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/cli.py

@@ -12,6 +12,7 @@ app = typer.Typer(help="codex — personal knowledge base for scientific papers.
 discover_app = typer.Typer(help="Discovery queries over the citation graph.")
 prov_app = typer.Typer(help="Provenance: @cite scan, code_links, bib export.")
 wiki_app = typer.Typer(help="Wiki-compile: grounded concept pages over the RAG substrate.")
+synth_app = typer.Typer(help="Synthesis: grounded leads and quarantined conjectures (F-13).")
 # F-09: search sub-app with paper (semantic) and formula (FTS) subcommands
 search_app = typer.Typer(
     help="Search: semantic paper search and formula full-text search.",
@@ -20,6 +21,7 @@ search_app = typer.Typer(
 app.add_typer(discover_app, name="discover")
 app.add_typer(prov_app, name="provenance")
 app.add_typer(wiki_app, name="wiki")
+app.add_typer(synth_app, name="synthesis")
 app.add_typer(search_app, name="search")
 
 
@@ -346,3 +348,119 @@ def wiki_check(
         raise typer.Exit(1)
     else:
         typer.echo("All claims grounded.")
+
+
+# ---------------------------------------------------------------------------
+# F-13: Synthesis command group
+# ---------------------------------------------------------------------------
+
+
+@synth_app.command("leads")
+def synthesis_leads(
+    lib_path: Optional[str] = typer.Option(  # noqa: UP045
+        None,
+        "--lib-path",
+        help=(
+            "Path to a C++ source tree. Enables improvement leads (@cite-aware) and "
+            "code-vs-corpus gap detection. Without it only connection + topic gaps run."
+        ),
+    ),
+    output_dir: Optional[str] = typer.Option(  # noqa: UP045
+        None, "--output-dir", help="Override config.leads_dir."
+    ),
+) -> None:
+    """Generate grounded leads (stages 2-4) and write them to leads/grounded/."""
+    from codex.config import get_settings
+    from codex.synthesis import (
+        default_llm_client,
+        find_connections,
+        find_gaps,
+        find_improvements,
+        write_leads,
+    )
+
+    settings = get_settings()
+    leads_dir = output_dir or settings.leads_dir
+    llm = default_llm_client()
+
+    connections = find_connections(top_k=settings.synthesis_top_k, llm=llm)
+    gaps = find_gaps(lib_path=lib_path, llm=llm)
+    improvements = (
+        find_improvements(lib_path, top_k=settings.synthesis_top_k, llm=llm) if lib_path else []
+    )
+
+    all_leads = connections + gaps + improvements
+    write_leads(all_leads, leads_dir)
+
+    typer.echo(
+        f"Grounded leads written to {leads_dir}/grounded/: "
+        f"{len(connections)} connection · {len(gaps)} gap · {len(improvements)} improvement"
+    )
+
+
+@synth_app.command("conjectures")
+def synthesis_conjectures(
+    output_dir: Optional[str] = typer.Option(  # noqa: UP045
+        None, "--output-dir", help="Override config.leads_dir."
+    ),
+) -> None:
+    """Generate stage-5 conjecture leads — quarantined to leads/conjectures/.
+
+    INVARIANT (F-13 HARD): conjectures are NEVER written to wiki/. They
+    require a ``suggested_validation`` spike before they may be promoted.
+    """
+    from codex.config import get_settings
+    from codex.synthesis import default_llm_client, propose_conjectures, write_leads
+
+    settings = get_settings()
+    leads_dir = output_dir or settings.leads_dir
+    llm = default_llm_client()
+
+    conjectures = propose_conjectures(top_k=settings.synthesis_top_k, llm=llm)
+    write_leads(conjectures, leads_dir)
+
+    typer.echo(
+        f"Conjectures (UNVERIFIED) written to {leads_dir}/conjectures/: {len(conjectures)}"
+    )
+
+
+@synth_app.command("report")
+def synthesis_report(
+    output_dir: Optional[str] = typer.Option(  # noqa: UP045
+        None, "--output-dir", help="Override config.leads_dir."
+    ),
+) -> None:
+    """Show grounded leads and conjectures — visibly separated."""
+    from pathlib import Path
+
+    from codex.config import get_settings
+
+    settings = get_settings()
+    leads_dir = Path(output_dir or settings.leads_dir)
+    grounded_dir = leads_dir / "grounded"
+    conj_dir = leads_dir / "conjectures"
+
+    grounded_files = sorted(grounded_dir.glob("*.md")) if grounded_dir.exists() else []
+    conj_files = sorted(conj_dir.glob("*.md")) if conj_dir.exists() else []
+
+    typer.echo("=" * 72)
+    typer.echo(f"GROUNDED LEADS  ({len(grounded_files)})  → {grounded_dir}")
+    typer.echo("=" * 72)
+    if not grounded_files:
+        typer.echo("(none)")
+    for f in grounded_files:
+        first = f.read_text(encoding="utf-8").splitlines()[0]
+        typer.echo(f"  {first}")
+
+    typer.echo("")
+    typer.echo("=" * 72)
+    typer.echo(
+        f"CONJECTURES  ({len(conj_files)})  → {conj_dir}  "
+        "[UNVERIFIED — never in wiki/]"
+    )
+    typer.echo("=" * 72)
+    if not conj_files:
+        typer.echo("(none)")
+    for f in conj_files:
+        first = f.read_text(encoding="utf-8").splitlines()[0]
+        typer.echo(f"  {first}")