{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CIZ46YYOJRMPOBQCBPCD7VQPYL","short_pith_number":"pith:CIZ46YYO","schema_version":"1.0","canonical_sha256":"1233cf630e4c58f706020bc43fd60fc2f9f51d3a403d4a87a78b3912a32a7e5b","source":{"kind":"arxiv","id":"1402.7374","version":1},"attestation_state":"computed","paper":{"title":"The Polynomial Form of the Scattering Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Louise Dolan, Peter Goddard","submitted_at":"2014-02-28T20:54:04Z","abstract_excerpt":"The scattering equations, recently proposed by Cachazo, He and Yuan as providing a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension (including scalars, gauge bosons and gravitons), are reformulated in polynomial form. The scattering equations for $N$ particles are shown to be equivalent to a Moebius invariant system of $N-3$ equations, $\\tilde h_m=0$, $2 \\leq m \\leq N-2$, in $N$ variables, where $\\tilde h_m$ is a homogeneous polynomial of degree m, with the exceptional property of being linear in each variable taken separately. Fixing the "},"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":"1402.7374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-02-28T20:54:04Z","cross_cats_sorted":[],"title_canon_sha256":"2c255bcee4ab78c567da38edad92e6992edebc9503353c48b7912cf850bf8572","abstract_canon_sha256":"ef556a092ca74c0f04a8a28a86b6e4e9975fb4a7b5a30c0c36acc9f3a7e9c2cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:21.700120Z","signature_b64":"VVD58esrGASdsO4Ixit3i+4JgKIvvG1tMI1T54OZM8FtGKABVS+9dg4h6pWezmdUbNUpU0P3SsVxnusjJTqvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1233cf630e4c58f706020bc43fd60fc2f9f51d3a403d4a87a78b3912a32a7e5b","last_reissued_at":"2026-05-18T01:44:21.699556Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:21.699556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Polynomial Form of the Scattering Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Louise Dolan, Peter Goddard","submitted_at":"2014-02-28T20:54:04Z","abstract_excerpt":"The scattering equations, recently proposed by Cachazo, He and Yuan as providing a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension (including scalars, gauge bosons and gravitons), are reformulated in polynomial form. The scattering equations for $N$ particles are shown to be equivalent to a Moebius invariant system of $N-3$ equations, $\\tilde h_m=0$, $2 \\leq m \\leq N-2$, in $N$ variables, where $\\tilde h_m$ is a homogeneous polynomial of degree m, with the exceptional property of being linear in each variable taken separately. Fixing the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7374","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":"1402.7374","created_at":"2026-05-18T01:44:21.699658+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.7374v1","created_at":"2026-05-18T01:44:21.699658+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.7374","created_at":"2026-05-18T01:44:21.699658+00:00"},{"alias_kind":"pith_short_12","alias_value":"CIZ46YYOJRMP","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CIZ46YYOJRMPOBQC","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CIZ46YYO","created_at":"2026-05-18T12:28:22.404517+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/CIZ46YYOJRMPOBQCBPCD7VQPYL","json":"https://pith.science/pith/CIZ46YYOJRMPOBQCBPCD7VQPYL.json","graph_json":"https://pith.science/api/pith-number/CIZ46YYOJRMPOBQCBPCD7VQPYL/graph.json","events_json":"https://pith.science/api/pith-number/CIZ46YYOJRMPOBQCBPCD7VQPYL/events.json","paper":"https://pith.science/paper/CIZ46YYO"},"agent_actions":{"view_html":"https://pith.science/pith/CIZ46YYOJRMPOBQCBPCD7VQPYL","download_json":"https://pith.science/pith/CIZ46YYOJRMPOBQCBPCD7VQPYL.json","view_paper":"https://pith.science/paper/CIZ46YYO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.7374&json=true","fetch_graph":"https://pith.science/api/pith-number/CIZ46YYOJRMPOBQCBPCD7VQPYL/graph.json","fetch_events":"https://pith.science/api/pith-number/CIZ46YYOJRMPOBQCBPCD7VQPYL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CIZ46YYOJRMPOBQCBPCD7VQPYL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CIZ46YYOJRMPOBQCBPCD7VQPYL/action/storage_attestation","attest_author":"https://pith.science/pith/CIZ46YYOJRMPOBQCBPCD7VQPYL/action/author_attestation","sign_citation":"https://pith.science/pith/CIZ46YYOJRMPOBQCBPCD7VQPYL/action/citation_signature","submit_replication":"https://pith.science/pith/CIZ46YYOJRMPOBQCBPCD7VQPYL/action/replication_record"}},"created_at":"2026-05-18T01:44:21.699658+00:00","updated_at":"2026-05-18T01:44:21.699658+00:00"}