fix(search): re-gate Tier 0 — synthesis self-refuse / timeout / empty answer 일관 처리

이전 버그: synthesis LLM self-refuse(status=completed + refused=True) 또는
timeout/parse_failed/llm_error/empty answer 시 grounding/verifier flag 가 0건이라
re-gate 체인이 `else clean` 분기로 빠지며 `completeness="full"` 초기값이 보존됨.
결과: `completeness=full + refused=True + re_gate=clean` 모순 row 생성.

실측: baseline v1-400char (2026-04-17) 223 row 중 24 (10.8%) 해당.
  - LLM self-refuse: 20 (completed + refused=True)
  - synthesis timeout: 4 (timeout + refused=False + empty answer)

수정: re-gate 최상위에 Tier 0 삽입 + 판정 로직을 `_detect_synthesis_failure()`
helper 로 분리. self-refuse 는 `synthesis_self_refuse`, 메커니즘 실패는
`synthesis_failed({status})` 라벨로 구분. no_reason fallback 도 refuse_reason 우선
활용하도록 보강.

테스트: tests/test_synthesis_failure_regate.py — self-refuse / timeout /
parse_failed / llm_error / empty answer / whitespace / valid answer 총 10 case.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

tests/test_synthesis_failure_regate.py

@@ -0,0 +1,123 @@
+"""Phase 3.5 fix3: re-gate Tier 0 — synthesis 자체 실패 처리.
+
+`_detect_synthesis_failure()` 단위 테스트.
+
+기존 버그:
+  synthesis LLM self-refuse (`sr.refused=True, status="completed"`) 또는
+  timeout/parse_failed/llm_error 시 grounding/verifier flag 0건 → re-gate else clean
+  분기로 빠져 `completeness="full"` 초기값이 남아 `full + refused=True` 모순.
+  baseline v1-400char 에서 24/223 (10.8%) 해당.
+
+Tier 0 판정:
+  - LLM self-refuse (completed + refused) → "synthesis_self_refuse"
+  - mechanical fail (timeout/parse_failed/llm_error) → "synthesis_failed({status})"
+  - answer 공백 → "synthesis_failed({status})"
+  - 유효 답변 → None (기존 tier 1~7 경로)
+"""
+
+from __future__ import annotations
+
+import os
+import sys
+
+sys.path.insert(0, os.path.join(os.path.dirname(__file__), "..", "app"))
+
+from api.search import _detect_synthesis_failure
+from services.search.synthesis_service import SynthesisResult
+
+
+def _sr(
+    status: str = "completed",
+    answer: str | None = "ok",
+    refused: bool = False,
+    refuse_reason: str | None = None,
+) -> SynthesisResult:
+    return SynthesisResult(
+        status=status,  # type: ignore[arg-type]
+        answer=answer,
+        used_citations=[],
+        confidence="low",
+        refused=refused,
+        refuse_reason=refuse_reason,
+        elapsed_ms=100.0,
+        cache_hit=False,
+    )
+
+
+# ─── self-refuse 케이스 ──────────────────────────────────
+
+
+def test_llm_self_refuse_completed():
+    """LLM 이 JSON 에 refused=true 반환 → synthesis_self_refuse."""
+    sr = _sr(status="completed", answer=None, refused=True, refuse_reason="범위 밖")
+    assert _detect_synthesis_failure(sr) == "synthesis_self_refuse"
+
+
+def test_llm_self_refuse_with_answer_still_refused():
+    """refused=True 면 answer 있어도 Tier 0 처리 (일관성)."""
+    sr = _sr(status="completed", answer="왜 답변함", refused=True)
+    assert _detect_synthesis_failure(sr) == "synthesis_self_refuse"
+
+
+# ─── mechanical failure 케이스 ──────────────────────────
+
+
+def test_timeout():
+    sr = _sr(status="timeout", answer=None, refused=False)
+    assert _detect_synthesis_failure(sr) == "synthesis_failed(timeout)"
+
+
+def test_parse_failed():
+    sr = _sr(status="parse_failed", answer=None, refused=False)
+    assert _detect_synthesis_failure(sr) == "synthesis_failed(parse_failed)"
+
+
+def test_llm_error():
+    sr = _sr(status="llm_error", answer=None, refused=False)
+    assert _detect_synthesis_failure(sr) == "synthesis_failed(llm_error)"
+
+
+def test_refused_with_mechanical_fail_propagates_status():
+    """refused=True + status!=completed → synthesis_failed({status}) 형식."""
+    sr = _sr(status="timeout", answer=None, refused=True)
+    assert _detect_synthesis_failure(sr) == "synthesis_failed(timeout)"
+
+
+# ─── empty answer 케이스 ───────────────────────────────
+
+
+def test_empty_answer_completed():
+    """status=completed 인데 answer 공백 → synthesis_failed(completed)."""
+    sr = _sr(status="completed", answer="", refused=False)
+    assert _detect_synthesis_failure(sr) == "synthesis_failed(completed)"
+
+
+def test_whitespace_only_answer():
+    """공백/탭/개행만 있어도 empty 로 간주."""
+    sr = _sr(status="completed", answer="   \n\t  ", refused=False)
+    assert _detect_synthesis_failure(sr) == "synthesis_failed(completed)"
+
+
+def test_none_answer_completed():
+    """answer=None + status=completed → failed."""
+    sr = _sr(status="completed", answer=None, refused=False)
+    assert _detect_synthesis_failure(sr) == "synthesis_failed(completed)"
+
+
+# ─── 유효 답변 케이스 (None 반환) ──────────────────────
+
+
+def test_valid_answer_returns_none():
+    """status=completed + answer 있고 refused=False → Tier 0 통과 (None)."""
+    sr = _sr(status="completed", answer="교육 시간은 매년 6시간 이상이다 [1].", refused=False)
+    assert _detect_synthesis_failure(sr) is None
+
+
+def test_skipped_status_with_answer_passes():
+    """status=skipped 는 Tier 0 대상 아님 — 초기 refusal gate 에서 이미 early-return 처리됨.
+
+    (skipped 는 여기까지 도달하지 않는다는 전제. 만약 도달하더라도 refused 가 True 일 것.)
+    """
+    sr = _sr(status="skipped", answer="abc", refused=False)
+    # 이 경우 Tier 0 미발동 (answer 있고 refused 아님) — 정상 경로로 나감.
+    assert _detect_synthesis_failure(sr) is None