{"paper":{"title":"The next-to-next-to-leading order BFKL eigenvalue at odd conformal spin in planar N=4 super Yang-Mills: closed form, coefficient structure, and arithmetic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alex Prygarin, Claudelle Capasia Madjuogang Sandeu","submitted_at":"2026-07-20T07:02:49Z","abstract_excerpt":"We present the three-loop (next-to-next-to-leading order) BFKL eigenvalue of planar N=4 super Yang-Mills at odd conformal spin n in closed form, as a finite combination of continued nested harmonic sums and rational functions of z=(|n|-1)/2 + i nu on an integer-shifted ladder. For each odd spin the atom table is extracted exactly, in rational arithmetic, from the Caron-Huot-Herranen three-loop integrand; a shipped command regenerates it for any odd n>=3, with n=1 a supplied boundary block. A resummed master generating function, conjectured to reproduce those integrands at every spin (verified "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17613","kind":"arxiv","version":1},"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/2607.17613/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"}