{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6GYQ6XLDDTWRKLS44YRLXC7KGB","short_pith_number":"pith:6GYQ6XLD","schema_version":"1.0","canonical_sha256":"f1b10f5d631ced152e5ce622bb8bea3075d1a4c2cb41a12cc757f693180f2f7f","source":{"kind":"arxiv","id":"1802.03384","version":2},"attestation_state":"computed","paper":{"title":"Biadjoint scalar tree amplitudes and intersecting dual associahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Hadleigh Frost","submitted_at":"2018-02-09T18:46:36Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.03384","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-02-09T18:46:36Z","cross_cats_sorted":[],"title_canon_sha256":"79b77e1bcec7d7edcf44c5925ab25b98f103447956e530aaad632b25042e2919","abstract_canon_sha256":"982cb05a15236a46c9a19bb533823c0597a0ed496da7d122a786bb5c7ac6e51a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:27.136122Z","signature_b64":"1dX36ULvnFdsxecthOanJ2bU/5HGVi3bthtKp9OixD4BCGgCszxXfU4be18mhzzqh79z8L/sc1wsaFyRK+5VAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1b10f5d631ced152e5ce622bb8bea3075d1a4c2cb41a12cc757f693180f2f7f","last_reissued_at":"2026-05-18T00:09:27.135641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:27.135641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biadjoint scalar tree amplitudes and intersecting dual associahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Hadleigh Frost","submitted_at":"2018-02-09T18:46:36Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03384","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1802.03384","created_at":"2026-05-18T00:09:27.135718+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.03384v2","created_at":"2026-05-18T00:09:27.135718+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03384","created_at":"2026-05-18T00:09:27.135718+00:00"},{"alias_kind":"pith_short_12","alias_value":"6GYQ6XLDDTWR","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"6GYQ6XLDDTWRKLS4","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"6GYQ6XLD","created_at":"2026-05-18T12:32:08.215937+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1909.02517","citing_title":"Cosmological Polytopes and the Wavefuncton of the Universe for Light States","ref_index":40,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6GYQ6XLDDTWRKLS44YRLXC7KGB","json":"https://pith.science/pith/6GYQ6XLDDTWRKLS44YRLXC7KGB.json","graph_json":"https://pith.science/api/pith-number/6GYQ6XLDDTWRKLS44YRLXC7KGB/graph.json","events_json":"https://pith.science/api/pith-number/6GYQ6XLDDTWRKLS44YRLXC7KGB/events.json","paper":"https://pith.science/paper/6GYQ6XLD"},"agent_actions":{"view_html":"https://pith.science/pith/6GYQ6XLDDTWRKLS44YRLXC7KGB","download_json":"https://pith.science/pith/6GYQ6XLDDTWRKLS44YRLXC7KGB.json","view_paper":"https://pith.science/paper/6GYQ6XLD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.03384&json=true","fetch_graph":"https://pith.science/api/pith-number/6GYQ6XLDDTWRKLS44YRLXC7KGB/graph.json","fetch_events":"https://pith.science/api/pith-number/6GYQ6XLDDTWRKLS44YRLXC7KGB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6GYQ6XLDDTWRKLS44YRLXC7KGB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6GYQ6XLDDTWRKLS44YRLXC7KGB/action/storage_attestation","attest_author":"https://pith.science/pith/6GYQ6XLDDTWRKLS44YRLXC7KGB/action/author_attestation","sign_citation":"https://pith.science/pith/6GYQ6XLDDTWRKLS44YRLXC7KGB/action/citation_signature","submit_replication":"https://pith.science/pith/6GYQ6XLDDTWRKLS44YRLXC7KGB/action/replication_record"}},"created_at":"2026-05-18T00:09:27.135718+00:00","updated_at":"2026-05-18T00:09:27.135718+00:00"}