[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"BfJ4hriLaY":3},"# Group Approximation\n\nThe remote `verified` branch is automatically fast-forwarded after every complete Lean Prover CI success on `main`. Use that for the most recent correct Lean code.\n\n## A non-MF group\n\n[`non_mf_groups_exist.tex`](non_mf_groups_exist.tex) proves that not every group is MF. [`non_mf_group_notes.tex`](non_mf_group_notes.tex) is an archived research notebook for an earlier construction and is not a companion to the current manuscript.\n\n## Lean library\n\nThe Lean code is organized as a reusable library. Generic definitions and theorems are separated from concrete presentations and finite certificates, so other projects can import only the layers they need. [`GroupApproximation.lean`](GroupApproximation.lean) imports the complete library.\n\n| Area | Directories | Contents |\n| --- | --- | --- |\n| Group theory | `Algebra/`, `GroupTheory/`, `Higman/`, `Covers/` | Presentations, normal forms, free products, HNN extensions, quotients, embeddings, and torsion |\n| Finite approximation | `Sofic/`, `Criterion/`, `Stability/`, `Domination/`, `Matching/` | MF, sofic, and hyperlinear interfaces; finite models; residuals; matrix coronas; permanence and obstruction theorems |\n| Rigidity | `PropertyT/`, `Kazhdan/`, `PropertyTT/` | Fixed-point methods, relative property (T), spectral and Hodge certificates, and property (TT)/T |\n| Analysis | `Analysis/`, `KOne/`, `Leavitt/`, `Steinberg/` | Matrix estimates, projections, traces, C*-algebras, K-theory, and noncommutative rings |\n| Other group constructions | `Kun/`, `KunThom/`, `Quantum/`, `Monsters/` | Graph, permutation, quantum, and embedding constructions |\n| Public and checked interfaces | `Endpoint/`, `Meta/`, `Computability/`, `Manuscript/` | Stable exports, certificate replay, computability wrappers, statement matching, and axiom audits |\n\nModules named `Literal*` contain fully specified examples and certificate data; the generic modules do not depend on any particular presentation.\n",1788025905115]