diff --git a/CHANGELOG.md b/CHANGELOG.md
index 6c34ef4..e05a297 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,21 @@ All notable changes to EigenScript are documented here.
 ## [Unreleased]
 
 ### Added
+- **`lib/supervise` — observer-native supervision (#409).** A supervisor over
+  the #408 cooperative task layer that, beyond BEAM-style crash-restart, also
+  catches the silently **wedged** worker — alive, not crashed, never timing
+  out, but no longer making progress — a signal BEAM structurally cannot see.
+  Workers publish raw progress with `heartbeat of [slot, value]`; the
+  supervisor samples each alive worker every tick, feeds a **bounded** signature
+  (`1.5 + v % 8`, dodging the #294 flat-entropy blind spot) into that slot's
+  observer trajectory, and restarts a worker whose signature has gone `stable`
+  after a warm-up window (the EigenOS red-title pattern, generalized) or that
+  died with an uncaught raise — each up to a per-worker restart-intensity cap.
+  `supervisor_new`, `supervise of [sup, fn, slot]`, `supervise_step`, and
+  `supervise_run of [sup, max_ticks]`. Deterministic by construction; flagship
+  `examples/supervisor_tree.eigs`. Surfaced a gap: a task cannot learn its own
+  id (no `task_self`), so the message-link supervision variant is not yet
+  expressible — filed separately.
 - **Lint `W018` — `e.kind` compared against an out-of-set error kind (#469).**
   A `catch` handler comparing a caught error's `.kind` against a string that is
   a near-miss of a real kind — a case variant (`"IO"`), a single-character typo
diff --git a/docs/STDLIB.md b/docs/STDLIB.md
index 4d1425a..9ab99b3 100644
--- a/docs/STDLIB.md
+++ b/docs/STDLIB.md
@@ -752,6 +752,19 @@ and the claim). `lock_new`, `lock_acquire`, `lock_release`, and
 if the body raises). Acquire only from within tasks — it spins with
 `task_yield`, so it needs the scheduler active.
 
+### lib/supervise.eigs
+Observer-native supervision over the #408 task layer. Beyond BEAM-style
+crash-restart, it also detects the silently **wedged** worker — alive, not
+crashed, never timing out, but no longer making progress — by sampling each
+worker's progress trajectory and seeing it go `stable` (the EigenOS
+red-title pattern generalized). Workers publish raw progress with
+`heartbeat of [slot, value]`; the supervisor turns it into a bounded
+signature (dodging the #294 flat-entropy blind spot). `supervisor_new`,
+`supervise of [sup, fn, slot]`, `supervise_step`, and `supervise_run of
+[sup, max_ticks]` (drive to settled); wedged and crashed workers are
+restarted from their spec under a per-worker restart-intensity cap. Eight
+slots. See `examples/supervisor_tree.eigs`.
+
 ### lib/store.eigs
 EigenStore high-level layer: `find`, `find_one`, `upsert`, `bulk_put`,
 `to_dataframe`.
diff --git a/examples/supervisor_tree.eigs b/examples/supervisor_tree.eigs
new file mode 100644
index 0000000..79c5b0d
--- /dev/null
+++ b/examples/supervisor_tree.eigs
@@ -0,0 +1,46 @@
+# ============================================================
+# supervisor_tree.eigs — observer-native supervision (#409)
+# ============================================================
+#
+# A worker pool of three tasks. Two are healthy; one silently WEDGES partway
+# through — it never crashes and never times out, so a crash-reactive
+# supervisor (BEAM-style) would watch it hang forever. Here the supervisor
+# samples each worker's progress trajectory and sees the frozen one go
+# `stable`, then restarts it from its spec. The restarted worker runs to
+# completion. Deterministic: this prints identically on every run.
+
+load_file of "lib/supervise.eigs"
+
+# A worker advances a counter, publishing progress each step. The one in the
+# "wedge slot" freezes on its FIRST life (infinite yield, progress stuck), and
+# on its restarted life runs cleanly to the end.
+wedge_slot is 1
+lives is [0, 0, 0]
+
+define worker(slot) as:
+    lives is set_at of [lives, slot, lives[slot] + 1]
+    life is lives[slot]
+    n is 0
+    loop while n < 12:
+        heartbeat of [slot, n]
+        # First life of the wedge-slot worker gets stuck at step 4.
+        if slot == wedge_slot and life == 1 and n == 4:
+            loop while 1 == 1:
+                heartbeat of [slot, 4]     # frozen — alive but no progress
+                task_yield of null
+        task_yield of null
+        n is n + 1
+    return f"worker {slot} finished"
+
+sup is supervisor_new of 3
+supervise of [sup, worker, 0]
+supervise of [sup, worker, 1]
+supervise of [sup, worker, 2]
+
+restarts is supervise_run of [sup, 1000]
+
+print of f"restarts performed: {restarts}"
+print of f"worker 0 completed: {_sup_done[0]}"
+print of f"worker 1 completed: {_sup_done[1]}"
+print of f"worker 2 completed: {_sup_done[2]}"
+print of "supervision tree settled"
diff --git a/lib/supervise.eigs b/lib/supervise.eigs
new file mode 100644
index 0000000..2856bc7
--- /dev/null
+++ b/lib/supervise.eigs
@@ -0,0 +1,227 @@
+# ============================================================
+# Supervise Library — observer-native supervision (#408 task layer)
+# ============================================================
+#
+# BEAM-style supervision restarts a worker when it CRASHES. An observer
+# supervisor also catches the worker that is silently WEDGED — alive, not
+# crashed, never timing out, but no longer making progress — a signal BEAM
+# structurally cannot see, because its processes carry no free per-value
+# trajectory measurement. This is the EigenOS window manager's red-title
+# pattern (a hung window detected via `stable of`), generalized over the #408
+# cooperative task layer.
+#
+# The model (share-nothing messages are unnecessary here — cooperative tasks
+# share the module-global heap on one thread):
+#   * A worker publishes RAW progress each step with `heartbeat of [slot, v]`.
+#   * The SUPERVISOR samples each alive worker's progress every tick, feeds a
+#     BOUNDED signature (1.5 + v % 8 — never a raw counter, which hits the
+#     #294 flat-entropy blind spot) into that slot's observer trajectory, and
+#     flags a worker whose signature has gone `stable` (frozen) after a
+#     warm-up window. Sampling on the SUPERVISOR side is what makes a wedge
+#     visible: a frozen worker stops calling heartbeat, so only the poller
+#     keeps adding the (now constant) samples that read `stable`.
+#   * A worker that returns normally is `done`; one that raises is `crashed`
+#     (caught by the wrapper, so a supervised crash never fails the process).
+#   * Wedged and crashed workers are restarted from their spec, up to
+#     `max_restarts` per worker (restart-intensity cap).
+#
+# How to use:
+#   load_file of "lib/supervise.eigs"
+#
+#   define worker(slot) as:
+#       n is 0
+#       loop while n < 100:
+#           heartbeat of [slot, n]     # publish progress
+#           task_yield of null
+#           n is n + 1
+#       return "ok"
+#
+#   sup is supervisor_new of 3          # up to 3 restarts per worker
+#   supervise of [sup, worker, 0]       # worker in slot 0
+#   supervise of [sup, worker, 1]
+#   restarts is supervise_run of [sup, 500]   # drive until done / 500 ticks
+#
+# Eight slots (the WM/task-table precedent). Slots are the caller's index
+# space; one supervised worker per slot.
+
+# --- Shared per-slot state (indexed by slot 0..7) ------------------------
+_sup_progress is [0, 0, 0, 0, 0, 0, 0, 0]   # each worker's latest raw progress
+_sup_done     is [0, 0, 0, 0, 0, 0, 0, 0]   # 1 when the worker returned normally
+_sup_crashed  is [0, 0, 0, 0, 0, 0, 0, 0]   # 1 when the worker raised
+_sup_warm     is [0, 0, 0, 0, 0, 0, 0, 0]   # observer samples since (re)start
+
+# --- Observer trajectory scalars (one NAMED binding per slot; a list element
+# has no trajectory, #262, so the eight signals need eight named scalars) ---
+_sup_o0 is 0.0
+_sup_o1 is 0.0
+_sup_o2 is 0.0
+_sup_o3 is 0.0
+_sup_o4 is 0.0
+_sup_o5 is 0.0
+_sup_o6 is 0.0
+_sup_o7 is 0.0
+
+# _sup_feed(slot, sig) — write the bounded signature into slot's trajectory.
+# `+ 0.0` forces a fresh value so an aliased iterate can't smuggle in an old
+# trajectory (#262).
+define _sup_feed(pair) as:
+    slot is pair[0]
+    sig is pair[1]
+    if slot == 0:
+        _sup_o0 is sig + 0.0
+    elif slot == 1:
+        _sup_o1 is sig + 0.0
+    elif slot == 2:
+        _sup_o2 is sig + 0.0
+    elif slot == 3:
+        _sup_o3 is sig + 0.0
+    elif slot == 4:
+        _sup_o4 is sig + 0.0
+    elif slot == 5:
+        _sup_o5 is sig + 0.0
+    elif slot == 6:
+        _sup_o6 is sig + 0.0
+    elif slot == 7:
+        _sup_o7 is sig + 0.0
+    else:
+        throw of "supervise: slot out of range (8 slots)"
+    return 1
+
+# _sup_stable(slot) — 1 if slot's signature trajectory has frozen.
+define _sup_stable(slot) as:
+    if slot == 0:
+        return stable of _sup_o0
+    elif slot == 1:
+        return stable of _sup_o1
+    elif slot == 2:
+        return stable of _sup_o2
+    elif slot == 3:
+        return stable of _sup_o3
+    elif slot == 4:
+        return stable of _sup_o4
+    elif slot == 5:
+        return stable of _sup_o5
+    elif slot == 6:
+        return stable of _sup_o6
+    elif slot == 7:
+        return stable of _sup_o7
+    throw of "supervise: slot out of range (8 slots)"
+
+# --- Public API ----------------------------------------------------------
+
+# supervisor_new(max_restarts) — a fresh supervisor with a per-worker restart
+# cap.
+define supervisor_new(max_restarts) as:
+    return {"children": [], "max_restarts": max_restarts}
+
+# heartbeat([slot, value]) — a worker calls this each step to publish its raw
+# progress. Any value that ADVANCES while the worker is healthy works; the
+# supervisor turns it into a bounded observer signature.
+define heartbeat(pair) as:
+    slot is pair[0]
+    value is pair[1]
+    _sup_progress is set_at of [_sup_progress, slot, value]
+    return 1
+
+# _run_child([fn, slot]) — the wrapper task. Runs the worker, records normal
+# completion; catches a raise as `crashed` so a supervised crash never turns
+# into an uncaught task death (which would fail the process, #493).
+define _run_child(pair) as:
+    fn is pair[0]
+    slot is pair[1]
+    try:
+        r is fn of slot
+        _sup_done is set_at of [_sup_done, slot, 1]
+        return r
+    catch e:
+        _sup_crashed is set_at of [_sup_crashed, slot, 1]
+        return null
+
+# _reset_slot(slot) — clear a slot's bookkeeping before a (re)start.
+define _reset_slot(slot) as:
+    _sup_progress is set_at of [_sup_progress, slot, 0]
+    _sup_done     is set_at of [_sup_done, slot, 0]
+    _sup_crashed  is set_at of [_sup_crashed, slot, 0]
+    _sup_warm     is set_at of [_sup_warm, slot, 0]
+    return 1
+
+# supervise([sup, fn, slot]) — spawn `fn` as a supervised worker in `slot`.
+# `fn` must accept its slot index and publish progress via `heartbeat`.
+define supervise(triple) as:
+    sup is triple[0]
+    fn is triple[1]
+    slot is triple[2]
+    _reset_slot of slot
+    id is task_spawn of [_run_child, [fn, slot]]
+    child is {"fn": fn, "slot": slot, "id": id, "restarts": 0}
+    sup.children is append of [sup.children, child]
+    return child
+
+# _restart([sup, child]) — restart a worker if under its cap. Returns 1 if it
+# restarted, else 0.
+define _restart(pair) as:
+    sup is pair[0]
+    child is pair[1]
+    if child.restarts >= sup.max_restarts:
+        return 0
+    slot is child.slot
+    if (task_alive of child.id) == 1:
+        task_kill of child.id
+    _reset_slot of slot
+    child.id is task_spawn of [_run_child, [child.fn, slot]]
+    child.restarts is child.restarts + 1
+    return 1
+
+# supervise_step(sup) — one supervision tick. Feeds each alive worker's
+# progress into its trajectory and restarts wedged (alive + frozen after the
+# warm-up window) or crashed (dead, raised) workers under the cap. Returns the
+# number of restarts performed this tick.
+define supervise_step(sup) as:
+    restarted is 0
+    for child in sup.children:
+        slot is child.slot
+        if (task_alive of child.id) == 1:
+            sig is 1.5 + (_sup_progress[slot] % 8)
+            _sup_feed of [slot, sig]
+            _sup_warm is set_at of [_sup_warm, slot, _sup_warm[slot] + 1]
+            warmed is _sup_warm[slot] >= 10
+            if warmed == 1 and (_sup_stable of slot) == 1:
+                restarted is restarted + (_restart of [sup, child])
+        else:
+            if _sup_crashed[slot] == 1:
+                restarted is restarted + (_restart of [sup, child])
+    return restarted
+
+# _all_settled(sup) — every worker has finished normally, or exhausted its
+# restart cap while still failing (so no further supervision can help).
+define _all_settled(sup) as:
+    for child in sup.children:
+        slot is child.slot
+        finished is (task_alive of child.id) == 0
+        done is _sup_done[slot] == 1
+        capped is child.restarts >= sup.max_restarts
+        if done == 1:
+            settled is 1
+        elif finished == 1 and capped == 1:
+            settled is 1
+        else:
+            settled is 0
+        if settled == 0:
+            return 0
+    return 1
+
+# supervise_run([sup, max_ticks]) — drive supervision from the main task until
+# every worker is settled or `max_ticks` elapse. Deterministic: the same
+# program replays identically. Returns the total number of restarts performed.
+define supervise_run(pair) as:
+    sup is pair[0]
+    max_ticks is pair[1]
+    t is 0
+    total is 0
+    loop while t < max_ticks:
+        if (_all_settled of sup) == 1:
+            return total
+        total is total + (supervise_step of sup)
+        task_yield of null
+        t is t + 1
+    return total
diff --git a/tests/run_all_tests.sh b/tests/run_all_tests.sh
index 3e10361..0ad551d 100755
--- a/tests/run_all_tests.sh
+++ b/tests/run_all_tests.sh
@@ -2179,6 +2179,12 @@ check_eigs_suite "cooperative tasks: yield/join/deadlock/teardown (#408)" test_t
 # with_lock releases + re-raises on abort.
 check_eigs_suite "lib/sync cooperative locks (#488)" test_sync.eigs "All tests passed" 1
 
+# lib/supervise — observer-native supervision over the #408 task layer (#409):
+# a wedged worker (alive, progress frozen) is detected via its observer
+# trajectory and restarted; a crashed worker is restarted; a healthy worker is
+# left alone; restart-intensity is capped.
+check_eigs_suite "lib/supervise observer supervision (#409)" test_supervise.eigs "All tests passed" 1
+
 # #408 determinism-by-construction: a task program with cooperative yields must
 # print byte-identically on two fresh processes (the signature property — the
 # interleaving is a pure function of program order, no tape).
diff --git a/tests/test_supervise.eigs b/tests/test_supervise.eigs
new file mode 100644
index 0000000..e83ed24
--- /dev/null
+++ b/tests/test_supervise.eigs
@@ -0,0 +1,73 @@
+# lib/supervise.eigs — observer-native supervision over the #408 task layer:
+# a wedged worker (alive, progress frozen, no crash, no timeout) is detected
+# via its observer trajectory and restarted; a crashed worker is restarted;
+# a healthy worker is left alone; restart-intensity is capped. Deterministic
+# by construction (the cooperative task layer).
+load_file of "lib/test.eigs"
+load_file of "lib/supervise.eigs"
+
+# --- 1. Healthy worker is never restarted; wedged worker (frozen progress) is
+#        detected and restarted once, then recovers ------------------------
+define healthy(slot) as:
+    n is 0
+    loop while n < 20:
+        heartbeat of [slot, n]
+        task_yield of null
+        n is n + 1
+    return "ok"
+
+wedge_lives is 0
+define flaky(slot) as:
+    wedge_lives is wedge_lives + 1
+    life is wedge_lives
+    if life == 1:
+        # WEDGE: alive forever, progress frozen — no crash, no timeout.
+        loop while 1 == 1:
+            heartbeat of [slot, 5]
+            task_yield of null
+    n is 0
+    loop while n < 20:
+        heartbeat of [slot, n]
+        task_yield of null
+        n is n + 1
+    return "recovered"
+
+sup is supervisor_new of 3
+supervise of [sup, healthy, 0]
+supervise of [sup, flaky, 1]
+r1 is supervise_run of [sup, 500]
+assert_eq of [r1, 1, "wedged worker detected + restarted exactly once"]
+assert_eq of [_sup_done[0], 1, "healthy worker completed (never restarted)"]
+assert_eq of [_sup_done[1], 1, "flaky worker recovered after its restart"]
+
+# --- 2. Crashed worker is restarted, and the caught crash does NOT fail the
+#        run (supervised crash is recovered, not fatal) --------------------
+crash_lives is 0
+define crasher(slot) as:
+    crash_lives is crash_lives + 1
+    life is crash_lives
+    heartbeat of [slot, 1]
+    task_yield of null
+    if life == 1:
+        throw of "boom"
+    return "recovered"
+
+sup2 is supervisor_new of 3
+supervise of [sup2, crasher, 0]
+r2 is supervise_run of [sup2, 200]
+assert_eq of [r2, 1, "crashed worker restarted exactly once"]
+assert_eq of [_sup_done[0], 1, "crashed worker recovered on restart"]
+
+# --- 3. Restart-intensity cap: a worker that always wedges is restarted at
+#        most max_restarts times, then supervision gives up ----------------
+define always_wedge(slot) as:
+    loop while 1 == 1:
+        heartbeat of [slot, 7]
+        task_yield of null
+
+sup3 is supervisor_new of 2
+supervise of [sup3, always_wedge, 0]
+r3 is supervise_run of [sup3, 400]
+assert_eq of [r3, 2, "restart-intensity cap honored (max_restarts=2)"]
+
+test_summary of null