Enhance documentation and update syncback features

- Updated the `audit.md` documentation to clarify the syncback process and the structure of the `FsSnapshot`.
- Revised the `atlas-api.mdc` to reflect changes in the Git metadata handling, including the introduction of a separate endpoint for fetching Git metadata.
- Improved the `atlas-dedup.mdc` to include handling for the reserved name "init" during slugification.
- Enhanced the `atlas-syncback.mdc` to document the new `SyncbackResult` structure and its integration with the syncback process.
- Updated various sections across multiple documentation files to ensure consistency and clarity regarding the project's architecture and API endpoints.

These changes aim to improve the overall understanding of the system and its components, facilitating better usage and integration.

.cursor/rules/atlas-syncback.mdc

@@ -85,9 +85,17 @@ pub fn syncback_loop(
     new_tree: WeakDom,             // Roblox file contents
     project: &Project,             // Project configuration
     incremental: bool,             // Preserve structure vs rebuild
-) -> anyhow::Result<FsSnapshot>
+) -> anyhow::Result<SyncbackResult>
+
+pub struct SyncbackResult {
+    pub fs_snapshot: FsSnapshot,
+    pub new_tree: WeakDom,
+    pub instance_paths: HashMap<Ref, String>,
+}
 ```
 
+Also available: `syncback_loop_with_stats()` accepts `external_stats: Option<&SyncbackStats>` for callers that track stats externally.
+
 ## Syncback Modes
 
 ### Incremental Mode (`incremental: true`)
@@ -215,10 +223,11 @@ pub struct SyncbackRules {
 ```
 
 **Property filtering** (`property_filter.rs`):
-- Filters out `Name`, `Parent` (always)
+- Filters out `Name`, `Parent`, `Source`, `Value`, `Contents` via reflection DB (`DoesNotSerialize`), not explicit property lists
+- Explicitly filters `Variant::Ref` and `Variant::UniqueId` by variant type
 - Filters out properties in `ignore_properties`
 - Filters out unscriptable properties if `sync_unscriptable: false`
-- Filters out middleware-specific properties (e.g., `Script.Source` when writing to `.luau` file)
+- Middleware-specific filtering (e.g., `Script.Source` for `.luau` files) is handled in `snapshot.rs` via `filter_out_property`, not in `property_filter.rs`
 
 ### Hidden Services
 
@@ -296,17 +305,14 @@ pub struct SyncbackSnapshot<'sync> {
 **Methods:**
 
 ```rust
-// Join child to current path
-snapshot.with_joined_path(new_ref, old_ref)?
-// Result: parent_path/ChildName.luau
+// Join child to current path (returns (Self, needs_meta_name, dedup_key))
+snapshot.with_joined_path(new_ref, old_ref, &taken_names)?
 
-// Use base path
-snapshot.with_base_path(&base, new_ref, old_ref)?
-// Result: base/ChildName.luau
+// Use base path (same return type)
+snapshot.with_base_path(&base, new_ref, old_ref, &taken_names)?
 
 // Explicit path
 snapshot.with_new_path(path, new_ref, old_ref)
-// Result: path (exactly as provided)
 ```
 
 **Filename generation** (`file_names.rs`):
@@ -366,7 +372,7 @@ fs_snapshot.merge(other)  // Combine snapshots
 
 // Apply to filesystem
 fs_snapshot.write_to_vfs(base_path, vfs)?;
-fs_snapshot.write_to_vfs_parallel(base_path, vfs)?;  // Parallel writes (see below)
+fs_snapshot.write_to_vfs_parallel(base_path, vfs, git_cache)?;  // Parallel writes; git_cache: Option<&GitIndexCache> skips unchanged files
 
 // Post-process ref paths
 fs_snapshot.fix_ref_paths(&substitutions);  // Replace placeholder paths with final relative paths
@@ -416,7 +422,7 @@ Forward sync also reads `Rojo_Target_*` attributes and resolves via `get_specifi
 - `collect_referents(dom, paths, final_paths)` - Finds all Ref properties, stores as (source, target_path) pairs
 - `tentative_fs_path(dom, ref)` - Computes pre-dedup path: slugified name + extension based on class/children
 - `tentative_fs_path_public()` - Public wrapper used in post-processing
-- `link_referents(dom, referents)` - Writes `Rojo_Ref_*` attributes to instances
+- `link_referents(links: RefLinks, dom: &mut WeakDom)` - Writes `Rojo_Ref_*` attributes to instances
 
 **Ref path post-processing (in `mod.rs`):**
 
@@ -577,6 +583,22 @@ diff place.rbxl rebuilt.rbxl
 - Globally optimal matching (Hungarian algorithm) for large ambiguous groups
 - ~~Matching cache (parent_ref -> match_assignments) for avoiding redundant scoring~~ (session-level caching now implemented via `MatchingSession`; per-parent invalidation cache still deferred)
 
+## GitIndexCache Integration
+
+`write_to_vfs_parallel()` accepts `git_cache: Option<&GitIndexCache>`. When provided (by `src/cli/syncback.rs` and `src/cli/serve.rs`), files whose SHA1 blob hash matches the git index are skipped. `GitIndexCache` is created via `GitIndexCache::new(project_root)` which runs `git ls-files --stage`.
+
+## $schema Roundtrip
+
+`.project.json5`, `.meta.json5`, and `.model.json5` files preserve a `$schema` field during syncback. Implemented via `schema: Option<String>` on `Project`, `AdjacentMetadata`, `DirectoryMetadata`, and `JsonModel` structs. Old instance metadata carries the schema through the pipeline.
+
+## Reserved Name: `init`
+
+`slugify_name()` appends `_` to `"init"` (case-insensitive): `"init"` -> `"init_"`. `name_needs_slugify()` returns `true` for `"init"`. This prevents collision with the init file convention (`init.luau`, `init.server.luau`, etc.).
+
+## MCP Syncback
+
+`POST /api/mcp/syncback` runs syncback inline and returns stats with a `syncback_complete` status. Unlike `/api/syncback` which restarts the serve loop, the MCP variant completes without server restart.
+
 ## Key Files to Reference
 
 - `src/syncback/mod.rs` - Main orchestration loop, ref path post-processing