{"paper":{"title":"A Complete Characterization of Finite-Order Entire Solutions to Fermat-Type Partial Differential-Difference Systems in $\\mathbb{C}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Abhijit Banerjee, Jhilik Banerjee, Sujoy Majumder","submitted_at":"2026-06-03T06:59:47Z","abstract_excerpt":"The primary objective of this paper is to determine the explicit existence form and structure of finite-order entire solutions in $\\mathbb{C}^n$ of the following system of Fermat-type partial differential-difference equations: \\[\\begin{cases} \\left(\\frac{\\partial f_1\\left(z\\right)}{\\partial z_1}\\right)^{n_1} + (f_2 \\left(z+c\\right)-f_1(z) )^{m_1}= 1,\n  \\medskip \\left(\\frac{\\partial f_2\\left(z\\right)}{\\partial z_1}\\right)^{n_2} + (f_1 \\left(z+c \\right)-f_2(z) )^{m_2}= 1, \\end{cases}\\] \nfor different choices of the positive integers $n_1$, $n_2$, $m_1$, and $m_2$, where $c=(c_1,c_2,\\ldots,c_n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05240","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/2606.05240/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"}