{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MTQP5ZFAIGFNUIOUYOTNPQ6BVS","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":"9d3fe31c288f33bca06f903feddf0b7ba4f6065aad2f8b65a7d2e9b153531c39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-22T03:09:12Z","title_canon_sha256":"b04741a8163b598b1b23d8bbb5728f52868e01399e33586947181e84897509fe"},"schema_version":"1.0","source":{"id":"1608.06040","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06040","created_at":"2026-05-18T00:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06040v3","created_at":"2026-05-18T00:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06040","created_at":"2026-05-18T00:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"MTQP5ZFAIGFN","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTQP5ZFAIGFNUIOU","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTQP5ZFA","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:5ee900d4dcc92e34c1ef9ff20fc30ddd35ca710d03c00052a007ce5ca6b37213","target":"graph","created_at":"2026-05-18T00:58:03Z","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":"In this paper we define, independent of theories, two discriminant matrices involving a solution to the scattering equations in four dimensions, the ranks of which are used to divide the solution set into a disjoint union of subsets. We further demonstrate, {entirely within the Cachazo-He-Yuan formalism,} that each subset of solutions gives nonzero contribution to tree-level $\\text{N}^{k}\\text{MHV}$ gauge/gravity amplitudes only for a specific value of $k$. Thus the solutions can be characterized by the rank of their discriminant matrices, which in turn determines the value of $k$ of the $\\tex","authors_text":"Fei Teng, Yi-Jian Du, Yong-Shi Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-22T03:09:12Z","title":"Characterizing the solutions to scattering equations that support tree-level $\\text{N}^{k}\\text{MHV}$ gauge/gravity amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06040","kind":"arxiv","version":3},"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:b95ec42938f863d581566f228bcb7d62b806b6149d050370eb1cbbb97c14235b","target":"record","created_at":"2026-05-18T00:58:03Z","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":"9d3fe31c288f33bca06f903feddf0b7ba4f6065aad2f8b65a7d2e9b153531c39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-22T03:09:12Z","title_canon_sha256":"b04741a8163b598b1b23d8bbb5728f52868e01399e33586947181e84897509fe"},"schema_version":"1.0","source":{"id":"1608.06040","kind":"arxiv","version":3}},"canonical_sha256":"64e0fee4a0418ada21d4c3a6d7c3c1ac8634256f35a37a3e58d3c2b27cddea03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64e0fee4a0418ada21d4c3a6d7c3c1ac8634256f35a37a3e58d3c2b27cddea03","first_computed_at":"2026-05-18T00:58:03.841752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:03.841752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FjVMduOYaokoN/Nsbd6z4pzGlzDTSZgO1xJmHS0t26QzjAFFYyriOHJc+OyVpe2QEG0PQXlT4NbdfyYtRX1dCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:03.842342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06040","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b95ec42938f863d581566f228bcb7d62b806b6149d050370eb1cbbb97c14235b","sha256:5ee900d4dcc92e34c1ef9ff20fc30ddd35ca710d03c00052a007ce5ca6b37213"],"state_sha256":"d1449e4b37e31ec0b67e084fd0d2da15dc3a1a038889a50e56bf90855f77137d"}