{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:E5AU4OHMWKLX2VXOGC33NJHP2P","short_pith_number":"pith:E5AU4OHM","schema_version":"1.0","canonical_sha256":"27414e38ecb2977d56ee30b7b6a4efd3ea2e6d3d86ae71f70d13b600a3de3477","source":{"kind":"arxiv","id":"hep-th/0501052","version":2},"attestation_state":"computed","paper":{"title":"Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Bo Feng, Edward Witten, Freddy Cachazo, Ruth Britto","submitted_at":"2005-01-07T20:04:03Z","abstract_excerpt":"Recently, by using the known structure of one-loop scattering amplitudes for gluons in Yang-Mills theory, a recursion relation for tree-level scattering amplitudes has been deduced. Here, we give a short and direct proof of this recursion relation based on properties of tree-level amplitudes only."},"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":"hep-th/0501052","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2005-01-07T20:04:03Z","cross_cats_sorted":[],"title_canon_sha256":"4d855d7775676e2eea7782e1ca6c807eff2f70fbc0f2a67a583fac547cce4e07","abstract_canon_sha256":"1c284bae86c465f6d2d657b7d9a5ab21a025a1104451b271f4dc2811bdff863c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:25:46.284583Z","signature_b64":"76e7EykBOPbEg9gCJOS29WjEyuwzKO9gbTFHTclxBmI9MFcmBSy3a1FkMojEWCWdT9rbH/+ZJsMjb6fCZED9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27414e38ecb2977d56ee30b7b6a4efd3ea2e6d3d86ae71f70d13b600a3de3477","last_reissued_at":"2026-07-04T17:25:46.284191Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:25:46.284191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Bo Feng, Edward Witten, Freddy Cachazo, Ruth Britto","submitted_at":"2005-01-07T20:04:03Z","abstract_excerpt":"Recently, by using the known structure of one-loop scattering amplitudes for gluons in Yang-Mills theory, a recursion relation for tree-level scattering amplitudes has been deduced. Here, we give a short and direct proof of this recursion relation based on properties of tree-level amplitudes only."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0501052","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/hep-th/0501052/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":"hep-th/0501052","created_at":"2026-07-04T17:25:46.284251+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0501052v2","created_at":"2026-07-04T17:25:46.284251+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0501052","created_at":"2026-07-04T17:25:46.284251+00:00"},{"alias_kind":"pith_short_12","alias_value":"E5AU4OHMWKLX","created_at":"2026-07-04T17:25:46.284251+00:00"},{"alias_kind":"pith_short_16","alias_value":"E5AU4OHMWKLX2VXO","created_at":"2026-07-04T17:25:46.284251+00:00"},{"alias_kind":"pith_short_8","alias_value":"E5AU4OHM","created_at":"2026-07-04T17:25:46.284251+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":28,"internal_anchor_count":24,"sample":[{"citing_arxiv_id":"2607.06661","citing_title":"Perturbiner methods in scattering amplitude","ref_index":15,"is_internal_anchor":true},{"citing_arxiv_id":"2606.25032","citing_title":"A Cosmological BCFW Bridge and Its Canonical Geometry","ref_index":2,"is_internal_anchor":true},{"citing_arxiv_id":"2606.05289","citing_title":"Unitarity, Recursion and Soft Limits in (EA)dS through Dressing","ref_index":24,"is_internal_anchor":true},{"citing_arxiv_id":"2606.02702","citing_title":"Perturbative construction of amplitudes from on-shell trees with vacuum pairs: the all-plus four-gluon amplitude through order $\\boldsymbol{g}^{\\boldsymbol{6}}$","ref_index":3,"is_internal_anchor":true},{"citing_arxiv_id":"2606.02686","citing_title":"On-Shell Bootstrap of Loop Inflation Correlators with Spectral Dispersion","ref_index":111,"is_internal_anchor":true},{"citing_arxiv_id":"2606.28193","citing_title":"Quantum anomalies from three-point on-shell bootstrap","ref_index":32,"is_internal_anchor":true},{"citing_arxiv_id":"2212.12892","citing_title":"Tree level amplitudes from soft theorems","ref_index":6,"is_internal_anchor":true},{"citing_arxiv_id":"2305.04620","citing_title":"Tree and $1$-loop fundamental BCJ relations from soft theorems","ref_index":7,"is_internal_anchor":true},{"citing_arxiv_id":"2306.09733","citing_title":"Note on tree NLSM amplitudes and soft theorems","ref_index":16,"is_internal_anchor":true},{"citing_arxiv_id":"2306.14774","citing_title":"Expanding single trace YMS amplitudes with gauge invariant coefficients","ref_index":33,"is_internal_anchor":true},{"citing_arxiv_id":"2310.15893","citing_title":"New recursive construction for tree NLSM and SG amplitudes, and new understanding of enhanced Adler zero","ref_index":2,"is_internal_anchor":true},{"citing_arxiv_id":"2311.03112","citing_title":"Recursive construction for expansions of tree Yang-Mills amplitudes from soft theorem","ref_index":26,"is_internal_anchor":true},{"citing_arxiv_id":"2401.03879","citing_title":"Multi-trace YMS amplitudes from soft behavior","ref_index":4,"is_internal_anchor":true},{"citing_arxiv_id":"2406.03034","citing_title":"Towards tree Yang-Mills and Yang-Mills-scalar amplitudes with higher-derivative interactions","ref_index":4,"is_internal_anchor":true},{"citing_arxiv_id":"2406.04622","citing_title":"On soft factors and transmutation operators","ref_index":9,"is_internal_anchor":true},{"citing_arxiv_id":"2411.07944","citing_title":"Understanding zeros and splittings of ordered tree amplitudes via Feynman diagrams","ref_index":2,"is_internal_anchor":true},{"citing_arxiv_id":"2504.14215","citing_title":"Hidden Zeros and $2$-split via BCFW Recursion Relation","ref_index":24,"is_internal_anchor":true},{"citing_arxiv_id":"2505.16436","citing_title":"QFT in Klein space","ref_index":42,"is_internal_anchor":true},{"citing_arxiv_id":"2506.00747","citing_title":"Soft theorems of tree-level ${\\rm Tr}(\\phi^3)$, YM and NLSM amplitudes from $2$-splits","ref_index":15,"is_internal_anchor":true},{"citing_arxiv_id":"2507.14583","citing_title":"BCFW like recursion for Deformed Associahedron","ref_index":36,"is_internal_anchor":true},{"citing_arxiv_id":"2508.12894","citing_title":"A new recursion relation for tree-level NLSM amplitudes based on hidden zeros","ref_index":2,"is_internal_anchor":true},{"citing_arxiv_id":"2508.14263","citing_title":"Tropicalized quantum field theory and global tropical sampling","ref_index":20,"is_internal_anchor":true},{"citing_arxiv_id":"2601.11705","citing_title":"String Theory from Maximal Supersymmetry","ref_index":42,"is_internal_anchor":true},{"citing_arxiv_id":"2603.11164","citing_title":"Learning to Unscramble: Simplifying Symbolic Expressions via Self-Supervised Oracle Trajectories","ref_index":21,"is_internal_anchor":true},{"citing_arxiv_id":"2605.04009","citing_title":"Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit","ref_index":124,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E5AU4OHMWKLX2VXOGC33NJHP2P","json":"https://pith.science/pith/E5AU4OHMWKLX2VXOGC33NJHP2P.json","graph_json":"https://pith.science/api/pith-number/E5AU4OHMWKLX2VXOGC33NJHP2P/graph.json","events_json":"https://pith.science/api/pith-number/E5AU4OHMWKLX2VXOGC33NJHP2P/events.json","paper":"https://pith.science/paper/E5AU4OHM"},"agent_actions":{"view_html":"https://pith.science/pith/E5AU4OHMWKLX2VXOGC33NJHP2P","download_json":"https://pith.science/pith/E5AU4OHMWKLX2VXOGC33NJHP2P.json","view_paper":"https://pith.science/paper/E5AU4OHM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/0501052&json=true","fetch_graph":"https://pith.science/api/pith-number/E5AU4OHMWKLX2VXOGC33NJHP2P/graph.json","fetch_events":"https://pith.science/api/pith-number/E5AU4OHMWKLX2VXOGC33NJHP2P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E5AU4OHMWKLX2VXOGC33NJHP2P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E5AU4OHMWKLX2VXOGC33NJHP2P/action/storage_attestation","attest_author":"https://pith.science/pith/E5AU4OHMWKLX2VXOGC33NJHP2P/action/author_attestation","sign_citation":"https://pith.science/pith/E5AU4OHMWKLX2VXOGC33NJHP2P/action/citation_signature","submit_replication":"https://pith.science/pith/E5AU4OHMWKLX2VXOGC33NJHP2P/action/replication_record"}},"created_at":"2026-07-04T17:25:46.284251+00:00","updated_at":"2026-07-04T17:25:46.284251+00:00"}