fix(llm): commit the staged head hash unconditionally on a recorded response

An unchained request with no system message staged None, and the record
step skipped the commit, so the previous head hash survived a transcript
that never received a head; a later chained request restoring that head
would have omitted it. The staged value is now committed as-is, None
included. Also pins each rejection predicate of is_usable_compression_point
with its own test.

application/llm/openai.py

@@ -1423,10 +1423,12 @@ class OpenAILLM(BaseLLM):
         if rid:
             self._last_response_id = rid
         # The provider recorded this request, so the head it carried (or
-        # kept) is now the chain's head.
-        if self._pending_system_hash is not None:
-            self._chain_system_hash = self._pending_system_hash
-            self._pending_system_hash = None
+        # kept) is now the chain's head — including "no head at all", when
+        # an unchained request went out without a system message: a stale
+        # hash would let a later chained request omit a head this
+        # transcript never received.
+        self._chain_system_hash = self._pending_system_hash
+        self._pending_system_hash = None
         self._last_response_call_ids = self._function_call_ids(response)
         usage = getattr(response, "usage", None)
         if usage is not None:

tests/api/answer/services/compression/test_compression_reuse.py

@@ -499,3 +499,34 @@ class TestUnusableSavedPoints:
 
         assert result.compression_performed
         assert svc.compress_and_save.call_args.kwargs["start_index"] == 2
+
+
+@pytest.mark.unit
+class TestUsablePointPredicates:
+    """Each rejection predicate of ``is_usable_compression_point`` on its own."""
+
+    def _with_later_point(self, **point):
+        conv = _compressed_conversation()
+        conv["queries"].append({"prompt": "q4", "response": "r4"})
+        conv["compression_metadata"]["compression_points"].append(
+            {"timestamp": "2026-09-04T09:00:00+00:00", "query_index": 3, **point}
+        )
+        return conv
+
+    def test_a_positive_count_does_not_rescue_a_blank_summary(self):
+        conv = self._with_later_point(compressed_summary="   ", compressed_token_count=12)
+        summary, recent = CompressionService(llm=None, model_id="m").get_compressed_context(conv)
+        assert summary == "S"
+        assert [q["prompt"] for q in recent] == ["q2", "q3", "q4"]
+
+    def test_a_zero_count_does_not_rescue_a_non_blank_summary(self):
+        conv = self._with_later_point(compressed_summary="newer", compressed_token_count=0)
+        summary, recent = CompressionService(llm=None, model_id="m").get_compressed_context(conv)
+        assert summary == "S"
+        assert [q["prompt"] for q in recent] == ["q2", "q3", "q4"]
+
+    def test_a_missing_count_with_a_summary_is_usable(self):
+        conv = self._with_later_point(compressed_summary="newer")
+        summary, recent = CompressionService(llm=None, model_id="m").get_compressed_context(conv)
+        assert summary == "newer"
+        assert [q["prompt"] for q in recent] == ["q4"]

tests/llm/test_responses_chain_budget.py

@@ -402,3 +402,17 @@ def test_output_capped_response_still_records_chain_state(monkeypatch):
     assert llm._responses_gen("gpt-5.6", _messages(), tools=None) == "partial"
     assert llm._last_response_id == "resp_len"
     assert llm._chain_system_hash is not None
+
+
+@pytest.mark.unit
+def test_recorded_request_without_a_head_clears_the_committed_hash(monkeypatch):
+    llm = _make_llm(monkeypatch)
+    llm._build_responses_input(_messages("sys v1"), None)
+    _accepted(llm, "resp_1")
+    # An unchained fallback with no system message at all is recorded: the
+    # new transcript holds no head, so the old hash must not survive it.
+    llm._build_responses_input([{"role": "user", "content": "q"}], None)
+    _accepted(llm, "resp_2")
+    assert llm._chain_system_hash is None
+    chained, _ = llm._build_responses_input(_messages("sys v1"), "resp_2")
+    assert _roles(chained) == ["system", "user"]