diff --git a/rdflib/compare.py b/rdflib/compare.py
index ec4bd44eb..7c808b1a5 100644
--- a/rdflib/compare.py
+++ b/rdflib/compare.py
@@ -453,13 +453,13 @@ def _traces(
             elif best_score > color_score:
                 # prune this branch.
                 if stats is not None:
-                    stats["prunings"] += 1  # type: ignore[operator]
+                    stats["prunings"] = int(stats.get("prunings", 0)) + 1
             elif experimental_score != best_experimental_score:
                 best.append(refined_coloring)
             else:
                 # prune this branch.
                 if stats is not None:
-                    stats["prunings"] += 1  # type: ignore[operator]
+                    stats["prunings"] = int(stats.get("prunings", 0)) + 1
         discrete: list[list[Color]] = [x for x in best if self._discrete(x)]
         if len(discrete) == 0:
             best_score = None
diff --git a/rdflib/plugins/parsers/jsonld.py b/rdflib/plugins/parsers/jsonld.py
index f6574874d..0031c8662 100644
--- a/rdflib/plugins/parsers/jsonld.py
+++ b/rdflib/plugins/parsers/jsonld.py
@@ -662,6 +662,7 @@ def _add_list(
                 continue
 
             if rest:
+                # type error: Statement is unreachable
                 graph.add((subj, RDF.rest, rest))
                 subj = rest
 
diff --git a/rdflib/plugins/serializers/patch.py b/rdflib/plugins/serializers/patch.py
index 58928c6a0..da32ead97 100644
--- a/rdflib/plugins/serializers/patch.py
+++ b/rdflib/plugins/serializers/patch.py
@@ -2,7 +2,6 @@
 
 import warnings
 from typing import IO, Any
-from uuid import uuid4
 
 from rdflib import Dataset
 from rdflib.plugins.serializers.nquads import _nq_row
@@ -51,8 +50,6 @@ def serialize(
         target = kwargs.get("target")
         header_id = kwargs.get("header_id")
         header_prev = kwargs.get("header_prev")
-        if not header_id:
-            header_id = f"uuid:{uuid4()}"
         encoding = self.encoding
         if base is not None:
             warnings.warn("PatchSerializer does not support base.")
@@ -63,9 +60,10 @@ def serialize(
             )
 
         def write_header():
-            stream.write(f"H id <{header_id}> .\n".encode(encoding, "replace"))
+            if header_id:
+                stream.write(f"H id <{header_id}> .\n".encode(encoding, "replace"))
             if header_prev:
-                stream.write(f"H prev <{header_prev}>\n".encode(encoding, "replace"))
+                stream.write(f"H prev <{header_prev}> .\n".encode(encoding, "replace"))
             stream.write("TX .\n".encode(encoding, "replace"))
 
         def write_triples(contexts, op_code, use_passed_contexts=False):
diff --git a/rdflib/store.py b/rdflib/store.py
index f31902547..51d6d8422 100644
--- a/rdflib/store.py
+++ b/rdflib/store.py
@@ -121,6 +121,8 @@ def register(self, object: Any, id: str) -> None:
 
     def loads(self, s: bytes) -> Node:
         up = Unpickler(BytesIO(s))
+        # NOTE on type error: https://github.com/python/mypy/issues/2427
+        # type error: Cannot assign to a method
         up.persistent_load = self._get_object
         try:
             return up.load()
@@ -130,6 +132,8 @@ def loads(self, s: bytes) -> Node:
     def dumps(self, obj: Node, protocol: Any | None = None, bin: Any | None = None):
         src = BytesIO()
         p = Pickler(src)
+        # NOTE on type error: https://github.com/python/mypy/issues/2427
+        # type error: Cannot assign to a method
         p.persistent_id = self._get_ids
         p.dump(obj)
         return src.getvalue()
diff --git a/test/test_serializers/test_serializer_patch.py b/test/test_serializers/test_serializer_patch.py
index 6d8a05055..c0c44ca87 100644
--- a/test/test_serializers/test_serializer_patch.py
+++ b/test/test_serializers/test_serializer_patch.py
@@ -176,3 +176,18 @@ def test_prev_header():
     )
     result = ds.serialize(format="patch", operation="add", header_prev="uuid:123")
     assert """H prev <uuid:123>""" in result
+
+
+def test_no_headers():
+    ds = Dataset()
+    ds.add(
+        (
+            URIRef("http://example.org/subject1"),
+            URIRef("http://example.org/predicate2"),
+            Literal("object2"),
+        )
+    )
+    result = ds.serialize(format="patch", operation="add")
+    lines = result.split("\n")
+    for line in lines:
+        assert not line.startswith("H ")