{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:PEEKK67XYIZZMWN3PP2SVCGHXS","short_pith_number":"pith:PEEKK67X","schema_version":"1.0","canonical_sha256":"7908a57bf7c2339659bb7bf52a88c7bc9a9dae20150e2b6c46fcfb81f7b56576","source":{"kind":"arxiv","id":"hep-ph/0609007","version":2},"attestation_state":"computed","paper":{"title":"Reducing full one-loop amplitudes to scalar integrals at the integrand level","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Costas G.Papadopoulos, Giovanni Ossola, Roberto Pittau","submitted_at":"2006-09-01T14:41:51Z","abstract_excerpt":"We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no information on the analytical structure of the amplitude is required, making our method appealing for an efficient numerical implementation"},"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":"hep-ph/0609007","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2006-09-01T14:41:51Z","cross_cats_sorted":[],"title_canon_sha256":"b9e7e2d40ee2b3212e372091120f5149fda9a7b7815269c82f7cd04325f961b3","abstract_canon_sha256":"20e58ac44c08a5dd960bcaad3a9617c71e5d9261beea1f4a098e1e3950e8a8df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:17:09.392442Z","signature_b64":"quK7GDn7+YUqZ4Sgowauc9eNNFShDNbD0hxrBSxSE0UZwPCIHXUd4k11G4yCycsu4BNOgPa4T+ZXzkay7dWoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7908a57bf7c2339659bb7bf52a88c7bc9a9dae20150e2b6c46fcfb81f7b56576","last_reissued_at":"2026-07-04T15:17:09.391940Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:17:09.391940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reducing full one-loop amplitudes to scalar integrals at the integrand level","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Costas G.Papadopoulos, Giovanni Ossola, Roberto Pittau","submitted_at":"2006-09-01T14:41:51Z","abstract_excerpt":"We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no information on the analytical structure of the amplitude is required, making our method appealing for an efficient numerical implementation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0609007","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/hep-ph/0609007/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":"hep-ph/0609007","created_at":"2026-07-04T15:17:09.391999+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0609007v2","created_at":"2026-07-04T15:17:09.391999+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0609007","created_at":"2026-07-04T15:17:09.391999+00:00"},{"alias_kind":"pith_short_12","alias_value":"PEEKK67XYIZZ","created_at":"2026-07-04T15:17:09.391999+00:00"},{"alias_kind":"pith_short_16","alias_value":"PEEKK67XYIZZMWN3","created_at":"2026-07-04T15:17:09.391999+00:00"},{"alias_kind":"pith_short_8","alias_value":"PEEKK67X","created_at":"2026-07-04T15:17:09.391999+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":8,"internal_anchor_count":6,"sample":[{"citing_arxiv_id":"2606.28052","citing_title":"Planar loop integrands from cuts in $D$ dimensions","ref_index":52,"is_internal_anchor":true},{"citing_arxiv_id":"2606.22007","citing_title":"Monte Carlo Event Generators for Future Lepton Colliders","ref_index":32,"is_internal_anchor":true},{"citing_arxiv_id":"1906.11862","citing_title":"A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons","ref_index":46,"is_internal_anchor":true},{"citing_arxiv_id":"2412.15962","citing_title":"Feynman Integral Reduction without Integration-By-Parts","ref_index":30,"is_internal_anchor":true},{"citing_arxiv_id":"2512.18391","citing_title":"Complete NLO corrections to off-shell $\\boldsymbol{t\\bar{t}}$ production in the $\\boldsymbol{\\ell+j}$ decay channel","ref_index":43,"is_internal_anchor":true},{"citing_arxiv_id":"2512.21210","citing_title":"Twisted Feynman Integrals: from generating functions to spin-resummed post-Minkowskian dynamics","ref_index":10,"is_internal_anchor":true},{"citing_arxiv_id":"2605.03051","citing_title":"Pseudo-Evanescent Feynman Integrals from Local Subtraction","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"1405.0301","citing_title":"The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations","ref_index":18,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PEEKK67XYIZZMWN3PP2SVCGHXS","json":"https://pith.science/pith/PEEKK67XYIZZMWN3PP2SVCGHXS.json","graph_json":"https://pith.science/api/pith-number/PEEKK67XYIZZMWN3PP2SVCGHXS/graph.json","events_json":"https://pith.science/api/pith-number/PEEKK67XYIZZMWN3PP2SVCGHXS/events.json","paper":"https://pith.science/paper/PEEKK67X"},"agent_actions":{"view_html":"https://pith.science/pith/PEEKK67XYIZZMWN3PP2SVCGHXS","download_json":"https://pith.science/pith/PEEKK67XYIZZMWN3PP2SVCGHXS.json","view_paper":"https://pith.science/paper/PEEKK67X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/0609007&json=true","fetch_graph":"https://pith.science/api/pith-number/PEEKK67XYIZZMWN3PP2SVCGHXS/graph.json","fetch_events":"https://pith.science/api/pith-number/PEEKK67XYIZZMWN3PP2SVCGHXS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PEEKK67XYIZZMWN3PP2SVCGHXS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PEEKK67XYIZZMWN3PP2SVCGHXS/action/storage_attestation","attest_author":"https://pith.science/pith/PEEKK67XYIZZMWN3PP2SVCGHXS/action/author_attestation","sign_citation":"https://pith.science/pith/PEEKK67XYIZZMWN3PP2SVCGHXS/action/citation_signature","submit_replication":"https://pith.science/pith/PEEKK67XYIZZMWN3PP2SVCGHXS/action/replication_record"}},"created_at":"2026-07-04T15:17:09.391999+00:00","updated_at":"2026-07-04T15:17:09.391999+00:00"}