chore(nix): add style tooling

flake.nix

@@ -62,6 +62,12 @@
       inputs.nixpkgs.follows = "nixpkgs";
     };
 
+    # Repository formatter and Nix lint wiring.
+    treefmt-nix = {
+      url = "github:numtide/treefmt-nix";
+      inputs.nixpkgs.follows = "nixpkgs";
+    };
+
     # CachyOS kernel and binary cache.
     # This must not follow this flake's nixpkgs because Chaotic builds against its own pinned package set.
     # Its cache serves the kernel only when the overlay stays on the cache-friendly path.
@@ -69,8 +75,48 @@
   };
 
   outputs =
-    { self, nixpkgs, ... }@inputs:
     {
+      self,
+      nixpkgs,
+      treefmt-nix,
+      ...
+    }@inputs:
+    let
+      supportedSystems = [ "x86_64-linux" ];
+      forAllSystems = nixpkgs.lib.genAttrs supportedSystems;
+      pkgsFor = system: nixpkgs.legacyPackages.${system};
+      treefmtEvalFor = system: treefmt-nix.lib.evalModule (pkgsFor system) ./treefmt.nix;
+    in
+    {
+      formatter = forAllSystems (system: (treefmtEvalFor system).config.build.wrapper);
+
+      apps = forAllSystems (
+        system:
+        let
+          pkgs = pkgsFor system;
+          treefmtEval = treefmtEvalFor system;
+          nixStyleCheck = pkgs.writeShellApplication {
+            name = "nix-style-check";
+            runtimeInputs = [
+              treefmtEval.config.build.wrapper
+              pkgs.statix
+              pkgs.deadnix
+            ];
+            text = ''
+              treefmt --fail-on-change
+              statix check .
+              deadnix --fail --no-lambda-pattern-names --no-underscore .
+            '';
+          };
+        in
+        {
+          nix-style-check = {
+            type = "app";
+            program = "${nixStyleCheck}/bin/nix-style-check";
+          };
+        }
+      );
+
       nixosConfigurations = (import ./src/dotfiles {
         inherit inputs self;
         lib = nixpkgs.lib;