{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RQQZTEZY74BRAZZZSQDM72VDS2","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":"99e56cd78df13741a4bba8b4e922b3ff3b449a63b423ce96efcf6234ec09775a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-12T19:22:18Z","title_canon_sha256":"5361e585ee6d5782180b790636643ce59e3078d560ad51d8771c6f90e26f2b87"},"schema_version":"1.0","source":{"id":"1411.3289","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3289","created_at":"2026-05-18T01:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3289v2","created_at":"2026-05-18T01:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3289","created_at":"2026-05-18T01:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"RQQZTEZY74BR","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RQQZTEZY74BRAZZZ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RQQZTEZY","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:014ef2656e67c003e610c639d93623d7836f2cfd018307c65b0e3d87652470f7","target":"graph","created_at":"2026-05-18T01:41:31Z","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 apply a bootstrap procedure to two-loop MHV amplitudes in planar N=4 super-Yang-Mills theory. We argue that the mathematically most complicated part (the $\\Lambda^2 B_2$ coproduct component) of the n-particle amplitude is uniquely determined by a simple cluster algebra property together with a few physical constraints (dihedral symmetry, analytic structure, supersymmetry, and well-defined collinear limits). We present a concise, closed-form expression which manifests these properties for all n.","authors_text":"John Golden, Marcus Spradlin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-12T19:22:18Z","title":"A Cluster Bootstrap for Two-Loop MHV Amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3289","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":"sha256:81386fe76b4669e7eca1b28fa54acb541f9b368b86be114925acbf41e8ab09ca","target":"record","created_at":"2026-05-18T01:41:31Z","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":"99e56cd78df13741a4bba8b4e922b3ff3b449a63b423ce96efcf6234ec09775a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-12T19:22:18Z","title_canon_sha256":"5361e585ee6d5782180b790636643ce59e3078d560ad51d8771c6f90e26f2b87"},"schema_version":"1.0","source":{"id":"1411.3289","kind":"arxiv","version":2}},"canonical_sha256":"8c21999338ff031067399406cfeaa3968a94e3ab2bc39083436e3c3cf3132815","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c21999338ff031067399406cfeaa3968a94e3ab2bc39083436e3c3cf3132815","first_computed_at":"2026-05-18T01:41:31.143612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:31.143612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fiaa0FYDX2KqzZauNcMq5HwmbojuLFzFio3wI2OaZETPda3ZIFIX9RdCJqU/QVst3YTHSjgULbJGbw6i5kTXDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:31.144308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3289","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81386fe76b4669e7eca1b28fa54acb541f9b368b86be114925acbf41e8ab09ca","sha256:014ef2656e67c003e610c639d93623d7836f2cfd018307c65b0e3d87652470f7"],"state_sha256":"d08d233bbc3ba61fb1e9d0751312a002aaa7812390e5c018dc9f5adce8797e21"}