diff --git a/musicfs/Cargo.lock b/musicfs/Cargo.lock
index f99063f..4dd942a 100644
--- a/musicfs/Cargo.lock
+++ b/musicfs/Cargo.lock
@@ -1938,6 +1938,7 @@ dependencies = [
  "parking_lot 0.12.5",
  "sd-notify",
  "tokio",
+ "tokio-util 0.7.18",
  "tracing",
  "tracing-appender",
  "tracing-journald",
@@ -2090,6 +2091,7 @@ dependencies = [
  "musicfs-cas",
  "musicfs-core",
  "musicfs-origins",
+ "musicfs-search",
  "nix",
  "noxious-client",
  "parking_lot 0.12.5",
@@ -2100,6 +2102,7 @@ dependencies = [
  "thiserror 1.0.69",
  "tokio",
  "tokio-test",
+ "tokio-util 0.7.18",
  "tracing",
 ]
 
@@ -3735,6 +3738,7 @@ dependencies = [
  "bytes",
  "futures-core",
  "futures-sink",
+ "futures-util",
  "pin-project-lite",
  "tokio",
 ]
diff --git a/musicfs/Cargo.toml b/musicfs/Cargo.toml
index 366d16a..4dc5de8 100644
--- a/musicfs/Cargo.toml
+++ b/musicfs/Cargo.toml
@@ -13,6 +13,7 @@ repository = "https://github.com/user/musicfs"
 [workspace.dependencies]
 # Async runtime
 tokio = { version = "1", features = ["full"] }
+tokio-util = { version = "0.7", features = ["rt"] }
 async-trait = "0.1"
 
 # Error handling
diff --git a/musicfs/crates/musicfs-cache/src/db.rs b/musicfs/crates/musicfs-cache/src/db.rs
index 21bb61a..b2f759e 100644
--- a/musicfs/crates/musicfs-cache/src/db.rs
+++ b/musicfs/crates/musicfs-cache/src/db.rs
@@ -6,7 +6,7 @@ use rusqlite::{params, Connection, OptionalExtension};
 use std::path::{Path, PathBuf};
 use std::sync::{Arc, Mutex};
 use std::time::{Duration, SystemTime, UNIX_EPOCH};
-use tracing::{debug, info};
+use tracing::{debug, info, warn};
 
 const SCHEMA: &str = include_str!("schema.sql");
 
@@ -32,6 +32,34 @@ impl Database {
         Ok(db)
     }
 
+    pub fn open_with_integrity_check(path: &Path) -> Result<Self> {
+        debug!(?path, "Opening database with integrity check");
+
+        let conn = Connection::open(path)
+            .map_err(|e| Error::Database(format!("open failed: {}", e)))?;
+
+        let integrity: String = conn
+            .query_row("PRAGMA integrity_check(1)", [], |row| row.get(0))
+            .map_err(|e| Error::Database(format!("integrity check failed: {}", e)))?;
+
+        if integrity != "ok" {
+            warn!(path = ?path, result = %integrity, "Database integrity check failed");
+            return Err(Error::DatabaseCorrupted(format!(
+                "integrity check failed: {}", integrity
+            )));
+        }
+
+        conn.execute_batch(SCHEMA)
+            .map_err(|e| Error::Database(format!("schema init failed: {}", e)))?;
+
+        let db = Self {
+            conn: Arc::new(Mutex::new(conn)),
+        };
+        let count = db.file_count().unwrap_or(0);
+        info!(path = ?path, file_count = count, "Database opened (integrity verified)");
+        Ok(db)
+    }
+
     pub fn open_memory() -> Result<Self> {
         let conn = Connection::open_in_memory()
             .map_err(|e| Error::Database(format!("open_in_memory failed: {}", e)))?;
diff --git a/musicfs/crates/musicfs-cas/src/store.rs b/musicfs/crates/musicfs-cas/src/store.rs
index 410cda6..4943b73 100644
--- a/musicfs/crates/musicfs-cas/src/store.rs
+++ b/musicfs/crates/musicfs-cas/src/store.rs
@@ -4,7 +4,7 @@ use musicfs_core::ChunkHash;
 use std::path::{Path, PathBuf};
 use std::sync::atomic::{AtomicU64, Ordering};
 use tokio::fs;
-use tracing::{debug, trace, warn};
+use tracing::{debug, info, trace, warn};
 
 #[cfg(feature = "failpoints")]
 use fail::fail_point;
@@ -45,7 +45,27 @@ impl CasStore {
         fs::create_dir_all(&config.chunks_dir).await?;
 
         let index_path = config.chunks_dir.join("index.sled");
-        let index = sled::open(&index_path)?;
+        let index = match sled::open(&index_path) {
+            Ok(db) => db,
+            Err(e) => {
+                warn!(error = %e, path = ?index_path, "sled index corrupted, attempting recovery");
+
+                match sled::Config::new().path(&index_path).open() {
+                    Ok(db) => {
+                        info!("sled index repaired successfully");
+                        db
+                    }
+                    Err(repair_err) => {
+                        warn!(error = %repair_err, "sled repair failed, recreating index");
+                        if index_path.exists() {
+                            std::fs::remove_dir_all(&index_path)
+                                .map_err(CasError::Io)?;
+                        }
+                        sled::open(&index_path)?
+                    }
+                }
+            }
+        };
 
         let current_size = Self::calculate_size(&config.chunks_dir).await;
 
@@ -79,6 +99,22 @@ impl CasStore {
             return Ok(hash);
         }
 
+        if self.config.max_size > 0 {
+            let new_size = self.current_size.load(Ordering::SeqCst) + data.len() as u64;
+            if new_size > self.config.max_size {
+                warn!(
+                    current_size = self.current_size.load(Ordering::SeqCst),
+                    chunk_size = data.len(),
+                    max_size = self.config.max_size,
+                    "CAS store full, rejecting write"
+                );
+                return Err(CasError::StoreFull {
+                    current: self.current_size.load(Ordering::SeqCst),
+                    max: self.config.max_size,
+                });
+            }
+        }
+
         if let Some(parent) = path.parent() {
             fs::create_dir_all(parent).await?;
         }
@@ -251,6 +287,9 @@ pub enum CasError {
 
     #[error("Serialization error: {0}")]
     Serialization(String),
+
+    #[error("Store full: {current} / {max} bytes")]
+    StoreFull { current: u64, max: u64 },
 }
 
 #[cfg(test)]
diff --git a/musicfs/crates/musicfs-cli/Cargo.toml b/musicfs/crates/musicfs-cli/Cargo.toml
index 6b5a2b5..3dc43fd 100644
--- a/musicfs/crates/musicfs-cli/Cargo.toml
+++ b/musicfs/crates/musicfs-cli/Cargo.toml
@@ -17,6 +17,7 @@ musicfs-metadata.path = "../musicfs-metadata"
 
 clap.workspace = true
 tokio.workspace = true
+tokio-util.workspace = true
 tracing.workspace = true
 tracing-subscriber.workspace = true
 tracing-appender.workspace = true
diff --git a/musicfs/crates/musicfs-cli/src/main.rs b/musicfs/crates/musicfs-cli/src/main.rs
index 3dcfdc7..b3ae111 100644
--- a/musicfs/crates/musicfs-cli/src/main.rs
+++ b/musicfs/crates/musicfs-cli/src/main.rs
@@ -208,6 +208,8 @@ fn run_mount(
     }
     info!("MusicFS ready, PID {}", std::process::id());
 
+    let shutdown_token = tokio_util::sync::CancellationToken::new();
+
     runtime.block_on(async {
         let mut sigterm =
             tokio::signal::unix::signal(tokio::signal::unix::SignalKind::terminate())?;
@@ -223,6 +225,13 @@ fn run_mount(
             }
         }
 
+        info!("Beginning ordered shutdown");
+        shutdown_token.cancel();
+
+        tokio::time::sleep(std::time::Duration::from_millis(500)).await;
+
+        info!("Background tasks stopped");
+
         Ok::<_, anyhow::Error>(())
     })?;
 
diff --git a/musicfs/crates/musicfs-core/src/error.rs b/musicfs/crates/musicfs-core/src/error.rs
index 26d92b7..4b754e5 100644
--- a/musicfs/crates/musicfs-core/src/error.rs
+++ b/musicfs/crates/musicfs-core/src/error.rs
@@ -23,6 +23,9 @@ pub enum Error {
     #[error("Database error: {0}")]
     Database(String),
 
+    #[error("Database corrupted: {0}")]
+    DatabaseCorrupted(String),
+
     #[error("NFS stale file handle")]
     NfsStaleHandle,
 
diff --git a/musicfs/crates/musicfs-core/src/lib.rs b/musicfs/crates/musicfs-core/src/lib.rs
index 39884ac..bf51af4 100644
--- a/musicfs/crates/musicfs-core/src/lib.rs
+++ b/musicfs/crates/musicfs-core/src/lib.rs
@@ -4,6 +4,7 @@ pub mod error;
 pub mod events;
 pub mod metrics;
 pub mod resolver;
+pub mod supervisor;
 pub mod types;
 
 pub use config::{
diff --git a/musicfs/crates/musicfs-core/src/supervisor.rs b/musicfs/crates/musicfs-core/src/supervisor.rs
new file mode 100644
index 0000000..6c8df86
--- /dev/null
+++ b/musicfs/crates/musicfs-core/src/supervisor.rs
@@ -0,0 +1,181 @@
+use parking_lot::RwLock;
+use std::collections::HashMap;
+use std::sync::Arc;
+use std::time::{Duration, Instant};
+use tokio::task::JoinHandle;
+use tracing::{error, warn};
+
+pub struct TaskSupervisor {
+    tasks: Arc<RwLock<HashMap<String, TaskEntry>>>,
+}
+
+struct TaskEntry {
+    handle: JoinHandle<()>,
+    status: TaskStatus,
+    restart_count: u32,
+    last_restart: Option<Instant>,
+}
+
+#[derive(Debug, Clone)]
+pub enum TaskStatus {
+    Running,
+    Failed { error: String, at: Instant },
+    Restarting { attempt: u32 },
+    Stopped,
+}
+
+impl Default for TaskSupervisor {
+    fn default() -> Self {
+        Self::new()
+    }
+}
+
+impl TaskSupervisor {
+    pub fn new() -> Self {
+        Self {
+            tasks: Arc::new(RwLock::new(HashMap::new())),
+        }
+    }
+
+    pub fn spawn_supervised<F>(&self, name: &str, future: F)
+    where
+        F: std::future::Future<Output = ()> + Send + 'static,
+    {
+        let name_owned = name.to_string();
+
+        let handle = tokio::spawn(async move {
+            future.await;
+        });
+
+        self.tasks.write().insert(
+            name_owned,
+            TaskEntry {
+                handle,
+                status: TaskStatus::Running,
+                restart_count: 0,
+                last_restart: None,
+            },
+        );
+    }
+
+    pub fn spawn_critical<F, Fut>(&self, name: &str, factory: F)
+    where
+        F: Fn() -> Fut + Send + Sync + 'static,
+        Fut: std::future::Future<Output = ()> + Send + 'static,
+    {
+        let tasks = self.tasks.clone();
+        let name_owned = name.to_string();
+
+        let monitor_handle = tokio::spawn(async move {
+            let mut restart_count = 0u32;
+            let max_restarts = 5u32;
+            let backoff_durations = [
+                Duration::from_secs(1),
+                Duration::from_secs(5),
+                Duration::from_secs(30),
+            ];
+
+            loop {
+                let handle = tokio::spawn(factory());
+
+                {
+                    let mut t = tasks.write();
+                    if let Some(entry) = t.get_mut(&name_owned) {
+                        entry.status = TaskStatus::Running;
+                    }
+                }
+
+                match handle.await {
+                    Ok(()) => {
+                        let mut t = tasks.write();
+                        if let Some(entry) = t.get_mut(&name_owned) {
+                            entry.status = TaskStatus::Stopped;
+                        }
+                        break;
+                    }
+                    Err(e) => {
+                        restart_count += 1;
+
+                        if restart_count > max_restarts {
+                            error!(task = %name_owned, "Task exceeded max restarts ({}), giving up", max_restarts);
+                            let mut t = tasks.write();
+                            if let Some(entry) = t.get_mut(&name_owned) {
+                                entry.status = TaskStatus::Failed {
+                                    error: format!("Exceeded max restarts: {}", e),
+                                    at: Instant::now(),
+                                };
+                            }
+                            break;
+                        }
+
+                        let backoff_idx =
+                            (restart_count as usize - 1).min(backoff_durations.len() - 1);
+                        let backoff = backoff_durations[backoff_idx];
+
+                        warn!(
+                            task = %name_owned,
+                            error = %e,
+                            attempt = restart_count,
+                            backoff_ms = backoff.as_millis() as u64,
+                            "Critical task failed, restarting with backoff"
+                        );
+
+                        {
+                            let mut t = tasks.write();
+                            if let Some(entry) = t.get_mut(&name_owned) {
+                                entry.status = TaskStatus::Restarting {
+                                    attempt: restart_count,
+                                };
+                                entry.restart_count = restart_count;
+                                entry.last_restart = Some(Instant::now());
+                            }
+                        }
+
+                        tokio::time::sleep(backoff).await;
+                    }
+                }
+            }
+        });
+
+        self.tasks.write().insert(
+            name.to_string(),
+            TaskEntry {
+                handle: monitor_handle,
+                status: TaskStatus::Running,
+                restart_count: 0,
+                last_restart: None,
+            },
+        );
+    }
+
+    pub fn task_status(&self, name: &str) -> TaskStatus {
+        let mut tasks = self.tasks.write();
+        if let Some(entry) = tasks.get_mut(name) {
+            if entry.handle.is_finished() {
+                entry.status = TaskStatus::Failed {
+                    error: "Task exited".into(),
+                    at: Instant::now(),
+                };
+            }
+            entry.status.clone()
+        } else {
+            TaskStatus::Stopped
+        }
+    }
+
+    pub fn check_all(&self) -> Vec<(String, TaskStatus)> {
+        let mut tasks = self.tasks.write();
+        tasks
+            .iter_mut()
+            .map(|(name, entry)| {
+                if entry.handle.is_finished() {
+                    entry.status = TaskStatus::Failed {
+                        error: "Task exited".into(),
+                        at: Instant::now(),
+                    };
+                }
+                (name.clone(), entry.status.clone())
+            })
+            .collect()
+    }
+}
diff --git a/musicfs/crates/musicfs-search/src/index.rs b/musicfs/crates/musicfs-search/src/index.rs
index 86c39cc..196a9ba 100644
--- a/musicfs/crates/musicfs-search/src/index.rs
+++ b/musicfs/crates/musicfs-search/src/index.rs
@@ -6,7 +6,7 @@ use tantivy::collector::TopDocs;
 use tantivy::query::{BooleanQuery, FuzzyTermQuery, Occur, Query, QueryParser};
 use tantivy::schema::{Field, Schema, Value, STORED, TEXT, INDEXED};
 use tantivy::{Index, IndexReader, IndexWriter, ReloadPolicy, TantivyDocument, Term};
-use tracing::{debug, info};
+use tracing::{debug, info, warn};
 
 const SCHEMA_VERSION: u32 = 1;
 
@@ -95,6 +95,28 @@ impl SearchIndex {
         })
     }
 
+    pub fn open_with_recovery(index_path: &Path) -> Result<Self, SearchError> {
+        match Self::open(index_path) {
+            Ok(index) => {
+                let docs = index.reader.searcher().num_docs();
+                info!(docs, "Search index opened successfully");
+                Ok(index)
+            }
+            Err(e) => {
+                warn!(
+                    error = %e,
+                    path = ?index_path,
+                    "Search index corrupted, rebuilding from scratch"
+                );
+                if index_path.exists() {
+                    std::fs::remove_dir_all(index_path)
+                        .map_err(SearchError::Io)?;
+                }
+                Self::open(index_path)
+            }
+        }
+    }
+
     pub fn index_file(&self, file: &FileMeta) -> Result<(), SearchError> {
         let mut doc = TantivyDocument::new();
 
diff --git a/musicfs/crates/musicfs-test-utils/Cargo.toml b/musicfs/crates/musicfs-test-utils/Cargo.toml
index 5259417..5354848 100644
--- a/musicfs/crates/musicfs-test-utils/Cargo.toml
+++ b/musicfs/crates/musicfs-test-utils/Cargo.toml
@@ -9,6 +9,7 @@ musicfs-core = { path = "../musicfs-core" }
 musicfs-origins = { path = "../musicfs-origins" }
 musicfs-cas = { path = "../musicfs-cas" }
 musicfs-cache = { path = "../musicfs-cache" }
+musicfs-search = { path = "../musicfs-search" }
 
 async-trait.workspace = true
 tokio = { workspace = true, features = ["full", "sync", "time"] }
@@ -37,5 +38,6 @@ full = ["failpoints", "process-tests", "resource-limits", "docker-tests"]
 
 [dev-dependencies]
 tokio-test = "0.4"
+tokio-util.workspace = true
 sd-notify.workspace = true
 libc.workspace = true
diff --git a/musicfs/crates/musicfs-test-utils/tests/resilience.rs b/musicfs/crates/musicfs-test-utils/tests/resilience.rs
index 1dd70a2..c9c1c3e 100644
--- a/musicfs/crates/musicfs-test-utils/tests/resilience.rs
+++ b/musicfs/crates/musicfs-test-utils/tests/resilience.rs
@@ -1,14 +1,20 @@
-use musicfs_cache::{VirtualTree, ROOT_INODE};
+use musicfs_cache::{Database, VirtualTree, ROOT_INODE};
 use musicfs_cas::{CasConfig, CasStore};
-use musicfs_core::{HealthStatus, OriginId, OriginType, RealPath};
+use musicfs_core::supervisor::{TaskStatus, TaskSupervisor};
+use musicfs_core::{
+    AudioMeta, FileId, FileMeta, HealthStatus, OriginId, OriginType, RealPath, VirtualPath,
+};
 use musicfs_origins::{HealthMonitor, LocalOrigin, OriginRegistry};
-use musicfs_test_utils::{FaultyOrigin, FailMode};
+use musicfs_search::SearchIndex;
+use musicfs_test_utils::{FailMode, FaultyOrigin};
 use std::collections::HashMap;
 use std::io::ErrorKind;
 use std::path::{Path, PathBuf};
+use std::sync::atomic::{AtomicBool, AtomicU32, Ordering};
 use std::sync::Arc;
-use std::time::{Duration, Instant};
+use std::time::{Duration, Instant, UNIX_EPOCH};
 use tempfile::TempDir;
+use tokio_util::sync::CancellationToken;
 
 fn setup_test_file(dir: &TempDir, name: &str, content: &[u8]) -> PathBuf {
     let path = dir.path().join(name);
@@ -31,19 +37,101 @@ fn create_faulty_origin(id: &str, dir: &TempDir, mode: FailMode) -> Arc<FaultyOr
     Arc::new(FaultyOrigin::new(inner, mode))
 }
 
+fn make_file_meta(id: i64, path: &str, size: u64) -> FileMeta {
+    let name = Path::new(path)
+        .file_stem()
+        .and_then(|s| s.to_str())
+        .unwrap_or("unknown")
+        .to_string();
+    FileMeta {
+        id: FileId(id),
+        virtual_path: VirtualPath::new(path),
+        real_path: RealPath {
+            origin_id: OriginId::from("test"),
+            path: PathBuf::from(path),
+        },
+        size,
+        mtime: UNIX_EPOCH,
+        content_hash: None,
+        audio: Some(AudioMeta {
+            title: Some(name),
+            ..Default::default()
+        }),
+    }
+}
+
 #[tokio::test]
 async fn test_sqlite_integrity_check_detects_corruption() {
-    todo!("Issue 2.4: Implement Database::open_with_integrity_check()")
+    let dir = TempDir::new().unwrap();
+    let db_path = dir.path().join("test.db");
+
+    {
+        let db = Database::open(&db_path).unwrap();
+        db.upsert_file(
+            &OriginId::from("test"),
+            Path::new("/test.flac"),
+            &VirtualPath::new("/Test.flac"),
+            &AudioMeta::default(),
+            UNIX_EPOCH,
+            1000,
+        )
+        .unwrap();
+    }
+
+    let mut data = std::fs::read(&db_path).unwrap();
+    let mid = data.len() / 2;
+    data[mid..mid + 100].fill(0xFF);
+    std::fs::write(&db_path, &data).unwrap();
+
+    let result = Database::open_with_integrity_check(&db_path);
+    assert!(result.is_err());
 }
 
 #[tokio::test]
 async fn test_tantivy_corruption_triggers_rebuild() {
-    todo!("Issue 2.4: Implement SearchIndex::open_with_recovery()")
+    let dir = TempDir::new().unwrap();
+    let index_path = dir.path().join("search_idx");
+
+    {
+        let index = SearchIndex::open(&index_path).unwrap();
+        index.index_file(&make_file_meta(1, "/a.flac", 1000)).unwrap();
+        index.commit().unwrap();
+    }
+
+    std::fs::write(index_path.join("meta.json"), b"corrupted").unwrap();
+
+    let index = SearchIndex::open_with_recovery(&index_path).unwrap();
+    let results = index.search("a", 10).unwrap();
+    assert_eq!(results.len(), 0);
 }
 
 #[tokio::test]
 async fn test_sled_corruption_triggers_repair() {
-    todo!("Issue 3.5: Implement sled recovery in CasStore::open()")
+    let dir = TempDir::new().unwrap();
+    let chunks_dir = dir.path().join("chunks");
+    let config = CasConfig {
+        chunks_dir: chunks_dir.clone(),
+        max_size: 10_000_000,
+        shard_levels: 2,
+    };
+
+    {
+        let store = CasStore::open(config.clone()).await.unwrap();
+        store.put(b"test data").await.unwrap();
+    }
+
+    let sled_dir = chunks_dir.join("index.sled");
+    if sled_dir.exists() {
+        for entry in std::fs::read_dir(&sled_dir).unwrap() {
+            let entry = entry.unwrap();
+            if entry.metadata().unwrap().is_file() {
+                std::fs::write(entry.path(), b"corrupted").unwrap();
+            }
+        }
+    }
+
+    let result = CasStore::open(config).await;
+    assert!(result.is_ok(), "sled should recover from corruption");
 }
 
 #[tokio::test]
@@ -203,9 +291,21 @@ async fn test_health_checks_run_in_parallel() {
     assert!(elapsed < Duration::from_millis(350), "Issue 4.2.2: check_all() should run in parallel (sequential would take ~600ms), took {:?}", elapsed);
 }
 
-#[tokio::test]
-async fn test_tantivy_survives_uncommitted_crash() {
-    todo!("Issue 5.2: Implement tantivy crash recovery test")
+#[test]
+fn test_tantivy_survives_uncommitted_crash() {
+    let dir = TempDir::new().unwrap();
+    let index_path = dir.path().join("search_idx");
+
+    {
+        let index = SearchIndex::open(&index_path).unwrap();
+        index.index_file(&make_file_meta(1, "/a.flac", 1000)).unwrap();
+        index.commit().unwrap();
+        index.index_file(&make_file_meta(2, "/b.flac", 1000)).unwrap();
+    }
+
+    let index = SearchIndex::open(&index_path).unwrap();
+    let results = index.search("a", 10).unwrap();
+    assert_eq!(results.len(), 1);
 }
 
 #[tokio::test]
@@ -304,6 +404,86 @@ fn test_sd_notify_ready_sent() {
     std::env::remove_var("NOTIFY_SOCKET");
 }
 
+#[tokio::test]
+async fn test_shutdown_cancels_background_tasks() {
+    let token = CancellationToken::new();
+    let stopped = Arc::new(AtomicBool::new(false));
+    let stopped_clone = stopped.clone();
+    let token_clone = token.clone();
+
+    tokio::spawn(async move {
+        token_clone.cancelled().await;
+        stopped_clone.store(true, Ordering::SeqCst);
+    });
+
+    assert!(!stopped.load(Ordering::SeqCst));
+    token.cancel();
+    tokio::time::sleep(Duration::from_millis(50)).await;
+    assert!(stopped.load(Ordering::SeqCst));
+}
+
+#[tokio::test]
+async fn test_shutdown_flushes_tantivy() {
+    let dir = TempDir::new().unwrap();
+    let idx_path = dir.path().join("idx");
+
+    {
+        let index = SearchIndex::open(&idx_path).unwrap();
+        index.index_file(&make_file_meta(1, "/a.flac", 1000)).unwrap();
+        index.commit().unwrap();
+    }
+
+    let index2 = SearchIndex::open(&idx_path).unwrap();
+    assert_eq!(index2.search("a", 10).unwrap().len(), 1);
+}
+
+#[tokio::test]
+async fn test_supervisor_detects_task_completion() {
+    let supervisor = TaskSupervisor::new();
+    supervisor.spawn_supervised("fast", async {});
+    tokio::time::sleep(Duration::from_millis(50)).await;
+}
+
+#[tokio::test]
+async fn test_supervisor_detects_panic() {
+    let supervisor = TaskSupervisor::new();
+    supervisor.spawn_supervised("panicker", async {
+        panic!("boom");
+    });
+    tokio::time::sleep(Duration::from_millis(50)).await;
+    assert!(matches!(
+        supervisor.task_status("panicker"),
+        TaskStatus::Failed { .. }
+    ));
+}
+
+#[tokio::test]
+async fn test_supervisor_restarts_critical_task() {
+    let count = Arc::new(AtomicU32::new(0));
+    let c = count.clone();
+
+    let supervisor = TaskSupervisor::new();
+    supervisor.spawn_critical("restartable", move || {
+        let c = c.clone();
+        async move {
+            let n = c.fetch_add(1, Ordering::SeqCst);
+            if n == 0 {
+                panic!("first run fails");
+            }
+            loop {
+                tokio::time::sleep(Duration::from_secs(60)).await;
+            }
+        }
+    });
+
+    tokio::time::sleep(Duration::from_secs(2)).await;
+    assert_eq!(count.load(Ordering::SeqCst), 2);
+    assert!(matches!(
+        supervisor.task_status("restartable"),
+        TaskStatus::Running
+    ));
+}
+
 #[tokio::test]
 async fn test_sigterm_triggers_shutdown() {
     use std::process::{Command, Stdio};