{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:2EABKKC32HHFKN3GONFAB4QQUC","short_pith_number":"pith:2EABKKC3","schema_version":"1.0","canonical_sha256":"d10015285bd1ce553766734a00f210a0ab94c7616401990d93205678ffd8f532","source":{"kind":"arxiv","id":"0806.4600","version":2},"attestation_state":"computed","paper":{"title":"Direct Extraction Of One Loop Rational Terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"S. D. Badger","submitted_at":"2008-06-27T19:41:48Z","abstract_excerpt":"We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. We use generalised unitarity in $D=4-2\\e$ dimensions to write the loop amplitudes in terms of products of massive tree amplitudes. We find that the rational terms in $4-2\\e$ dimensions can be determined from quadruple, triple and double cuts without the need for independent pentagon contributions using a massive integral basis. The additional mass-dependent integral coefficients may then be extracted from the large mass limit which"},"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":"0806.4600","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2008-06-27T19:41:48Z","cross_cats_sorted":[],"title_canon_sha256":"073c0fcac1c57a283040a45592ef4ac122b0a452569955e8fa9b6b8825d5af6e","abstract_canon_sha256":"1361c6971dd0feb147d8ac201dc1e5172e9d5ad219bc991fc599c9b49fbcd489"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:36:52.132784Z","signature_b64":"OB1NMMFPL+vTSdjfoiO7DFOIEdcySD+1dAuH6mpvTQk6tibd1E6tOrhjjYcHhNCeLdNI2+6MjdV/KwgSykcZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d10015285bd1ce553766734a00f210a0ab94c7616401990d93205678ffd8f532","last_reissued_at":"2026-07-04T15:36:52.132396Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:36:52.132396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Direct Extraction Of One Loop Rational Terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"S. D. Badger","submitted_at":"2008-06-27T19:41:48Z","abstract_excerpt":"We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. We use generalised unitarity in $D=4-2\\e$ dimensions to write the loop amplitudes in terms of products of massive tree amplitudes. We find that the rational terms in $4-2\\e$ dimensions can be determined from quadruple, triple and double cuts without the need for independent pentagon contributions using a massive integral basis. The additional mass-dependent integral coefficients may then be extracted from the large mass limit which"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4600","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/0806.4600/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":"0806.4600","created_at":"2026-07-04T15:36:52.132458+00:00"},{"alias_kind":"arxiv_version","alias_value":"0806.4600v2","created_at":"2026-07-04T15:36:52.132458+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4600","created_at":"2026-07-04T15:36:52.132458+00:00"},{"alias_kind":"pith_short_12","alias_value":"2EABKKC32HHF","created_at":"2026-07-04T15:36:52.132458+00:00"},{"alias_kind":"pith_short_16","alias_value":"2EABKKC32HHFKN3G","created_at":"2026-07-04T15:36:52.132458+00:00"},{"alias_kind":"pith_short_8","alias_value":"2EABKKC3","created_at":"2026-07-04T15:36:52.132458+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.15755","citing_title":"Negative running of gravitational positivity","ref_index":99,"is_internal_anchor":true},{"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":167,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2EABKKC32HHFKN3GONFAB4QQUC","json":"https://pith.science/pith/2EABKKC32HHFKN3GONFAB4QQUC.json","graph_json":"https://pith.science/api/pith-number/2EABKKC32HHFKN3GONFAB4QQUC/graph.json","events_json":"https://pith.science/api/pith-number/2EABKKC32HHFKN3GONFAB4QQUC/events.json","paper":"https://pith.science/paper/2EABKKC3"},"agent_actions":{"view_html":"https://pith.science/pith/2EABKKC32HHFKN3GONFAB4QQUC","download_json":"https://pith.science/pith/2EABKKC32HHFKN3GONFAB4QQUC.json","view_paper":"https://pith.science/paper/2EABKKC3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0806.4600&json=true","fetch_graph":"https://pith.science/api/pith-number/2EABKKC32HHFKN3GONFAB4QQUC/graph.json","fetch_events":"https://pith.science/api/pith-number/2EABKKC32HHFKN3GONFAB4QQUC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2EABKKC32HHFKN3GONFAB4QQUC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2EABKKC32HHFKN3GONFAB4QQUC/action/storage_attestation","attest_author":"https://pith.science/pith/2EABKKC32HHFKN3GONFAB4QQUC/action/author_attestation","sign_citation":"https://pith.science/pith/2EABKKC32HHFKN3GONFAB4QQUC/action/citation_signature","submit_replication":"https://pith.science/pith/2EABKKC32HHFKN3GONFAB4QQUC/action/replication_record"}},"created_at":"2026-07-04T15:36:52.132458+00:00","updated_at":"2026-07-04T15:36:52.132458+00:00"}