{"id":"d731f331-1d46-467b-b03a-0b843802e951","arxiv_id":"2608.10551","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A new stability condition for generalized cluster algebras is classified, a Markov-type Diophantine equation is solved with explicit orbit counts, and the Chen-Li conjecture on rank-3 Laurent mutation invariants is proved.","lead":"This paper studies algebraic structures built by repeatedly replacing variables according to mutation rules, and singles out the cases where the rules are stable across the whole structure. It uses this framework to classify when a family of number equations has whole-number solutions and to settle a conjecture about invariants of rank-3 mutations.","discovery_kind":"extension","skeptic_critique":null,"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-12T22:01:54.464296+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}