{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:UH3X4A3XQH2AYVHUYIYYAXH47C","short_pith_number":"pith:UH3X4A3X","schema_version":"1.0","canonical_sha256":"a1f77e037781f40c54f4c231805cfcf891842e481842d5fa8a6cf4aac5d89a38","source":{"kind":"arxiv","id":"2005.03638","version":2},"attestation_state":"computed","paper":{"title":"Efficient Calculation of Crossing Symmetric BCJ Tree Numerators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alex Edison, Fei Teng","submitted_at":"2020-05-07T17:41:38Z","abstract_excerpt":"In this paper, we propose an improved method for directly calculating double-copy-compatible tree numerators in (super-)Yang-Mills and Yang-Mills-scalar theories. Our new scheme gets rid of any explicit dependence on reference orderings, restoring a form of crossing symmetry to the numerators. This in turn improves the computational efficiency of the algorithm, allowing us to go well beyond the number of external particles accessible with the reference order based methods. Motivated by a parallel study of one-loop BCJ numerators from forward limits, we explore the generalization to include a p"},"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":"2005.03638","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-05-07T17:41:38Z","cross_cats_sorted":[],"title_canon_sha256":"16e6410cf2c67f336a2928a3bf23a7bc7e6eee8ec3029ee28e708932e964b57e","abstract_canon_sha256":"b3c25e8b79487936dcc0993497c8aba82ba1a52f293298e361bcd240d7d86a63"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:01:11.835928Z","signature_b64":"diQuHA9nlvq1L+7XjxZt0bwIWUvgFpNpxQ2Xi9uNfxSmx2tsR23wsZo9fA9Gdw+vdEYvv3WXQxX+KI1QsPUMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1f77e037781f40c54f4c231805cfcf891842e481842d5fa8a6cf4aac5d89a38","last_reissued_at":"2026-07-05T02:01:11.835409Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:01:11.835409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient Calculation of Crossing Symmetric BCJ Tree Numerators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alex Edison, Fei Teng","submitted_at":"2020-05-07T17:41:38Z","abstract_excerpt":"In this paper, we propose an improved method for directly calculating double-copy-compatible tree numerators in (super-)Yang-Mills and Yang-Mills-scalar theories. Our new scheme gets rid of any explicit dependence on reference orderings, restoring a form of crossing symmetry to the numerators. This in turn improves the computational efficiency of the algorithm, allowing us to go well beyond the number of external particles accessible with the reference order based methods. Motivated by a parallel study of one-loop BCJ numerators from forward limits, we explore the generalization to include a p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.03638","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2005.03638/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":"2005.03638","created_at":"2026-07-05T02:01:11.835477+00:00"},{"alias_kind":"arxiv_version","alias_value":"2005.03638v2","created_at":"2026-07-05T02:01:11.835477+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.03638","created_at":"2026-07-05T02:01:11.835477+00:00"},{"alias_kind":"pith_short_12","alias_value":"UH3X4A3XQH2A","created_at":"2026-07-05T02:01:11.835477+00:00"},{"alias_kind":"pith_short_16","alias_value":"UH3X4A3XQH2AYVHU","created_at":"2026-07-05T02:01:11.835477+00:00"},{"alias_kind":"pith_short_8","alias_value":"UH3X4A3X","created_at":"2026-07-05T02:01:11.835477+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2607.01790","citing_title":"Uniqueness and Analytic Structures of Bosonic String Effective Amplitudes","ref_index":48,"is_internal_anchor":false},{"citing_arxiv_id":"2511.05441","citing_title":"$D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions","ref_index":42,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UH3X4A3XQH2AYVHUYIYYAXH47C","json":"https://pith.science/pith/UH3X4A3XQH2AYVHUYIYYAXH47C.json","graph_json":"https://pith.science/api/pith-number/UH3X4A3XQH2AYVHUYIYYAXH47C/graph.json","events_json":"https://pith.science/api/pith-number/UH3X4A3XQH2AYVHUYIYYAXH47C/events.json","paper":"https://pith.science/paper/UH3X4A3X"},"agent_actions":{"view_html":"https://pith.science/pith/UH3X4A3XQH2AYVHUYIYYAXH47C","download_json":"https://pith.science/pith/UH3X4A3XQH2AYVHUYIYYAXH47C.json","view_paper":"https://pith.science/paper/UH3X4A3X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2005.03638&json=true","fetch_graph":"https://pith.science/api/pith-number/UH3X4A3XQH2AYVHUYIYYAXH47C/graph.json","fetch_events":"https://pith.science/api/pith-number/UH3X4A3XQH2AYVHUYIYYAXH47C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UH3X4A3XQH2AYVHUYIYYAXH47C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UH3X4A3XQH2AYVHUYIYYAXH47C/action/storage_attestation","attest_author":"https://pith.science/pith/UH3X4A3XQH2AYVHUYIYYAXH47C/action/author_attestation","sign_citation":"https://pith.science/pith/UH3X4A3XQH2AYVHUYIYYAXH47C/action/citation_signature","submit_replication":"https://pith.science/pith/UH3X4A3XQH2AYVHUYIYYAXH47C/action/replication_record"}},"created_at":"2026-07-05T02:01:11.835477+00:00","updated_at":"2026-07-05T02:01:11.835477+00:00"}