feat(synthesis): Lead/Provenance model + grounded leads + conjecture generator

- codex/synthesis.py: Lead/Provenance dataclasses, find_connections/gaps/improvements,
  propose_conjectures (status=unverified, quarantined in leads/conjectures/),
  write_leads (grounded→leads/grounded/, conjectures→leads/conjectures/ HARD invariant)
- codex/cli.py: synthesis leads/conjectures/report command group
- codex/config.py: F-13 settings (leads_dir, synthesis_llm_*, synthesis_top_k,
  synthesis_min_grounded_ratio, synthesis_gap_min_coverage)
- tests/synthesis/: 42 tests covering model, grounding, conjecture invariant, quarantine, CLI
- spike/: F-13 spike script + output (live run attempted)

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

codex/config.py

@@ -134,6 +134,59 @@ class Settings(BaseSettings):
         ),
     )
 
+    # ------------------------------------------------------------------
+    # F-13 Synthesis / Lead-Engine
+    # ------------------------------------------------------------------
+    leads_dir: str = Field(
+        default="leads/",
+        description=(
+            "Directory where generated leads are written. "
+            "Grounded leads → leads/grounded/, conjectures → leads/conjectures/. "
+            "Relative paths are resolved from the current working directory."
+        ),
+    )
+
+    synthesis_llm_model: str = Field(
+        default="qwen2.5:7b",
+        description=(
+            "Ollama model name used for synthesis. "
+            "Must be available at the configured Ollama endpoint."
+        ),
+    )
+
+    synthesis_llm_url: str | None = Field(
+        default=None,
+        description=(
+            "Ollama base URL for synthesis. "
+            "When None, falls back to OLLAMA_BASE_URL."
+        ),
+    )
+
+    synthesis_top_k: int = Field(
+        default=20,
+        gt=0,
+        description="Number of top chunks retrieved per topic for synthesis.",
+    )
+
+    synthesis_min_grounded_ratio: float = Field(
+        default=0.5,
+        ge=0.0,
+        le=1.0,
+        description=(
+            "Minimum fraction of claims that must be grounded for a lead to be "
+            "emitted as grounded (not marked ⚠)."
+        ),
+    )
+
+    synthesis_gap_min_coverage: int = Field(
+        default=2,
+        gt=0,
+        description=(
+            "Minimum number of papers covering a topic before it is NOT flagged as a gap. "
+            "Topics with fewer papers → gap lead generated."
+        ),
+    )
+
     # ------------------------------------------------------------------
     # F-09 Rich Parsing
     # ------------------------------------------------------------------