{"paper":{"title":"Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The term proportional to zeta(3) in the four-loop non-singlet twist-two quark anomalous dimension is given in closed form for arbitrary Lorentz spin N.","cross_cats":[],"primary_cat":"hep-ph","authors_text":"B.A. Kniehl, V.N. Velizhanin","submitted_at":"2026-05-11T09:44:34Z","abstract_excerpt":"Both for quark flavor asymmetry and valence, we consider the anomalous dimension of the non-singlet twist-two quark operator of arbitrary Lorentz spin N at four loops in SU(nc) color gauge theory and present its term proportional to zeta(3) in closed form. These results have been extracted from published Mellin moments, for N=1,...,16 and N=3,...,15, respectively, by analytic reconstruction using advanced methods of number theory. Via Mellin transformation, we obtain the exact functional forms in x of the respective pieces of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi splitting functions. This"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we present its term proportional to zeta(3) in closed form. These results have been extracted from published Mellin moments, for N=1,...,16 and N=3,...,15, respectively, by analytic reconstruction using advanced methods of number theory.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analytic reconstruction from a finite set of Mellin moments (N up to 16) yields the exact closed-form expression valid for all N, with no additional transcendental structures or gauge-group dependencies missed by the number-theory method.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Closed-form expression for the ζ(3) term of the four-loop non-singlet twist-two quark anomalous dimension for arbitrary N, extracted via analytic reconstruction from Mellin moments.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The term proportional to zeta(3) in the four-loop non-singlet twist-two quark anomalous dimension is given in closed form for arbitrary Lorentz spin N.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4153143563757ffc60a92bfc0788effdd060ed2ed3f4613a5e8481111c6c5e6e"},"source":{"id":"2605.10284","kind":"arxiv","version":2},"verdict":{"id":"f66ee055-ed1a-4d16-bd2a-ec90937696b8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T05:19:51.887974Z","strongest_claim":"we present its term proportional to zeta(3) in closed form. These results have been extracted from published Mellin moments, for N=1,...,16 and N=3,...,15, respectively, by analytic reconstruction using advanced methods of number theory.","one_line_summary":"Closed-form expression for the ζ(3) term of the four-loop non-singlet twist-two quark anomalous dimension for arbitrary N, extracted via analytic reconstruction from Mellin moments.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analytic reconstruction from a finite set of Mellin moments (N up to 16) yields the exact closed-form expression valid for all N, with no additional transcendental structures or gauge-group dependencies missed by the number-theory method.","pith_extraction_headline":"The term proportional to zeta(3) in the four-loop non-singlet twist-two quark anomalous dimension is given in closed form for arbitrary Lorentz spin N."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.10284/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T06:22:00.844378Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T15:37:12.233725Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T11:31:19.288049Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T09:29:42.397414Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"8614b9919518780457a18fa2c657644d386b4f0f5751024f4845f855191a1595"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a314379963e7c502c09f16e7c4b116a515da24a7917fda05e1fff18827f4222f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}