{"id":"43d270a8-d1a6-4a04-82f9-afd9d55c544b","arxiv_id":"2505.13984","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Weak symmetry of the hermitian form, dρ=0, is a necessary condition for existence of Levi-Civita connections in derivation based calculi, and sufficient for free modules with a dual basis.","lead":"This paper proves that a noncommutative version of the Levi-Civita connection exists exactly when a certain weak symmetry condition holds for the hermitian form, and it constructs such connections for noncommutative 3-tori. The result gives researchers a concrete test for when noncommutative spaces admit a Riemannian-like structure, replacing the classical symmetry of the metric with an algebraic closure condition.","discovery_kind":"first_principles","skeptic_critique":null,"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-07T15:43:25.724027+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}