{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GCJDNZ63BCEKWWY7OC2FFZHYTU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8f93b51f3535cb7e0ec6d7b62438e8bb4d9bdabdab3ec81e716a9917f3df06e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-06-19T20:00:27Z","title_canon_sha256":"22a3cc7b4dc1aa31b5f0f2d73da36b93234aa8630ff39a6796d714715f18efae"},"schema_version":"1.0","source":{"id":"1506.06137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06137","created_at":"2026-05-18T01:28:54Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06137v1","created_at":"2026-05-18T01:28:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06137","created_at":"2026-05-18T01:28:54Z"},{"alias_kind":"pith_short_12","alias_value":"GCJDNZ63BCEK","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GCJDNZ63BCEKWWY7","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GCJDNZ63","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:2d0a44812d9ad97d2ff5dcacd2befa859008895d0255d7547bc01e260d9bdccf","target":"graph","created_at":"2026-05-18T01:28:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Christian Baadsgaard, Jacob L. Bourjaily, N. E. J. Bjerrum-Bohr, Poul H. Damgaard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-06-19T20:00:27Z","title":"Integration Rules for Scattering Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06137","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:105a330601285706a6ca9a38df833a5c40e93b21b72dbbe456b38bff7df66a24","target":"record","created_at":"2026-05-18T01:28:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8f93b51f3535cb7e0ec6d7b62438e8bb4d9bdabdab3ec81e716a9917f3df06e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-06-19T20:00:27Z","title_canon_sha256":"22a3cc7b4dc1aa31b5f0f2d73da36b93234aa8630ff39a6796d714715f18efae"},"schema_version":"1.0","source":{"id":"1506.06137","kind":"arxiv","version":1}},"canonical_sha256":"309236e7db0888ab5b1f70b452e4f89d3798242682d1310f1e6b86b6789fc8a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"309236e7db0888ab5b1f70b452e4f89d3798242682d1310f1e6b86b6789fc8a7","first_computed_at":"2026-05-18T01:28:54.785131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:54.785131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2NJ8ZEer6kqv1/SYy23CvonwXAWApvDTRpebjt3bILfOv7jvWlTT4lxNdweRisMAPXgbBlDLAp8LvSn8vOMBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:54.785704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:105a330601285706a6ca9a38df833a5c40e93b21b72dbbe456b38bff7df66a24","sha256:2d0a44812d9ad97d2ff5dcacd2befa859008895d0255d7547bc01e260d9bdccf"],"state_sha256":"c493f2eecfbaf8d0ac876b09af2e73b55f7be3a95e4e07688a9eb886dc6a664b"}