{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZKEVQRJFAGO6UTO7XMLC5XHLBE","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":"ac90f828f77013db5cae3bccee910da504eb8b6bd6840a38b4acd21c6e7f0140","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-31T20:00:01Z","title_canon_sha256":"1038316c65faab630dc1c3399ee4b4ea3e2aaa2bd1a410e6d714b2ef78a95c93"},"schema_version":"1.0","source":{"id":"1609.00008","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00008","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00008v2","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00008","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZKEVQRJFAGO6","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZKEVQRJFAGO6UTO7","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZKEVQRJF","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:50491fbc99e5e3e4297843a9860d666cd302beeeda4ed3c5eec0612ec6ced82e","target":"graph","created_at":"2026-05-18T00:47:26Z","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":"We find $n(n-3)/2$-dimensional regions of the space of kinematic invariants, where all the solutions to the scattering equations (the core of the CHY formulation of amplitudes) for $n$ massless particles are real. On these regions, the scattering equations are equivalent to the problem of finding stationary points of $n-3$ mutually repelling particles on a finite real interval with appropriate boundary conditions. This identification directly implies that for each of the $(n-3)!$ possible orderings of the $n-3$ particles on the interval, there exists one stable stationary point. Furthermore, r","authors_text":"Freddy Cachazo, Guojun Zhang, Sebastian Mizera","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-31T20:00:01Z","title":"Scattering Equations: Real Solutions and Particles on a Line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00008","kind":"arxiv","version":2},"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:c389136e70fa95f3302bcc57d22830c0179afcdbba01c800a6defb3c1f8375bf","target":"record","created_at":"2026-05-18T00:47:26Z","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":"ac90f828f77013db5cae3bccee910da504eb8b6bd6840a38b4acd21c6e7f0140","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-31T20:00:01Z","title_canon_sha256":"1038316c65faab630dc1c3399ee4b4ea3e2aaa2bd1a410e6d714b2ef78a95c93"},"schema_version":"1.0","source":{"id":"1609.00008","kind":"arxiv","version":2}},"canonical_sha256":"ca89584525019dea4ddfbb162edceb0911e46f777e30b25d8061489c66cbddd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca89584525019dea4ddfbb162edceb0911e46f777e30b25d8061489c66cbddd6","first_computed_at":"2026-05-18T00:47:26.829420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:26.829420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5bKQW75qMlHRgomOk3ZCOw+w0OGzAMns/y1kh+RJQOgnysGKpOr6IAHIBUY+iLaX+RMDGhuttUtAINaQuFT0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:26.830253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00008","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c389136e70fa95f3302bcc57d22830c0179afcdbba01c800a6defb3c1f8375bf","sha256:50491fbc99e5e3e4297843a9860d666cd302beeeda4ed3c5eec0612ec6ced82e"],"state_sha256":"a32d8814d2b10e2d60b196f6b490478c5c760cc4bfc7e78fc9f6b6486e7eae2d"}