diff --git a/src/optimizer/app.py b/src/optimizer/app.py
index 6cf057c8b..9cd310624 100644
--- a/src/optimizer/app.py
+++ b/src/optimizer/app.py
@@ -46,20 +46,29 @@ def money(value):
     return None if value is None else round(value, 4)
 
 
-def dump_slow_request(payload, elapsed):
-    """Persist requests that exhausted the solver time limit, they are the ones worth replaying.
+# money the capped cost stage may leave unproven between its schedule and CBC's bound before
+# the request is dumped for replay. The cap keeps requests short of the time limit, so the gap
+# is what marks the ones worth replaying at a longer clock.
+DUMP_GAP = 1.0
+
+
+def dump_slow_request(payload, elapsed, gap):
+    """Persist requests worth replaying: those that exhausted the solver time limit, and those
+    the cost stage left more than DUMP_GAP of money unproven on.
 
     The elapsed time covers model building as well as solving, so a request that only exceeds
     the limit while building is caught too. That one is equally worth looking at.
     """
     path, limit = settings.dump_slow_requests, settings.time_limit
-    if not path or limit is None or elapsed < limit:
+    slow = limit is not None and elapsed >= limit
+    unproven = gap is not None and gap > DUMP_GAP
+    if not path or not (slow or unproven):
         return
 
     # one line per request, carrying the same "request" key as test_cases/*.json so a line
     # can be replayed by the existing harness
     line = json.dumps({"ts": datetime.now(timezone.utc).isoformat(timespec="seconds"),
-                       "elapsed": round(elapsed, 3), "request": payload}) + "\n"
+                       "elapsed": round(elapsed, 3), "gap": money(gap), "request": payload}) + "\n"
     try:
         pathlib.Path(path).parent.mkdir(parents=True, exist_ok=True)
         with open(path, "a") as f:
@@ -287,7 +296,7 @@ def post(self):
                 "steps": optimizer.T,
             }}), flush=True)
 
-            dump_slow_request(data, elapsed)
+            dump_slow_request(data, elapsed, optimizer.cost_stage_gap)
             return result
 
         except Exception as e:
diff --git a/src/optimizer/settings.py b/src/optimizer/settings.py
index 39c3ebf1b..34f72ddb1 100644
--- a/src/optimizer/settings.py
+++ b/src/optimizer/settings.py
@@ -21,4 +21,5 @@ class OptimizerSettings(BaseSettings):
     time_limit: float | None = Field(default=None, description="Time limit for the optimization process in seconds")
     log_subject: bool = Field(default=False, description="Log the JWT subject of every request. Off by default, it names accounts in the logs")
     dump_slow_requests: str | None = Field(default=None,
-                                           description="JSON Lines file requests that exhaust the solver time limit are appended to. Unset disables the dump")
+                                           description="JSON Lines file requests that exhaust the solver time limit, or leave more than one currency "
+                                                       "unit unproven in the cost stage, are appended to. Unset disables the dump")
diff --git a/tests/test_app.py b/tests/test_app.py
index a442e1840..52325c1bb 100644
--- a/tests/test_app.py
+++ b/tests/test_app.py
@@ -7,6 +7,7 @@
 import pulp
 import pytest
 
+import optimizer.app as app_module
 from optimizer.app import app, settings
 
 
@@ -138,6 +139,25 @@ def test_slow_requests_are_dumped(tmp_path, monkeypatch):
     assert json.loads(lines[1])["elapsed"] > 0
 
 
+def test_requests_with_an_open_gap_are_dumped(tmp_path, monkeypatch):
+    request = json.loads(pathlib.Path('test_cases/026-attenuate-grid-peaks.json').read_text())["request"]
+    dump = tmp_path / "gap.jsonl"
+    client = app.test_client()
+    monkeypatch.setattr(settings, "dump_slow_requests", str(dump))
+    # the solver reads its own settings from the environment, so force the split there
+    monkeypatch.setenv("OPTIMIZER_PROBE_SECONDS", "0")
+
+    # a proven cost stage has no gap to replay for
+    client.post("/optimize/charge-schedule", json=request)
+    assert not dump.exists()
+
+    monkeypatch.setattr(app_module, "DUMP_GAP", -1.0)
+    client.post("/optimize/charge-schedule", json=request)
+    line = json.loads(dump.read_text())
+    assert line["gap"] == 0
+    assert line["request"] == request
+
+
 def test_every_request_logs_a_solve_line(capsys):
     # the key names are the Log Analytics contract: the dashboard's KQL queries parse this line,
     # so renaming one breaks production attribution silently