{"paper":{"title":"An adaptive inverse-problem framework for one-loop five-gluon BCJ numerators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Lin Mai, Yaobo Zhang","submitted_at":"2026-07-15T03:27:30Z","abstract_excerpt":"An inverse problem comprises a matrix equation together with its unknown space, physical data, equivalence relation, and validation tests. We formulate Bern--Carrasco--Johansson (BCJ) numerator construction as an exact adaptive inverse problem. A fixed scientific specification determines the theory, graph conventions, coefficient field, locality and power counting, cut data, observable equivalence, and independent checks. Each finite working specification compiles to $\\mathcal{P}_\\sigma=(A,b;\\mathcal{S};\\mathcal{T})$, where $Ax=b$ reconstructs numerator coefficients, $\\mathcal{S}$ classifies t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13412","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/2607.13412/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"}