diff --git a/BUGS.md b/BUGS.md
index 0a470ef..1a9d1d6 100644
--- a/BUGS.md
+++ b/BUGS.md
@@ -40,17 +40,6 @@ remains the last prerequisite for running unattended.
 
 ## High — security
 
-### B-56 — `RateLimiter._buckets` is never pruned
-
-`app/auth/rate_limit.py:37`.
-
-The dict grows without bound, keyed by attacker-chosen strings (arbitrary
-usernames, and — via B-54 — arbitrary IPs). `decay_seconds` ages a bucket's
-*counter* but never removes the entry.
-
-Fix: evict entries whose last failure is older than `decay_seconds` (opportunistically
-on `record_failure`, or on a periodic sweep), and cap the dict size.
-
 ### B-57 — username matching is case-sensitive while the login throttle key is not
 
 `app/auth/routes.py:126` (`body.username.lower()`) vs `:132`
diff --git a/CLAUDE.md b/CLAUDE.md
index 891ea64..9549b70 100644
--- a/CLAUDE.md
+++ b/CLAUDE.md
@@ -8,7 +8,7 @@ The user communicates in Italian in chat — reply to them in Italian. Everythin
 
 ## Project status
 
-All 10 stages of the original build order are code-complete and unit-tested — 281 tests, all under `tests/unit/` (`tests/integration/` is an empty package). Beyond them: Docker + Caddy deployment, admin dashboard (`/admin`), static test UI (`/`), pending-inclusive balance display, an SSE push channel layered over the original polling, self-service password change + admin password reset, and the reconciliation/corroboration machinery below.
+All 10 stages of the original build order are code-complete and unit-tested — 287 tests, all under `tests/unit/` (`tests/integration/` is an empty package). Beyond them: Docker + Caddy deployment, admin dashboard (`/admin`), static test UI (`/`), pending-inclusive balance display, an SSE push channel layered over the original polling, self-service password change + admin password reset, and the reconciliation/corroboration machinery below.
 
 Verified on mainnet with real money: registration + address derivation, deposit crediting (1-conf), a real 10 PLM bet (broadcast → confirmed → change credited back), and one full round cycle (close → draw on a real block hash → 70/30 payout with sat math checked against the broadcast tx → confirmation → close → next round auto-opened). **Withdrawal and the RBF bump path have never been exercised against a live broadcast** — unit-tested only.
 
@@ -33,7 +33,7 @@ PYTHONPATH=. python scripts/decrypt_master_key.py     # ops recovery: decrypt+pr
 PYTHONPATH=. python scripts/encrypt_master_key.py     # ops bootstrap: import an externally-generated xprv (--overwrite to replace)
 PYTHONPATH=. python scripts/electrum_smoke_test.py    # manual check: connect, handshake, subscribe to headers, print the tip
 
-python -m pytest                                      # all 281 tests
+python -m pytest                                      # all 287 tests
 python -m pytest tests/unit/test_hd.py                # one file
 python -m pytest tests/unit/test_hd.py::test_derivation_is_deterministic   # one test
 ```
diff --git a/app/auth/rate_limit.py b/app/auth/rate_limit.py
index becd568..375a314 100644
--- a/app/auth/rate_limit.py
+++ b/app/auth/rate_limit.py
@@ -1,6 +1,15 @@
 import time
 from dataclasses import dataclass
 
+# B-56: bounds on _buckets, which is keyed by strings the caller chooses.
+# 50k entries is a few MB at ~100 bytes each — far more than any real deployment's
+# active attacker set, and small enough that filling it isn't a memory attack.
+_MAX_BUCKETS = 50_000
+# How often record_failure sweeps out spent entries. Cheap (one pass over a dict
+# that the sweep itself keeps small) and off the request's critical path in the
+# normal case, since a successful login records no failure at all.
+_SWEEP_INTERVAL_SECONDS = 60.0
+
 
 @dataclass
 class _Bucket:
@@ -29,22 +38,65 @@ class RateLimiter:
         base_delay: float = 2.0,
         max_delay: float = 300.0,
         decay_seconds: float = 900.0,
+        max_buckets: int = _MAX_BUCKETS,
+        sweep_interval_seconds: float = _SWEEP_INTERVAL_SECONDS,
     ) -> None:
         self._threshold = threshold
         self._base_delay = base_delay
         self._max_delay = max_delay
         self._decay_seconds = decay_seconds
+        self._max_buckets = max_buckets
+        self._sweep_interval_seconds = sweep_interval_seconds
         self._buckets: dict[str, _Bucket] = {}
+        self._last_sweep_at = time.monotonic()
+
+    def _is_spent(self, bucket: _Bucket, now: float) -> bool:
+        """Nothing left to remember: the lockout has expired *and* the failure count
+        would decay to zero on the next failure anyway. Dropping such a bucket is
+        indistinguishable from keeping it — which is what makes eviction safe."""
+        return bucket.locked_until <= now and now - bucket.last_failure_at > self._decay_seconds
+
+    def _prune(self, now: float) -> None:
+        """B-56: the dict was keyed by attacker-chosen strings (any username, and via
+        B-54 any IP) and only ever grew — `decay_seconds` aged a bucket's counter but
+        never removed the entry, so hammering login with random usernames was an
+        unbounded memory leak.
+
+        Spent buckets go first, and they carry no information, so that alone keeps
+        the dict at the size of the genuinely active attack surface. The hard cap
+        below is the backstop for a burst faster than the sweep interval: it evicts
+        the entries closest to expiry, i.e. the ones whose loss buys an attacker the
+        least — never the freshest lockouts, which are the ones actually holding an
+        attack back."""
+        for key in [k for k, b in self._buckets.items() if self._is_spent(b, now)]:
+            del self._buckets[key]
+        self._last_sweep_at = now
+
+        excess = len(self._buckets) - self._max_buckets
+        if excess > 0:
+            by_expiry = sorted(
+                self._buckets.items(), key=lambda item: (item[1].locked_until, item[1].last_failure_at)
+            )
+            for key, _ in by_expiry[:excess]:
+                del self._buckets[key]
 
     def retry_after(self, key: str) -> float:
         bucket = self._buckets.get(key)
         if bucket is None:
             return 0.0
-        remaining = bucket.locked_until - time.monotonic()
+        now = time.monotonic()
+        if self._is_spent(bucket, now):
+            # Self-cleaning read path: a key that's merely being probed never
+            # accumulates an entry that outlives its own usefulness.
+            del self._buckets[key]
+            return 0.0
+        remaining = bucket.locked_until - now
         return remaining if remaining > 0 else 0.0
 
     def record_failure(self, key: str) -> None:
         now = time.monotonic()
+        if now - self._last_sweep_at >= self._sweep_interval_seconds or len(self._buckets) > self._max_buckets:
+            self._prune(now)
         bucket = self._buckets.setdefault(key, _Bucket())
         if bucket.failures and now - bucket.last_failure_at > self._decay_seconds:
             bucket.failures = 0
diff --git a/tests/unit/test_rate_limit.py b/tests/unit/test_rate_limit.py
new file mode 100644
index 0000000..a7f00d4
--- /dev/null
+++ b/tests/unit/test_rate_limit.py
@@ -0,0 +1,91 @@
+"""B-56: RateLimiter._buckets is keyed by strings the caller chooses — any
+username, and (before B-54) any IP — and used to only ever grow. decay_seconds
+aged a bucket's *counter* but never removed the entry, so hammering login with
+random usernames was an unbounded memory leak. These tests pin both halves of
+the bound: spent entries are swept, and the dict has a hard cap.
+
+The throttling behaviour itself is exercised end-to-end in test_auth.py; what
+matters here is that pruning never hands an attacker a free pass.
+"""
+
+import time
+
+from app.auth.rate_limit import RateLimiter
+
+
+def _limiter(**kwargs) -> RateLimiter:
+    # sweep_interval_seconds=0 makes every record_failure sweep, so the tests are
+    # deterministic instead of depending on wall-clock timing.
+    kwargs.setdefault("sweep_interval_seconds", 0.0)
+    return RateLimiter(**kwargs)
+
+
+def test_spent_buckets_are_swept_on_the_next_failure():
+    limiter = _limiter(decay_seconds=0.05)
+    for i in range(50):
+        limiter.record_failure(f"user:{i}")
+    assert len(limiter._buckets) == 50
+
+    time.sleep(0.06)  # every bucket is now past decay_seconds and unlocked
+    limiter.record_failure("user:fresh")
+
+    assert list(limiter._buckets) == ["user:fresh"]
+
+
+def test_a_bucket_still_locking_someone_out_is_never_swept():
+    """The whole point of the entry: evicting it would reset the backoff and let the
+    attacker start over from a free attempt."""
+    limiter = _limiter(threshold=1, base_delay=300.0, decay_seconds=0.05)
+    limiter.record_failure("user:victim")
+    assert limiter.retry_after("user:victim") > 0
+
+    time.sleep(0.06)  # past decay_seconds, but the lockout is still running
+    limiter.record_failure("user:someone-else")
+
+    assert "user:victim" in limiter._buckets
+    assert limiter.retry_after("user:victim") > 0
+
+
+def test_the_dict_is_capped_even_within_one_sweep_interval():
+    """The cap is the backstop for a burst faster than the sweep interval, where
+    nothing has had time to expire yet."""
+    limiter = _limiter(max_buckets=10, sweep_interval_seconds=3600.0, decay_seconds=3600.0)
+    for i in range(200):
+        limiter.record_failure(f"ip:{i}")
+
+    assert len(limiter._buckets) <= 11  # the cap, plus the entry recorded after the last prune
+
+
+def test_the_cap_evicts_the_entries_closest_to_expiry_first():
+    """What gets dropped under pressure must buy an attacker the least. The deepest
+    lockout — the one built up over the most failures, and so the one actually
+    holding an attack back — has to be the last thing evicted, not collateral of a
+    flood of one-failure keys."""
+    limiter = _limiter(max_buckets=3, threshold=1, base_delay=1.0, max_delay=600.0)
+    for _ in range(10):
+        limiter.record_failure("ip:persistent")  # backoff doubles: locked for ~512s
+    for i in range(20):
+        limiter.record_failure(f"ip:filler{i}")  # one failure each: locked for ~1s
+
+    assert "ip:persistent" in limiter._buckets
+    assert limiter.retry_after("ip:persistent") > 100
+
+
+def test_retry_after_drops_a_spent_bucket_it_looks_at():
+    limiter = _limiter(decay_seconds=0.05)
+    limiter.record_failure("user:probe")
+
+    time.sleep(0.06)
+    assert limiter.retry_after("user:probe") == 0.0
+    assert limiter._buckets == {}
+
+
+def test_pruning_does_not_reset_a_live_failure_count():
+    """A bucket below the lockout threshold still carries state worth keeping: the
+    next failure must count as the second, not the first."""
+    limiter = _limiter(threshold=2, base_delay=300.0, decay_seconds=3600.0)
+    limiter.record_failure("user:a")
+    limiter.record_failure("user:b")  # triggers a sweep
+
+    limiter.record_failure("user:a")
+    assert limiter.retry_after("user:a") > 0