Phase 13.9.Fix1b: Fix ROOT path serialization for registered_functions

Previous commit (189b768) only fixed JSON path (export_schema_v2/apply_schema).
ROOT path (_serialize_schema/_deserialize_schema) was missing registered_functions.

Fixed: _serialize_schema, _deserialize_schema, _restore_schema, read_tree.
Added export_tree/read_tree roundtrip invariance test that catches this.

Code duplication between JSON and ROOT serialization paths identified
as technical debt — both should use single serialize/deserialize.

9 tests (was 8), 1440 passed, 6 failed (pre-existing).

Author: miranov25

UTILS/dfextensions/AliasDataFrame/AliasDataFrame.py

@@ -354,6 +354,10 @@ def _serialize_schema(schema):
                 serialized_spec[key] = value
         result["columns"][name] = serialized_spec
 
+    # Phase 13.9.Fix1: Include registered_functions if present
+    if "registered_functions" in schema:
+        result["registered_functions"] = schema["registered_functions"]
+    
     return result
 
 
@@ -434,6 +438,10 @@ def _deserialize_schema(serialized):
                 deserialized_spec[key] = value
         result["columns"][name] = deserialized_spec
 
+    # Phase 13.9.Fix1: Restore registered_functions if present
+    if "registered_functions" in serialized:
+        result["registered_functions"] = serialized["registered_functions"]
+    
     return result
 
 
@@ -1285,6 +1293,12 @@ def _restore_schema(self, serialized_schema):
 
         # Restore subframes metadata (not actual subframe objects)
         self._schema["subframes"] = serialized_schema.get("subframes", {})
+        
+        # Phase 13.9.Fix1: Restore registered_functions schema
+        # NOTE: Reconstruction is deferred — subframes must be loaded first.
+        # Call _reconstruct_registered_functions() after subframes are registered.
+        if "registered_functions" in serialized_schema:
+            self._schema["registered_functions"] = serialized_schema["registered_functions"]
 
     def update_schema(self, update, validate=True, apply=True, errors="raise"):
         """
@@ -5182,6 +5196,10 @@ def read_branch(branch_name):
                         f"Failed to load subframe '{sf_name}' from {filename}: {e}"
                     ) from e
 
+        # Phase 13.9.Fix1: Reconstruct registered functions after subframes loaded
+        if adf._schema.get('registered_functions'):
+            adf._reconstruct_registered_functions()
+
         return adf
 
     # =========================================================================

UTILS/dfextensions/AliasDataFrame/tests/test_polynomial_persistence.py

@@ -179,3 +179,42 @@ def test_invariance_before_after_schema_roundtrip(self, adf_with_polynomial, tmp
 
         np.testing.assert_allclose(before, after, atol=1e-10,
                                     err_msg="Polynomial values differ after schema roundtrip")
+
+    @pytest.mark.invariance
+    def test_invariance_export_tree_read_tree_roundtrip(self, adf_with_polynomial, tmp_path):
+        """Full chain: register polynomial → export_tree → read_tree → polynomial works."""
+        adf, _, _ = adf_with_polynomial
+
+        # Materialize and get reference values
+        adf.materialize_alias('correction')
+        before = adf.df['correction'].values.copy()
+
+        # Verify schema has registered_functions before export
+        assert 'poly' in adf._schema.get('registered_functions', {}), \
+            "registered_functions missing from schema before export"
+
+        # Export to ROOT file
+        root_path = str(tmp_path / 'test_poly_persistence.root')
+        adf.export_tree(root_path)
+
+        # Read back — polynomials should auto-reconstruct
+        adf2 = AliasDataFrame.read_tree(root_path)
+
+        # Verify schema was restored
+        assert 'registered_functions' in adf2._schema, \
+            "registered_functions missing from schema after read_tree"
+        assert 'poly' in adf2._schema['registered_functions'], \
+            "poly not in registered_functions after read_tree"
+
+        # Verify function was reconstructed
+        assert hasattr(adf2, '_registered_functions'), \
+            "_registered_functions attribute missing after read_tree"
+        assert 'poly' in adf2._registered_functions, \
+            "poly not reconstructed in _registered_functions after read_tree"
+
+        # Verify alias works — materialize and compare
+        adf2.materialize_alias('correction')
+        after = adf2.df['correction'].values.copy()
+
+        np.testing.assert_allclose(before, after, atol=1e-10,
+                                    err_msg="Polynomial values differ after export_tree/read_tree roundtrip")