docs: runnable partial-clone worked example

.formatter.exs

@@ -1,4 +1,4 @@
 # Used by "mix format"
 [
-  inputs: ["{mix,.formatter}.exs", "{config,lib,test}/**/*.{ex,exs}"]
+  inputs: ["{mix,.formatter}.exs", "{config,lib,test,examples}/**/*.{ex,exs}"]
 ]

README.md

@@ -82,6 +82,15 @@ refetch. Perfect for agent loops that want snapshot semantics.
 
 The on-disk format is a standard bare git repo — `git log`, `git fsck`, and friends all work on it.
 
+There's a runnable worked example at
+[`examples/partial_clone_demo.exs`](examples/partial_clone_demo.exs) —
+`Mix.install`, partial clone, one file read, with `memory_report/1`
+showing `blob_count: 0 -> 1` around the read:
+
+```sh
+elixir examples/partial_clone_demo.exs
+```
+
 ### Private repos
 
 ```elixir

examples/partial_clone_demo.exs

@@ -0,0 +1,32 @@
+# Partial clone, worked example.
+#
+# Clones a public repo under a `blob:none` filter — the server ships
+# refs + commits + trees but NO file contents — then reads one file.
+# The `blob_count: 0 -> 1` transition around the read is the proof
+# that exactly one blob crossed the wire.
+#
+# Run with:  elixir examples/partial_clone_demo.exs
+
+Mix.install([{:exgit, "~> 0.1.0"}])
+
+stats = fn repo ->
+  Exgit.Repository.memory_report(repo) |> Map.take([:blob_count, :tree_count, :cache_bytes])
+end
+
+# Partial clone: refs + commits + trees cross the wire. No file contents.
+{:ok, repo} = Exgit.clone("https://github.com/elixir-ai-tools/just_bash", filter: {:blob, :none})
+IO.inspect(stats.(repo), label: "after clone   ")
+
+# The size probe refuses to fetch — gate on it before pulling big files.
+{:error, :not_local} = Exgit.FS.size(repo, "HEAD", "README.md")
+
+# Reading ONE file fetches ONE blob.
+{:ok, {_mode, blob}, repo} = Exgit.FS.read_path(repo, "HEAD", "README.md")
+first_line = blob.data |> String.split("\n", parts: 2) |> hd()
+IO.puts(~s(read README.md:  #{byte_size(blob.data)} bytes — "#{first_line}"))
+IO.inspect(stats.(repo), label: "after one read")
+
+# Navigation stays free: directory listings come from the local
+# trees, so blob_count doesn't move.
+{:ok, entries, repo} = Exgit.FS.ls(repo, "HEAD", "")
+IO.puts("ls /:  #{length(entries)} entries — blob_count still #{stats.(repo).blob_count}")