{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:EQRDS75NAZH4CTSG5U4XDAXV2D","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4094c2000972421021a3c8ebdab5ab73265d73ed412863bf60d1ff65f8341887","cross_cats_sorted":["nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-12-06T13:14:30Z","title_canon_sha256":"b27b662e2790f1b1fb08c5d0d2aaf8ba165bd5f4a5dd419ec354eb720870b32c"},"schema_version":"1.0","source":{"id":"2012.03256","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.03256","created_at":"2026-07-05T02:55:35Z"},{"alias_kind":"arxiv_version","alias_value":"2012.03256v2","created_at":"2026-07-05T02:55:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.03256","created_at":"2026-07-05T02:55:35Z"},{"alias_kind":"pith_short_12","alias_value":"EQRDS75NAZH4","created_at":"2026-07-05T02:55:35Z"},{"alias_kind":"pith_short_16","alias_value":"EQRDS75NAZH4CTSG","created_at":"2026-07-05T02:55:35Z"},{"alias_kind":"pith_short_8","alias_value":"EQRDS75N","created_at":"2026-07-05T02:55:35Z"}],"graph_snapshots":[{"event_id":"sha256:4946358505cbfceb19af84967c4f1ab64e0e947282025afbe35998d04380016f","target":"graph","created_at":"2026-07-05T02:55:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2012.03256/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we calculate analytically the perturbative matching coefficients for unpolarized quark and gluon Transverse-Momentum-Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs) through Next-to-Next-to-Next-to-Leading Order (N$^3$LO) in QCD. The N$^3$LO TMD PDFs are calculated by solving a system of differential equation of Feynman and phase space integrals. The TMD FFs are obtained by analytic continuation from space-like quantities to time-like quantities, taking into account the probability interpretation of TMD PDFs and FFs properly. The coefficient ","authors_text":"Hua Xing Zhu, Ming-Xing Luo, Tong-Zhi Yang, Yu Jiao Zhu","cross_cats":["nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-12-06T13:14:30Z","title":"Unpolarized Quark and Gluon TMD PDFs and FFs at N$^3$LO"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.03256","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f7623269933a6b98fdf1252840dfa41ebb0694649a0b5634ad2777e5f99d0efc","target":"record","created_at":"2026-07-05T02:55:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4094c2000972421021a3c8ebdab5ab73265d73ed412863bf60d1ff65f8341887","cross_cats_sorted":["nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-12-06T13:14:30Z","title_canon_sha256":"b27b662e2790f1b1fb08c5d0d2aaf8ba165bd5f4a5dd419ec354eb720870b32c"},"schema_version":"1.0","source":{"id":"2012.03256","kind":"arxiv","version":2}},"canonical_sha256":"2422397fad064fc14e46ed397182f5d0e45add3c24102961ed2fdc5005c5931d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2422397fad064fc14e46ed397182f5d0e45add3c24102961ed2fdc5005c5931d","first_computed_at":"2026-07-05T02:55:35.908895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:55:35.908895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xg7ZyIHLxohREx39n2q3e4Dc7tiWIxSyJgXA1CNiQ8b0fpfjT1MNRwS6lwqM2DWatDttyVrnCFoGHvRKlIx3Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:55:35.909330Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.03256","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7623269933a6b98fdf1252840dfa41ebb0694649a0b5634ad2777e5f99d0efc","sha256:4946358505cbfceb19af84967c4f1ab64e0e947282025afbe35998d04380016f"],"state_sha256":"65f249f83e80ad274391ee36abe7c548772a7072174aea882e6236ceda683103"}