{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6GYQ6XLDDTWRKLS44YRLXC7KGB","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":"982cb05a15236a46c9a19bb533823c0597a0ed496da7d122a786bb5c7ac6e51a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-02-09T18:46:36Z","title_canon_sha256":"79b77e1bcec7d7edcf44c5925ab25b98f103447956e530aaad632b25042e2919"},"schema_version":"1.0","source":{"id":"1802.03384","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03384","created_at":"2026-05-18T00:09:27Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03384v2","created_at":"2026-05-18T00:09:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03384","created_at":"2026-05-18T00:09:27Z"},{"alias_kind":"pith_short_12","alias_value":"6GYQ6XLDDTWR","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6GYQ6XLDDTWRKLS4","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6GYQ6XLD","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:83e7d4547127bec4d627b50b42866bfa802262e0f9e5d09db67123ad0958874e","target":"graph","created_at":"2026-05-18T00:09:27Z","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 present a new formula for the biadjoint scalar tree amplitudes $m(\\alpha|\\beta)$ based on the combinatorics of dual associahedra. Our construction makes essential use of the cones in 'kinematic space' introduced by Arkani-Hamed, Bai, He, and Yan. We then consider dual associahedra in 'dual kinematic space.' If appropriately embedded, the intersections of these dual associahedra encode the amplitudes $m(\\alpha|\\beta)$. In fact, we encode all the partial amplitudes at $n$-points using a single object (a fan) in dual kinematic space. Equivalently, as a pleasant corollary of our construction, a","authors_text":"Hadleigh Frost","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-02-09T18:46:36Z","title":"Biadjoint scalar tree amplitudes and intersecting dual associahedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03384","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":"sha256:90bba5caf30e63c132effb03207dde537f7dee58fde5e401524083c40cffc7b9","target":"record","created_at":"2026-05-18T00:09:27Z","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":"982cb05a15236a46c9a19bb533823c0597a0ed496da7d122a786bb5c7ac6e51a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-02-09T18:46:36Z","title_canon_sha256":"79b77e1bcec7d7edcf44c5925ab25b98f103447956e530aaad632b25042e2919"},"schema_version":"1.0","source":{"id":"1802.03384","kind":"arxiv","version":2}},"canonical_sha256":"f1b10f5d631ced152e5ce622bb8bea3075d1a4c2cb41a12cc757f693180f2f7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1b10f5d631ced152e5ce622bb8bea3075d1a4c2cb41a12cc757f693180f2f7f","first_computed_at":"2026-05-18T00:09:27.135641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:27.135641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1dX36ULvnFdsxecthOanJ2bU/5HGVi3bthtKp9OixD4BCGgCszxXfU4be18mhzzqh79z8L/sc1wsaFyRK+5VAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:27.136122Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03384","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90bba5caf30e63c132effb03207dde537f7dee58fde5e401524083c40cffc7b9","sha256:83e7d4547127bec4d627b50b42866bfa802262e0f9e5d09db67123ad0958874e"],"state_sha256":"976657de56ab2a2c195c323e95d49ea129950ac4c709409d0184156f62918855"}