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We introduce and study two classes: minimal non-sofic groups and $\\omega$-non-sofic groups. For minimal non-sofic groups, we establish strong structural restrictions. In particular, we show that if $G$ is a minimal non-sofic group and $M$ is a finitely generated residually finite maximal normal subgroup of $G$, then $M$ is central and $G$ is a perfect central extension of a finitely generated non-amenable simple group.\n  On the other hand, we show that locally graded non-sofic groups are necessarily $\\om"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"if G is a minimal non-sofic group and M is a finitely generated residually finite maximal normal subgroup of G, then M is central and G is a perfect central extension of a finitely generated non-amenable simple group","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The paper assumes the existence of non-sofic groups and, for the minimal case, the existence of a finitely generated residually finite maximal normal subgroup M whose properties can be analyzed via residual finiteness and centrality (abstract, paragraph on minimal non-sofic groups)","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Assuming non-sofic groups exist, minimal non-sofic groups with a finitely generated residually finite maximal normal subgroup are perfect central extensions of finitely generated non-amenable simple groups, and locally graded non-sofic groups are ω-non-sofic with nontrivial profinite residual chains","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"If a minimal non-sofic group has a finitely generated residually finite maximal normal subgroup, then that subgroup is central and the group is a perfect central extension of a finitely generated non-amenable simple group.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"efa45fb6346e899d4ceafde6f50bc05aaa9c373ab710f7de2e266e12d39bda00"},"source":{"id":"2604.19174","kind":"arxiv","version":3},"verdict":{"id":"27da77aa-38b7-4708-99a1-842381f849ff","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:50:49.325347Z","strongest_claim":"if G is a minimal non-sofic group and M is a finitely generated residually finite maximal normal subgroup of G, then M is central and G is a perfect central extension of a finitely generated non-amenable simple group","one_line_summary":"Assuming non-sofic groups exist, minimal non-sofic groups with a finitely generated residually finite maximal normal subgroup are perfect central extensions of finitely generated non-amenable simple groups, and locally graded non-sofic groups are ω-non-sofic with nontrivial profinite residual chains","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The paper assumes the existence of non-sofic groups and, for the minimal case, the existence of a finitely generated residually finite maximal normal subgroup M whose properties can be analyzed via residual finiteness and centrality (abstract, paragraph on minimal non-sofic groups)","pith_extraction_headline":"If a minimal non-sofic group has a finitely generated residually finite maximal normal subgroup, then that subgroup is central and the group is a perfect central extension of a finitely generated non-amenable simple group."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.19174/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":13,"sample":[{"doi":"","year":1999,"title":"M. 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