{"paper":{"title":"Monogenic functions over real alternative *-algebras: the several hypercomplex variables case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Monogenic functions in several hypercomplex variables over real alternative *-algebras satisfy the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","cross_cats":[],"primary_cat":"math.CV","authors_text":"Chao Ding, Haiyan Wang, Zhenghua Xu","submitted_at":"2025-06-10T00:33:46Z","abstract_excerpt":"The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of monogenic functions over real alternative $\\ast$-algebras has been introduced to unify several classical monogenic functions theories. In this paper, we initiate the study of monogenic functions of several hypercomplex variables over real alternative $\\ast$-algebras, which naturally extends the theory of several complex variables to a very general setting. In"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We initiate the study of monogenic functions of several hypercomplex variables over real alternative *-algebras and develop fundamental properties such as the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the single-variable monogenic theory over real alternative *-algebras extends directly to the several-variable case while preserving the listed integral and extension properties without additional structural restrictions on the algebra or the functions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces monogenic functions of several hypercomplex variables over real alternative *-algebras and establishes Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Monogenic functions in several hypercomplex variables over real alternative *-algebras satisfy the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"434c0b409eeaf452c00f32be645ab2ee3a7928f0b261d070f1fee7c871781140"},"source":{"id":"2506.08307","kind":"arxiv","version":3},"verdict":{"id":"4e18f0ee-655a-485e-bfe0-a356765970e2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T10:35:01.344546Z","strongest_claim":"We initiate the study of monogenic functions of several hypercomplex variables over real alternative *-algebras and develop fundamental properties such as the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","one_line_summary":"Introduces monogenic functions of several hypercomplex variables over real alternative *-algebras and establishes Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the single-variable monogenic theory over real alternative *-algebras extends directly to the several-variable case while preserving the listed integral and extension properties without additional structural restrictions on the algebra or the functions.","pith_extraction_headline":"Monogenic functions in several hypercomplex variables over real alternative *-algebras satisfy the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.08307/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":2,"snapshot_sha256":"8002aec0d1256210ce5be507c1363397daa970abe2a5f19884faded4474e911b"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}