feat(installer): implement single-input flake architecture

- Refactor generated flake.nix to use the Appliance Model.
- Downstream flake now only defines the 'nomarchy' input.
- Dependencies (nixpkgs, home-manager) are inherited from nomarchy.inputs to ensure maximum stability and version alignment with upstream.

installer/install.sh

@@ -1369,13 +1369,7 @@ generate_flake_config() {
   description = "My Nomarchy Configuration";
 
   inputs = {
-    nixpkgs.url = "github:nixos/nixpkgs/nixos-25.11";
     nomarchy.url = "$nomarchy_url";
-    nixos-hardware.url = "github:NixOS/nixos-hardware/master";
-    home-manager = {
-      url = "github:nix-community/home-manager/release-25.11";
-      inputs.nixpkgs.follows = "nixpkgs";
-    };
   };
 
   # Two-track Nomarchy workflow:
@@ -1384,8 +1378,9 @@ generate_flake_config() {
   #
   # Both consume the same \`pkgs\` below so overlays and allowUnfree stay in
   # sync across the two paths.
-  outputs = { self, nixpkgs, nomarchy, home-manager, nixos-hardware, ... }@inputs:
+  outputs = { self, nomarchy, ... }@inputs:
     let
+      inherit (nomarchy.inputs) nixpkgs home-manager;
       system = "x86_64-linux";
       pkgs = import nixpkgs {
         inherit system;
@@ -1396,7 +1391,7 @@ generate_flake_config() {
     {
       nixosConfigurations.$HOSTNAME = nixpkgs.lib.nixosSystem {
         inherit pkgs;
-        specialArgs = { inputs = nomarchy.inputs // inputs; };
+        specialArgs = { inputs = nomarchy.inputs; };
         modules = [
           ./hardware-configuration.nix
           ./hardware-selection.nix
@@ -1410,7 +1405,7 @@ generate_flake_config() {
       # NixOS config so dotfile/theme iterations don't rebuild the system.
       homeConfigurations.$USERNAME = home-manager.lib.homeManagerConfiguration {
         inherit pkgs;
-        extraSpecialArgs = { inputs = nomarchy.inputs // inputs; };
+        extraSpecialArgs = { inputs = nomarchy.inputs; };
         modules = [
           nomarchy.nixosModules.home
           ./home.nix