{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GCJDNZ63BCEKWWY7OC2FFZHYTU","short_pith_number":"pith:GCJDNZ63","schema_version":"1.0","canonical_sha256":"309236e7db0888ab5b1f70b452e4f89d3798242682d1310f1e6b86b6789fc8a7","source":{"kind":"arxiv","id":"1506.06137","version":1},"attestation_state":"computed","paper":{"title":"Integration Rules for Scattering Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Christian Baadsgaard, Jacob L. Bourjaily, N. E. J. Bjerrum-Bohr, Poul H. Damgaard","submitted_at":"2015-06-19T20:00:27Z","abstract_excerpt":"As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any M\\\"obius-invariant integrand involving only simple poles. These rules have a si"},"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":"1506.06137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-06-19T20:00:27Z","cross_cats_sorted":[],"title_canon_sha256":"22a3cc7b4dc1aa31b5f0f2d73da36b93234aa8630ff39a6796d714715f18efae","abstract_canon_sha256":"8f93b51f3535cb7e0ec6d7b62438e8bb4d9bdabdab3ec81e716a9917f3df06e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:54.785704Z","signature_b64":"2NJ8ZEer6kqv1/SYy23CvonwXAWApvDTRpebjt3bILfOv7jvWlTT4lxNdweRisMAPXgbBlDLAp8LvSn8vOMBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"309236e7db0888ab5b1f70b452e4f89d3798242682d1310f1e6b86b6789fc8a7","last_reissued_at":"2026-05-18T01:28:54.785131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:54.785131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integration Rules for Scattering Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Christian Baadsgaard, Jacob L. Bourjaily, N. E. J. Bjerrum-Bohr, Poul H. Damgaard","submitted_at":"2015-06-19T20:00:27Z","abstract_excerpt":"As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any M\\\"obius-invariant integrand involving only simple poles. These rules have a si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06137","kind":"arxiv","version":1},"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":"1506.06137","created_at":"2026-05-18T01:28:54.785216+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.06137v1","created_at":"2026-05-18T01:28:54.785216+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06137","created_at":"2026-05-18T01:28:54.785216+00:00"},{"alias_kind":"pith_short_12","alias_value":"GCJDNZ63BCEK","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GCJDNZ63BCEKWWY7","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GCJDNZ63","created_at":"2026-05-18T12:29:22.688609+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.14523","citing_title":"HEFT Numerators from Kinematic Algebra","ref_index":68,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GCJDNZ63BCEKWWY7OC2FFZHYTU","json":"https://pith.science/pith/GCJDNZ63BCEKWWY7OC2FFZHYTU.json","graph_json":"https://pith.science/api/pith-number/GCJDNZ63BCEKWWY7OC2FFZHYTU/graph.json","events_json":"https://pith.science/api/pith-number/GCJDNZ63BCEKWWY7OC2FFZHYTU/events.json","paper":"https://pith.science/paper/GCJDNZ63"},"agent_actions":{"view_html":"https://pith.science/pith/GCJDNZ63BCEKWWY7OC2FFZHYTU","download_json":"https://pith.science/pith/GCJDNZ63BCEKWWY7OC2FFZHYTU.json","view_paper":"https://pith.science/paper/GCJDNZ63","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.06137&json=true","fetch_graph":"https://pith.science/api/pith-number/GCJDNZ63BCEKWWY7OC2FFZHYTU/graph.json","fetch_events":"https://pith.science/api/pith-number/GCJDNZ63BCEKWWY7OC2FFZHYTU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GCJDNZ63BCEKWWY7OC2FFZHYTU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GCJDNZ63BCEKWWY7OC2FFZHYTU/action/storage_attestation","attest_author":"https://pith.science/pith/GCJDNZ63BCEKWWY7OC2FFZHYTU/action/author_attestation","sign_citation":"https://pith.science/pith/GCJDNZ63BCEKWWY7OC2FFZHYTU/action/citation_signature","submit_replication":"https://pith.science/pith/GCJDNZ63BCEKWWY7OC2FFZHYTU/action/replication_record"}},"created_at":"2026-05-18T01:28:54.785216+00:00","updated_at":"2026-05-18T01:28:54.785216+00:00"}