Record the inputs a run actually starts from, not only the ones passed

A run submitted without explicit inputs recorded `params = {}`: Port
initials filled the values at node level and were never written back, so an
exported row had a blank `param.*` cell and the runs listing could not tell
a run that took every default from one submitted with those same numbers.
Declared initials are now folded in at submit, explicit values winning, and
the run-level seed still wins over a declared one.

`params_digest` is computed over the resolved values, so it changes shape
once: a run recorded before this does not dedupe against a newer identical
submit, and its stage-cache entries miss once.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_019Hra4ndWMCLU5F3KjUuVAc

backend/tests/api/routes/test_runs.py

@@ -400,6 +400,63 @@ def test_a_repeated_submit_returns_the_run_it_already_made():
     assert again.id == "dedup-1"
 
 
+class _OneFlow:
+    """A controller that has exactly one flow and no engine behind it."""
+
+    def __init__(self, flow):
+        self.store = self
+        self._flow = flow
+
+    def read_flow(self, name, draft=False):
+        return self._flow
+
+    def head(self):
+        return ""
+
+
+class _Collect:
+    def __init__(self):
+        self.items = []
+
+    def add(self, item):
+        self.items.append(item)
+
+
+def test_a_run_records_the_inputs_it_actually_starts_from():
+    """An input left out takes its declared value, and the row says so.
+
+    `params = {}` could not tell a run that took every default from one
+    submitted with those same numbers spelled out — and an export of the
+    first had a blank cell where its `lr` should be.
+    """
+    flow = FlowDef(
+        name="study",
+        mode="batch",
+        inputs=[
+            FlowInput(
+                spec=MessageSpec(name="lr", dtype=DType.FLOAT), initial=0.01
+            ),
+            FlowInput(spec=MessageSpec(name="epochs", dtype=DType.INT)),
+        ],
+    )
+    service = RunService(controller=_OneFlow(flow), queue=_Collect())
+    made = []
+    try:
+        defaulted = service.submit("study", {"epochs": 5})
+        made.append(defaulted.id)
+        assert defaulted.params == {"lr": 0.01, "epochs": 5}
+
+        # Spelling out the declared value is the same run, and now reads as it.
+        spelled = service.submit("study", {"lr": 0.01, "epochs": 5})
+        made.append(spelled.id)
+        assert spelled.params_digest == defaulted.params_digest
+    finally:
+        with Session(db_engine) as session:
+            for run in session.exec(select(Run).where(col(Run.id).in_(made))).all():
+                session.delete(run)
+            session.commit()
+
+
 def test_a_key_nobody_used_submits_normally(
     client, superuser_token_headers, monkeypatch
 ):