### Task A6: Wire patched repo into the pak install path

**Files:**
- Modify: `R/install_helpers.R:333-389` (`run_pak_install_with_mutex`)
- Modify: `R/install-deps.R:23-75` (`install_pkg_sys_deps`)
- Test: `tests/testthat/test-patches.R`

**Interfaces:**
- Consumes: `prepare_patched_repo()`.
- Produces: `run_pak_install_with_mutex(local_clone_dir_single, env_vars, patched_repo = NULL)` — prepends `file://<patched_repo>` to `options("repos")` for the install; `install_pkg_sys_deps(package_name, tag, local_clone_dir, platform, aggressive_cleanup = FALSE, patches = NULL, arch = NULL)` — builds the patched repo before installing.

- [ ] **Step 1: Write the failing test**

```r
test_that("run_pak_install_with_mutex prepends the patched repo to repos", {
  seen <- NULL
  local_mocked_bindings(
    acquire_pak_mutex = function(...) tempfile(),
    release_pak_mutex = function(...) invisible(NULL),
    retry_with_backoff = function(func, ...) func()
  )
  local_mocked_bindings(
    local_install_deps = function(...) {
      seen <<- getOption("repos")
      invisible(TRUE)
    },
    .package = "pak"
  )

  run_pak_install_with_mutex(
    tempfile(), list(), patched_repo = "/tmp/patched"
  )

  expect_true(any(grepl("file:///tmp/patched", seen)))
})
```

- [ ] **Step 2: Run test to verify it fails**

Run: `Rscript -e 'devtools::load_all("."); testthat::test_file("tests/testthat/test-patches.R")'`
Expected: FAIL — `patched_repo` argument not yet accepted / repos not prepended.

- [ ] **Step 3: Edit `run_pak_install_with_mutex` in `R/install_helpers.R`**

Change the signature line:

```r
run_pak_install_with_mutex <- function(local_clone_dir_single, env_vars) {
```

to:

```r
run_pak_install_with_mutex <- function(
  local_clone_dir_single,
  env_vars,
  patched_repo = NULL
) {
```

Replace the inner `retry_with_backoff(...)` block (the one wrapping `pak::local_install_deps`) with:

```r
          retry_with_backoff(function() {
            withr::with_envvar(env_vars, {
              repos <- getOption("repos")
              if (!is.null(patched_repo)) {
                repos <- c(
                  patched = sprintf("file://%s", patched_repo),
                  repos
                )
              }
              withr::with_options(list(repos = repos), {
                # Default to non-verbose (suppressed messages)
                suppressMessages(pak::local_install_deps(sprintf(
                  "%s",
                  local_clone_dir_single
                )))
              })
            })
          })
```

- [ ] **Step 4: Edit `install_pkg_sys_deps` in `R/install-deps.R`**

Change the signature to add `patches` and `arch`:

```r
install_pkg_sys_deps <- function(
  package_name,
  tag,
  local_clone_dir,
  platform = platform,
  aggressive_cleanup = FALSE,
  patches = NULL,
  arch = NULL
) {
```

Immediately before the `run_pak_install_with_mutex(...)` call, insert:

```r
  # Build a local repo of patched binaries (if any apply) and serve it to pak.
  r_minor <- paste(
    R.version$major,
    strsplit(R.version$minor, ".", fixed = TRUE)[[1L]][1L],
    sep = "."
  )
  patched_repo <- tryCatch(
    prepare_patched_repo(patches, platform, arch, r_minor),
    error = function(e) {
      log_warn(sprintf("Patch preparation failed: %s", conditionMessage(e)))
      NULL
    }
  )
```

and change the call from:

```r
  run_pak_install_with_mutex(
    local_clone_dir_single,
    env_vars
  )
```

to:

```r
  run_pak_install_with_mutex(
    local_clone_dir_single,
    env_vars,
    patched_repo = patched_repo
  )
```

- [ ] **Step 5: Run test to verify it passes**

Run: `Rscript -e 'devtools::load_all("."); testthat::test_file("tests/testthat/test-patches.R")'`
Expected: PASS.

- [ ] **Step 6: Commit**

```bash
git add R/install_helpers.R R/install-deps.R tests/testthat/test-patches.R
git commit -m "feat(patches): serve patched binaries to pak during dep install"
```

---