{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:NDPM7R2WNCJKBCJDPDSJATQIGO","short_pith_number":"pith:NDPM7R2W","schema_version":"1.0","canonical_sha256":"68decfc7566892a0892378e4904e083389ca3e181fc080f9fb831e14fec34a2a","source":{"kind":"arxiv","id":"0912.3249","version":2},"attestation_state":"computed","paper":{"title":"Local Spacetime Physics from the Grassmannian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Freddy Cachazo, Jacob Bourjaily, Jaroslav Trnka, Nima Arkani-Hamed","submitted_at":"2009-12-17T20:53:37Z","abstract_excerpt":"A duality has recently been conjectured between all leading singularities of n-particle N^(k-2)MHV scattering amplitudes in N=4 SYM and the residues of a contour integral with a natural measure over the Grassmannian G(k,n). In this note we show that a simple contour deformation converts the sum of Grassmannian residues associated with the BCFW expansion of NMHV tree amplitudes to the CSW expansion of the same amplitude. We propose that for general k the same deformation yields the (k-2) parameter Risager expansion. We establish this equivalence for all MHV-bar amplitudes and show that the Risa"},"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":"0912.3249","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-12-17T20:53:37Z","cross_cats_sorted":[],"title_canon_sha256":"6ac33a79bca952b530d2c10af4933ad683815e804237f5d9e0b316f795de7ed7","abstract_canon_sha256":"875be258622fd10aba16f8252f058cbda65b004df575eb872c045a1beeb079ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:36.907889Z","signature_b64":"uAjY32gFB3aag4NhOMNejtouDlYf5pWi/Ko5pNpmXfULOeHXNPLFv+pdhqjDYP2PfNwLAUQCwbwUIeOLBxcoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68decfc7566892a0892378e4904e083389ca3e181fc080f9fb831e14fec34a2a","last_reissued_at":"2026-05-18T04:30:36.907221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:36.907221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Spacetime Physics from the Grassmannian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Freddy Cachazo, Jacob Bourjaily, Jaroslav Trnka, Nima Arkani-Hamed","submitted_at":"2009-12-17T20:53:37Z","abstract_excerpt":"A duality has recently been conjectured between all leading singularities of n-particle N^(k-2)MHV scattering amplitudes in N=4 SYM and the residues of a contour integral with a natural measure over the Grassmannian G(k,n). In this note we show that a simple contour deformation converts the sum of Grassmannian residues associated with the BCFW expansion of NMHV tree amplitudes to the CSW expansion of the same amplitude. We propose that for general k the same deformation yields the (k-2) parameter Risager expansion. We establish this equivalence for all MHV-bar amplitudes and show that the Risa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3249","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":""},"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":"0912.3249","created_at":"2026-05-18T04:30:36.907313+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.3249v2","created_at":"2026-05-18T04:30:36.907313+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3249","created_at":"2026-05-18T04:30:36.907313+00:00"},{"alias_kind":"pith_short_12","alias_value":"NDPM7R2WNCJK","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"NDPM7R2WNCJKBCJD","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"NDPM7R2W","created_at":"2026-05-18T12:26:00.592388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NDPM7R2WNCJKBCJDPDSJATQIGO","json":"https://pith.science/pith/NDPM7R2WNCJKBCJDPDSJATQIGO.json","graph_json":"https://pith.science/api/pith-number/NDPM7R2WNCJKBCJDPDSJATQIGO/graph.json","events_json":"https://pith.science/api/pith-number/NDPM7R2WNCJKBCJDPDSJATQIGO/events.json","paper":"https://pith.science/paper/NDPM7R2W"},"agent_actions":{"view_html":"https://pith.science/pith/NDPM7R2WNCJKBCJDPDSJATQIGO","download_json":"https://pith.science/pith/NDPM7R2WNCJKBCJDPDSJATQIGO.json","view_paper":"https://pith.science/paper/NDPM7R2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.3249&json=true","fetch_graph":"https://pith.science/api/pith-number/NDPM7R2WNCJKBCJDPDSJATQIGO/graph.json","fetch_events":"https://pith.science/api/pith-number/NDPM7R2WNCJKBCJDPDSJATQIGO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NDPM7R2WNCJKBCJDPDSJATQIGO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NDPM7R2WNCJKBCJDPDSJATQIGO/action/storage_attestation","attest_author":"https://pith.science/pith/NDPM7R2WNCJKBCJDPDSJATQIGO/action/author_attestation","sign_citation":"https://pith.science/pith/NDPM7R2WNCJKBCJDPDSJATQIGO/action/citation_signature","submit_replication":"https://pith.science/pith/NDPM7R2WNCJKBCJDPDSJATQIGO/action/replication_record"}},"created_at":"2026-05-18T04:30:36.907313+00:00","updated_at":"2026-05-18T04:30:36.907313+00:00"}