCRGH7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PCZNOKUV4BTCKY2SAVHVFCRGH7/action/storage_attestation","attest_author":"https://pith.science/pith/PCZNOKUV4BTCKY2SAVHVFCRGH7/action/author_attestation","sign_citation":"https://pith.science/pith/PCZNOKUV4BTCKY2SAVHVFCRGH7/action/citation_signature","submit_replication":"https://pith.science/pith/PCZNOKUV4BTCKY2SAVHVFCRGH7/action/replication_record"}},"created_at":"2026-07-05T09:56:50.779814+00:00","updated_at":"2026-07-05T09:56:50.779814+00:00"}