def _ensure_strict_json_schema(
    json_schema: object,
    *,
    path: tuple[str, ...],
    root: dict[str, object],
) -> dict[str, Any]:
    """Mutates the given JSON schema to ensure it conforms to the `strict` standard
    that the API expects.
    """
    if not is_dict(json_schema):
        raise TypeError(f"Expected {json_schema} to be a dictionary; path={path}")

    defs = json_schema.get("$defs")
    if is_dict(defs):
        for def_name, def_schema in defs.items():
            _ensure_strict_json_schema(def_schema, path=(*path, "$defs", def_name), root=root)

    definitions = json_schema.get("definitions")
    if is_dict(definitions):
        for definition_name, definition_schema in definitions.items():
            _ensure_strict_json_schema(definition_schema, path=(*path, "definitions", definition_name), root=root)

    typ = json_schema.get("type")
    if typ == "object" and "additionalProperties" not in json_schema:
        json_schema["additionalProperties"] = False

    # object types
    # { 'type': 'object', 'properties': { 'a':  {...} } }
    properties = json_schema.get("properties")
    if is_dict(properties):
        json_schema["required"] = [prop for prop in properties.keys()]
        json_schema["properties"] = {
            key: _ensure_strict_json_schema(prop_schema, path=(*path, "properties", key), root=root)
            for key, prop_schema in properties.items()
        }

    # arrays
    # { 'type': 'array', 'items': {...} }
    items = json_schema.get("items")
    if is_dict(items):
        json_schema["items"] = _ensure_strict_json_schema(items, path=(*path, "items"), root=root)

    # unions
    any_of = json_schema.get("anyOf")
    if is_list(any_of):
        json_schema["anyOf"] = [
            _ensure_strict_json_schema(variant, path=(*path, "anyOf", str(i)), root=root)
            for i, variant in enumerate(any_of)
        ]

    # intersections
    all_of = json_schema.get("allOf")
    if is_list(all_of):
        if len(all_of) == 1:
            json_schema.update(_ensure_strict_json_schema(all_of[0], path=(*path, "allOf", "0"), root=root))
            json_schema.pop("allOf")
        else:
            json_schema["allOf"] = [
                _ensure_strict_json_schema(entry, path=(*path, "allOf", str(i)), root=root)
                for i, entry in enumerate(all_of)
            ]

    # strip `None` defaults as there's no meaningful distinction here
    # the schema will still be `nullable` and the model will default
    # to using `None` anyway
    if json_schema.get("default", NOT_GIVEN) is None:
        json_schema.pop("default")

    # we can't use `$ref`s if there are also other properties defined, e.g.
    # `{"$ref": "...", "description": "my description"}`
    #
    # so we unravel the ref
    # `{"type": "string", "description": "my description"}`
    ref = json_schema.get("$ref")
    if ref and has_more_than_n_keys(json_schema, 1):
        assert isinstance(ref, str), f"Received non-string $ref - {ref}"

        resolved = resolve_ref(root=root, ref=ref)
        if not is_dict(resolved):
            raise ValueError(f"Expected `$ref: {ref}` to resolved to a dictionary but got {resolved}")

        # properties from the json schema take priority over the ones on the `$ref`
        json_schema.update({**resolved, **json_schema})
        json_schema.pop("$ref")
        # Since the schema expanded from `$ref` might not have `additionalProperties: false` applied,
        # we call `_ensure_strict_json_schema` again to fix the inlined schema and ensure it's valid.
        return _ensure_strict_json_schema(json_schema, path=path, root=root)

    return json_schema
Mutates the given JSON schema to ensure it conforms to the `strict` standard
    that the API expects.
    
src/openai/lib/_pydantic.py