feat(nix): check the home-manager module's composition (task 0047)

Add a `home-manager` flake input, its nixpkgs following this flake's, and a
`home-manager-module` check that evaluates the real module through
home-manager's standalone entry point and builds the home files derivation
under four operator configurations, asserting on the tree each produces:
the Skill coexisting with an operator's own skills in both the attribute-set
and whole-directory forms, the sibling-enable gate leaving no Skill when
Claude Code is off, and the hook merging into an operator's own SessionStart
list. This is the first automated proof of the module's composition (ADR 0021),
replacing verification by maintainer rebuild.

.claude/tasks/0047-flake-check-hm-module-composition.md

@@ -26,11 +26,24 @@ This adds a module check alongside the existing package check in the flake's `ch
 
 ## Acceptance criteria
 
-- [ ] The flake has a home-manager input whose nixpkgs follows the flake's nixpkgs; `flake.lock` is updated.
-- [ ] A new check under the flake's `checks` output evaluates the real module through home-manager's standalone configuration entry point and builds the home files derivation — no Claude Code binary or running agent required.
-- [ ] The attribute-set-skills configuration asserts the module's Skill and the operator's skill both land, each at its own name.
-- [ ] The whole-directory-skills (path form) configuration asserts the module's Skill lands alongside the operator's directory contents; a non-recursive path-form install would fail this as a build-time collision.
-- [ ] The Claude-Code-disabled configuration asserts no gitea-axi Skill entry is written.
-- [ ] A configuration with an operator's own SessionStart hook asserts the module's hook merges into that list rather than replacing it.
-- [ ] The check asserts on the generation's file tree only, not on option values or store paths.
-- [ ] `nix flake check` runs the new check across the flake's systems and passes.
+- [x] The flake has a home-manager input whose nixpkgs follows the flake's nixpkgs; `flake.lock` is updated.
+- [x] A new check under the flake's `checks` output evaluates the real module through home-manager's standalone configuration entry point and builds the home files derivation — no Claude Code binary or running agent required.
+- [x] The attribute-set-skills configuration asserts the module's Skill and the operator's skill both land, each at its own name.
+- [x] The whole-directory-skills (path form) configuration asserts the module's Skill lands alongside the operator's directory contents; a non-recursive path-form install would fail this as a build-time collision.
+- [x] The Claude-Code-disabled configuration asserts no gitea-axi Skill entry is written.
+- [x] A configuration with an operator's own SessionStart hook asserts the module's hook merges into that list rather than replacing it.
+- [x] The check asserts on the generation's file tree only, not on option values or store paths.
+- [x] `nix flake check` runs the new check across the flake's systems and passes.
+
+## Implementation Notes
+
+The check lives in its own file, `checks/home-manager-module.nix`, imported from the flake's `checks` output beside the existing package check; the `forAllSystems` callback now destructures `{ pkgs, system }` because the check needs `pkgs` to build fixtures and the derivation.
+`home-manager` is added as a flake input with `inputs.nixpkgs.follows = "nixpkgs"`; it is a check-only development input with no bearing on the package or the module a consumer imports, and the comment in `flake.nix` says so.
+
+Each of the four configurations builds `config.home-files` — the home-manager file-linkage layer — and the final `runCommandLocal` asserts on that tree with `test`/`grep` only: skill files present or absent by path, and the two SessionStart commands present as quoted JSON string values in `settings.json`.
+The hook-merge assertion reads generated file content because that is the only place a list merge is observable; the spec's Testing Decisions name "the hook merges into the operator's own hooks" as a required assertion, so this stays within "assert on the file tree, not on option values or store paths".
+
+On the cross-system criterion: `nix flake check` builds the check for the host system and passes, and omits the incompatible systems (`aarch64-*`) with a warning — identical per-system semantics to the pre-existing package check, which also builds only natively.
+The check is import-from-derivation-bearing (the Claude Code module reads the fixture skill directories at evaluation time), so evaluating a foreign system's check forces a cross-platform fixture build rather than skipping cleanly; this is not exercised by the default `nix flake check` and does not affect the native run.
+
+Verified by `nix flake check` (passes, all outputs) and by inspecting each configuration's built `home-files` tree directly: the disabled-Claude-Code generation contains no `.claude` directory at all, and the merged-hook `settings.json` contains both hooks in the `SessionStart` array — confirming the assertions are not vacuous.