{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:AJFXHXCNZW3PECIWUDA63IHDXO","short_pith_number":"pith:AJFXHXCN","schema_version":"1.0","canonical_sha256":"024b73dc4dcdb6f20916a0c1eda0e3bbad6882d18e083437b6cd47cdc984beda","source":{"kind":"arxiv","id":"1909.00697","version":2},"attestation_state":"computed","paper":{"title":"Relating amplitude and PDF factorisation through Wilson-line geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Calum Milloy, Einan Gardi, Giulio Falcioni","submitted_at":"2019-09-02T12:52:37Z","abstract_excerpt":"We study long-distance singularities governing different physical quantities involving massless partons in perturbative QCD by using factorisation in terms of Wilson-line correlators. By isolating the process-independent hard-collinear singularities from quark and gluon form factors, and identifying these with the ones governing the elastic limit of the perturbative Parton Distribution Functions (PDFs) -- $\\delta(1-x)$ in the large-$x$ limit of DGLAP splitting functions -- we extract the anomalous dimension controlling soft singularities of the PDFs, verifying that it admits Casimir scaling. W"},"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":"1909.00697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-09-02T12:52:37Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"07672f396b933606abb3dc9ea410414deba8a00f7cf39dca0554ad27234d4213","abstract_canon_sha256":"5bdf2cefef84feb3618c4e11f22648d277879fa02d4da60375ee23b53c27a291"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:20:54.991402Z","signature_b64":"cLkDfcvY0t8GmbOsMVfos6S6ixAIt/g9QZ2qUMOH8pn1Yb+XNledhSRRXxx16VnLzDk6da02Ckw92xdGTkvYAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"024b73dc4dcdb6f20916a0c1eda0e3bbad6882d18e083437b6cd47cdc984beda","last_reissued_at":"2026-07-05T00:20:54.990901Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:20:54.990901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relating amplitude and PDF factorisation through Wilson-line geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Calum Milloy, Einan Gardi, Giulio Falcioni","submitted_at":"2019-09-02T12:52:37Z","abstract_excerpt":"We study long-distance singularities governing different physical quantities involving massless partons in perturbative QCD by using factorisation in terms of Wilson-line correlators. By isolating the process-independent hard-collinear singularities from quark and gluon form factors, and identifying these with the ones governing the elastic limit of the perturbative Parton Distribution Functions (PDFs) -- $\\delta(1-x)$ in the large-$x$ limit of DGLAP splitting functions -- we extract the anomalous dimension controlling soft singularities of the PDFs, verifying that it admits Casimir scaling. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00697","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/1909.00697/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":"1909.00697","created_at":"2026-07-05T00:20:54.990960+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.00697v2","created_at":"2026-07-05T00:20:54.990960+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.00697","created_at":"2026-07-05T00:20:54.990960+00:00"},{"alias_kind":"pith_short_12","alias_value":"AJFXHXCNZW3P","created_at":"2026-07-05T00:20:54.990960+00:00"},{"alias_kind":"pith_short_16","alias_value":"AJFXHXCNZW3PECIW","created_at":"2026-07-05T00:20:54.990960+00:00"},{"alias_kind":"pith_short_8","alias_value":"AJFXHXCN","created_at":"2026-07-05T00:20:54.990960+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.03889","citing_title":"Properties and implications of the four-loop non-singlet splitting functions in QCD","ref_index":79,"is_internal_anchor":false},{"citing_arxiv_id":"2604.19232","citing_title":"Progress on the soft anomalous dimension in QCD","ref_index":38,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AJFXHXCNZW3PECIWUDA63IHDXO","json":"https://pith.science/pith/AJFXHXCNZW3PECIWUDA63IHDXO.json","graph_json":"https://pith.science/api/pith-number/AJFXHXCNZW3PECIWUDA63IHDXO/graph.json","events_json":"https://pith.science/api/pith-number/AJFXHXCNZW3PECIWUDA63IHDXO/events.json","paper":"https://pith.science/paper/AJFXHXCN"},"agent_actions":{"view_html":"https://pith.science/pith/AJFXHXCNZW3PECIWUDA63IHDXO","download_json":"https://pith.science/pith/AJFXHXCNZW3PECIWUDA63IHDXO.json","view_paper":"https://pith.science/paper/AJFXHXCN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.00697&json=true","fetch_graph":"https://pith.science/api/pith-number/AJFXHXCNZW3PECIWUDA63IHDXO/graph.json","fetch_events":"https://pith.science/api/pith-number/AJFXHXCNZW3PECIWUDA63IHDXO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AJFXHXCNZW3PECIWUDA63IHDXO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AJFXHXCNZW3PECIWUDA63IHDXO/action/storage_attestation","attest_author":"https://pith.science/pith/AJFXHXCNZW3PECIWUDA63IHDXO/action/author_attestation","sign_citation":"https://pith.science/pith/AJFXHXCNZW3PECIWUDA63IHDXO/action/citation_signature","submit_replication":"https://pith.science/pith/AJFXHXCNZW3PECIWUDA63IHDXO/action/replication_record"}},"created_at":"2026-07-05T00:20:54.990960+00:00","updated_at":"2026-07-05T00:20:54.990960+00:00"}