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>

tests/synthesis/test_conjecture.py

@@ -0,0 +1,113 @@
+"""Tests for stage-5 conjecture generation.
+
+HARD invariant: every conjecture MUST carry status='unverified', a
+non-empty suggested_validation, and non-empty provenance.
+"""
+
+from __future__ import annotations
+
+from pathlib import Path
+
+from codex.synthesis import _parse_conjecture_output, propose_conjectures
+from tests.synthesis.conftest import StubLLM
+
+_VALID_CONJECTURE = (
+    "Title: A discrete cosmetic-surgery analogue exists for Yamabe flows.\n"
+    "Body: The combinatorial Yamabe flow [Luo2004 #chunk 0] is a discrete "
+    "analogue of conformal change. One could hope the cosmetic surgery "
+    "conjecture has a discrete formulation in this setting.\n"
+    "Validation: Search for a counter-example among simplicial 3-manifolds "
+    "with at most 12 tetrahedra using a CSP solver."
+)
+
+_MISSING_VALIDATION = (
+    "Title: A naive idea.\n"
+    "Body: Some thoughts that follow [Luo2004 #chunk 0]. No falsification path "
+    "is described."
+)
+
+
+def test_parse_valid_conjecture_output() -> None:
+    """_parse_conjecture_output extracts title / body / validation."""
+    parsed = _parse_conjecture_output(_VALID_CONJECTURE)
+    assert parsed is not None
+    title, body, validation = parsed
+    assert title.startswith("A discrete cosmetic-surgery")
+    assert "Luo2004" in body
+    assert "counter-example" in validation
+
+
+def test_parse_conjecture_missing_validation_returns_none() -> None:
+    """Output without a Validation: line is rejected."""
+    assert _parse_conjecture_output(_MISSING_VALIDATION) is None
+
+
+def test_parse_conjecture_empty_input() -> None:
+    """Empty LLM output → None."""
+    assert _parse_conjecture_output("") is None
+
+
+def test_propose_conjectures_marks_status_unverified(
+    mock_retrieve: None,
+    mock_paper_titles: None,
+    mock_settings: Path,
+) -> None:
+    """Every emitted conjecture has status='unverified'."""
+    llm = StubLLM(_VALID_CONJECTURE)
+    leads = propose_conjectures(top_k=6, llm=llm)
+    assert len(leads) >= 1
+    for lead in leads:
+        assert lead.kind == "conjecture"
+        assert lead.status == "unverified"
+
+
+def test_propose_conjectures_requires_validation(
+    mock_retrieve: None,
+    mock_paper_titles: None,
+    mock_settings: Path,
+) -> None:
+    """Every emitted conjecture has a non-empty suggested_validation."""
+    llm = StubLLM(_VALID_CONJECTURE)
+    leads = propose_conjectures(top_k=6, llm=llm)
+    assert len(leads) >= 1
+    for lead in leads:
+        assert lead.suggested_validation.strip() != ""
+
+
+def test_propose_conjectures_requires_provenance(
+    mock_retrieve: None,
+    mock_paper_titles: None,
+    mock_settings: Path,
+) -> None:
+    """Every conjecture has at least one Provenance entry (seed chunks)."""
+    llm = StubLLM(_VALID_CONJECTURE)
+    leads = propose_conjectures(top_k=6, llm=llm)
+    assert len(leads) >= 1
+    for lead in leads:
+        assert len(lead.provenance) >= 1
+
+
+def test_propose_conjectures_drops_when_validation_missing(
+    mock_retrieve: None,
+    mock_paper_titles: None,
+    mock_settings: Path,
+) -> None:
+    """LLM output without a Validation: line is rejected (zero leads)."""
+    llm = StubLLM(_MISSING_VALIDATION)
+    leads = propose_conjectures(top_k=6, llm=llm)
+    assert leads == []
+
+
+def test_propose_conjectures_handles_llm_failure(
+    mock_retrieve: None,
+    mock_paper_titles: None,
+    mock_settings: Path,
+) -> None:
+    """LLM raising → returns [] (mirrors F-12 graceful degradation)."""
+
+    class FailingLLM:
+        def generate(self, prompt: str, model: str) -> str:
+            raise ConnectionError("ollama unreachable")
+
+    leads = propose_conjectures(top_k=6, llm=FailingLLM())
+    assert leads == []