{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T2U47UXWFVFWZO5X3SKVMLWKHV","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":"1581a857a2e5c028db73285692c7cbf54de36ae718dd1fa7468fdedfe42b90be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-10-25T13:19:18Z","title_canon_sha256":"68a2de2082b9aeaf171b682a562c987fbce85154c483c5e54802f7e7741b1954"},"schema_version":"1.0","source":{"id":"1310.6906","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6906","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6906v3","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6906","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"pith_short_12","alias_value":"T2U47UXWFVFW","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T2U47UXWFVFWZO5X","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T2U47UXW","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:1ded11d00a40f3ea85bec56bd9f11f6505bb68614293e8bdde0e641bfc8fc2b5","target":"graph","created_at":"2026-05-18T03:00:51Z","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 study the cluster algebra of the kinematic configuration space $Conf_n(\\mathbb{P}^3)$ of a n-particle scattering amplitude restricted to the special 2D kinematics. We found that the n-points two loop MHV remainder function found in special 2D kinematics depend on a selection of \\XX-coordinates that are part of a special structure of the cluster algebra related to snake triangulations of polygons. This structure forms a necklace of hypercubes beads in the corresponding Stasheff polytope. Furthermore in $n = 12$, the cluster algebra and the selection of \\XX-coordinates in special 2D kinematic","authors_text":"Marcus A. C. Torres","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-10-25T13:19:18Z","title":"Cluster algebras in scattering amplitudes with special 2D kinematics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6906","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":"sha256:34cafd8909661634584d96590a6745baa71013d503a27723f6ce2ade9dffa960","target":"record","created_at":"2026-05-18T03:00:51Z","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":"1581a857a2e5c028db73285692c7cbf54de36ae718dd1fa7468fdedfe42b90be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-10-25T13:19:18Z","title_canon_sha256":"68a2de2082b9aeaf171b682a562c987fbce85154c483c5e54802f7e7741b1954"},"schema_version":"1.0","source":{"id":"1310.6906","kind":"arxiv","version":3}},"canonical_sha256":"9ea9cfd2f62d4b6cbbb7dc95562eca3d6a4aa1b2fbfd251e93dfeab333e4b86f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ea9cfd2f62d4b6cbbb7dc95562eca3d6a4aa1b2fbfd251e93dfeab333e4b86f","first_computed_at":"2026-05-18T03:00:51.372969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:51.372969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gqN5lYaob12+Psc123Cy3CVYjRzdGRYSIsT1ACdBAerKMDv0mtYa3H4H2xHTsnWyDaQujz1GIxhaQ8gz75TpAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:51.373561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6906","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34cafd8909661634584d96590a6745baa71013d503a27723f6ce2ade9dffa960","sha256:1ded11d00a40f3ea85bec56bd9f11f6505bb68614293e8bdde0e641bfc8fc2b5"],"state_sha256":"04f542c52f6c19c1671d79aaea4df499b6bd1ac5b025b4c0ee91a51a6f8b2f4f"}