diff --git a/python/build_manifold.py b/python/build_manifold.py
index 6612b107..ee4aaa58 100644
--- a/python/build_manifold.py
+++ b/python/build_manifold.py
@@ -98,14 +98,14 @@ def lean_str_list(xs: list[str]) -> str:
 
 
 def load_matrices(path: Path) -> dict[str, list[list[int]]]:
-    """Load predictions JSON into equation_id → matrix lookup."""
+    """Load predictions JSON into object_id → matrix lookup."""
     if not path.exists():
         return {}
     data = json.loads(path.read_text())
     return {
-        p.get("equation_id", ""): p.get("matrix_8x8", [])
+        p.get("object_id") or p.get("equation_id", ""): p.get("matrix_8x8", [])
         for p in data.get("predictions", [])
-        if p.get("equation_id")
+        if p.get("object_id") or p.get("equation_id")
     }
 
 
diff --git a/python/build_pist_matrices_250.py b/python/build_pist_matrices_250.py
index 892a2ccb..9be4055c 100644
--- a/python/build_pist_matrices_250.py
+++ b/python/build_pist_matrices_250.py
@@ -61,15 +61,15 @@ def main() -> int:
     raw = preds.get("predictions", [])
     print(f"Loaded {len(raw)} predictions from {args.predictions}", file=sys.stderr)
 
-    raw_sorted = sorted(raw, key=lambda p: p.get("equation_id", ""))
+    raw_sorted = sorted(raw, key=lambda p: p.get("object_id", p.get("equation_id", "")))
 
     defs: list[str] = []
     find_cases: list[str] = []
     for p in raw_sorted:
-        eid = p.get("equation_id", "")
+        eid = p.get("object_id") or p.get("equation_id", "")
         mat = p.get("matrix_8x8", [])
         if not eid or len(mat) != 8:
-            print(f"WARNING: skipping malformed entry {eid}", file=sys.stderr)
+            print(f"WARNING: skipping malformed entry {p.get('equation_id', '?')}", file=sys.stderr)
             continue
         name = lean_matrix_def_name(eid)
         defs.append(f"def {name} : Array (Array Int) :=\n  {lean_matrix_rows(mat)}")
diff --git a/python/generate_predictions.py b/python/generate_predictions.py
index f8a6b99e..146c168d 100644
--- a/python/generate_predictions.py
+++ b/python/generate_predictions.py
@@ -41,13 +41,14 @@ def canonical_json_matrix(matrix: list[list[int]]) -> str:
     return json.dumps(matrix, separators=(",", ":"))
 
 
-def build_record(text: str, equation_id: str, name: str) -> dict:
+def build_record(text: str, equation_id: str, object_id: str, name: str) -> dict:
     tokens = tokenize(text)
     vocab = sorted(set(tokens))
     matrix = build_matrix(tokens)
     matrix_json = canonical_json_matrix(matrix)
     return {
         "equation_id": equation_id,
+        "object_id": object_id,
         "name": name,
         "equation": text,
         "schema": "rrc_pist_predictions_250_v1",
@@ -77,21 +78,23 @@ def main():
 
     print(f"Loaded {len(equations)} source equations", file=sys.stderr)
 
-    # Dedup by equation_id: deterministic representative selection per AGENTS.md
-    # representative = min(records, key = equation_record.equation_id)
+    # Dedup by object_id (invariant receipt) which matches the manifold's lookup key.
     merged: dict[str, dict] = OrderedDict()
     for eq in equations:
         rec = eq.get("equation_record", eq)
-        eid = rec["equation_id"]
+        ir = eq.get("invariant_receipt", {})
+        eid = ir.get("object_id", rec["equation_id"])  # use object_id for lookup match
         name = rec.get("name", eid)
         text = rec.get("equation", "")
 
         if eid not in merged:
-            merged[eid] = build_record(text, eid, name)
+            oid = ir.get("object_id", rec["equation_id"])
+            merged[eid] = build_record(text, rec["equation_id"], oid, name)
             merged[eid]["source_records"] = []
 
         merged[eid]["source_records"].append({
-            "equation_record_id": eid,
+            "equation_record_id": rec["equation_id"],
+            "object_id": ir.get("object_id", rec["equation_id"]),
             "name": name,
         })