{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VVRNLDQE2EALBICQYHQIC46KYY","short_pith_number":"pith:VVRNLDQE","schema_version":"1.0","canonical_sha256":"ad62d58e04d100b0a050c1e08173cac61f39c6ab1d687392166f745d7b3eb4f5","source":{"kind":"arxiv","id":"2504.01217","version":1},"attestation_state":"computed","paper":{"title":"BCFW tilings and cluster adjacency for the amplituhedron","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["hep-th","math-ph","math.AG","math.MP"],"primary_cat":"math.CO","authors_text":"Chaim Even-Zohar, Lauren Williams, Matteo Parisi, Melissa Sherman-Bennett, Ran Tessler, Tsviqa Lakrec","submitted_at":"2025-04-01T22:13:31Z","abstract_excerpt":"In 2005, Britto, Cachazo, Feng and Witten gave a recurrence (now known as the BCFW recurrence) for computing scattering amplitudes in N=4 super Yang Mills theory. Arkani-Hamed and Trnka subsequently introduced the amplituhedron to give a geometric interpretation of the BCFW recurrence. Arkani-Hamed and Trnka conjectured that each way of iterating the BCFW recurrence gives a \"triangulation\" or \"tiling\" of the m=4 amplituhedron. In this article we prove the BCFW tiling conjecture of Arkani-Hamed and Trnka. We also prove the cluster adjacency conjecture for BCFW tiles of the amplituhedron, which "},"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":"2504.01217","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-01T22:13:31Z","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"title_canon_sha256":"e4d176efc114b0a47f4043175a0282c5eb40fbc349ef87104f384a86d006a6fa","abstract_canon_sha256":"6601d400200513cbb586e9b3d9ed387bf9297f9d31b7a1cc66da30cb5f8520b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:45:20.223183Z","signature_b64":"0eLzkMsMPSeYYRVzzhL+Z7oclRvAqxzDP6DR/rNuvylpILqkNtQIoL5fb9GHGnZs9/k4Y2Dr8qMk495Ri7ccBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad62d58e04d100b0a050c1e08173cac61f39c6ab1d687392166f745d7b3eb4f5","last_reissued_at":"2026-07-05T10:45:20.222045Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:45:20.222045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"BCFW tilings and cluster adjacency for the amplituhedron","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["hep-th","math-ph","math.AG","math.MP"],"primary_cat":"math.CO","authors_text":"Chaim Even-Zohar, Lauren Williams, Matteo Parisi, Melissa Sherman-Bennett, Ran Tessler, Tsviqa Lakrec","submitted_at":"2025-04-01T22:13:31Z","abstract_excerpt":"In 2005, Britto, Cachazo, Feng and Witten gave a recurrence (now known as the BCFW recurrence) for computing scattering amplitudes in N=4 super Yang Mills theory. Arkani-Hamed and Trnka subsequently introduced the amplituhedron to give a geometric interpretation of the BCFW recurrence. Arkani-Hamed and Trnka conjectured that each way of iterating the BCFW recurrence gives a \"triangulation\" or \"tiling\" of the m=4 amplituhedron. In this article we prove the BCFW tiling conjecture of Arkani-Hamed and Trnka. We also prove the cluster adjacency conjecture for BCFW tiles of the amplituhedron, which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.01217","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.01217/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2504.01217","created_at":"2026-07-05T10:45:20.222114+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.01217v1","created_at":"2026-07-05T10:45:20.222114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.01217","created_at":"2026-07-05T10:45:20.222114+00:00"},{"alias_kind":"pith_short_12","alias_value":"VVRNLDQE2EAL","created_at":"2026-07-05T10:45:20.222114+00:00"},{"alias_kind":"pith_short_16","alias_value":"VVRNLDQE2EALBICQ","created_at":"2026-07-05T10:45:20.222114+00:00"},{"alias_kind":"pith_short_8","alias_value":"VVRNLDQE","created_at":"2026-07-05T10:45:20.222114+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.28926","citing_title":"Multi-Loop Negative Geometries","ref_index":57,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VVRNLDQE2EALBICQYHQIC46KYY","json":"https://pith.science/pith/VVRNLDQE2EALBICQYHQIC46KYY.json","graph_json":"https://pith.science/api/pith-number/VVRNLDQE2EALBICQYHQIC46KYY/graph.json","events_json":"https://pith.science/api/pith-number/VVRNLDQE2EALBICQYHQIC46KYY/events.json","paper":"https://pith.science/paper/VVRNLDQE"},"agent_actions":{"view_html":"https://pith.science/pith/VVRNLDQE2EALBICQYHQIC46KYY","download_json":"https://pith.science/pith/VVRNLDQE2EALBICQYHQIC46KYY.json","view_paper":"https://pith.science/paper/VVRNLDQE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.01217&json=true","fetch_graph":"https://pith.science/api/pith-number/VVRNLDQE2EALBICQYHQIC46KYY/graph.json","fetch_events":"https://pith.science/api/pith-number/VVRNLDQE2EALBICQYHQIC46KYY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VVRNLDQE2EALBICQYHQIC46KYY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VVRNLDQE2EALBICQYHQIC46KYY/action/storage_attestation","attest_author":"https://pith.science/pith/VVRNLDQE2EALBICQYHQIC46KYY/action/author_attestation","sign_citation":"https://pith.science/pith/VVRNLDQE2EALBICQYHQIC46KYY/action/citation_signature","submit_replication":"https://pith.science/pith/VVRNLDQE2EALBICQYHQIC46KYY/action/replication_record"}},"created_at":"2026-07-05T10:45:20.222114+00:00","updated_at":"2026-07-05T10:45:20.222114+00:00"}