fix(synthesis): namespace lead ids by kind to stop collisions (audit C-11)

Each stage (find_connections/gaps/improvements/propose_conjectures) numbered its
leads from seq=1, so connection L-0001, gap L-0001 and improvement L-0001 all
resolved to grounded/L-0001.md. The CLI concatenates them
(connections + gaps + improvements) and write_leads writes in order, so later
kinds silently overwrote earlier ones — survivors = max(per-kind count), not the
sum. Reproduced: 4 distinct leads -> 2 files.

_make_lead_id now takes the kind and emits L-C-/L-G-/L-I-/L-X- prefixes, keeping
same-seq ids distinct across stages. Regression tests cover the format and the
no-collision invariant.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

codex/synthesis.py

@@ -248,9 +248,23 @@ def _grounded_ratio(claims: list[Claim]) -> float:
     return n_grounded / len(claims)
 
 
-def _make_lead_id(seq: int) -> str:
-    """Format a sequential lead id like ``L-0001``."""
-    return f"L-{seq:04d}"
+_KIND_PREFIX: dict[LeadKind, str] = {
+    "connection": "C",
+    "gap": "G",
+    "improvement": "I",
+    "conjecture": "X",
+}
+
+
+def _make_lead_id(seq: int, kind: LeadKind) -> str:
+    """Format a per-kind sequential lead id like ``L-C-0001``.
+
+    Each synthesis stage numbers its leads from 1, so without a kind prefix a
+    connection, a gap, and an improvement all produce ``L-0001`` and clobber
+    one another in the shared ``grounded/`` directory (audit C-11). The kind
+    prefix namespaces the ids so they stay distinct.
+    """
+    return f"L-{_KIND_PREFIX[kind]}-{seq:04d}"
 
 
 def _safe_llm_generate(llm: LLMClient, prompt: str, model: str) -> str:
@@ -296,7 +310,7 @@ def _finalise_grounded_lead(
         return None
     marked = _mark_ungrounded(body, claims)
     return Lead(
-        id=_make_lead_id(seq),
+        id=_make_lead_id(seq, kind),
         kind=kind,
         title=title,
         body=marked,
@@ -428,7 +442,7 @@ def find_gaps(
             # No coverage at all → record the gap directly (LLM not strictly needed).
             leads.append(
                 Lead(
-                    id=_make_lead_id(seq),
+                    id=_make_lead_id(seq, "gap"),
                     kind="gap",
                     title=f"Gap: corpus has no material on '{topic}'",
                     body=(
@@ -481,7 +495,7 @@ def find_gaps(
         for bibkey in sorted(missing):
             leads.append(
                 Lead(
-                    id=_make_lead_id(seq),
+                    id=_make_lead_id(seq, "gap"),
                     kind="gap",
                     title=f"Gap: code cites '{bibkey}' but corpus does not contain it",
                     body=(
@@ -658,7 +672,7 @@ def propose_conjectures(
             continue
         leads.append(
             Lead(
-                id=_make_lead_id(seq),
+                id=_make_lead_id(seq, "conjecture"),
                 kind="conjecture",
                 title=title,
                 body=body,