```python
"""A storage report over a tree of named folders and byte-sized files."""


def check_node(node):
    if not isinstance(node, dict):
        raise ValueError("each node must be a mapping")
    name = node.get("name")
    if not isinstance(name, str) or not name or "/" in name:
        raise ValueError("each name must be a non-empty string without slashes")
    if ("bytes" in node) == ("children" in node):
        raise ValueError("a node holds either bytes or children")
    size = node.get("bytes", 0)
    if isinstance(size, bool) or not isinstance(size, int) or size < 0:
        raise ValueError("bytes must be a non-negative whole number")
    if "children" in node and not isinstance(node["children"], list):
        raise ValueError("children must be a list")


def file_paths(root: dict) -> list:
    paths = []
    stack = [(root, "")]
    while stack:
        node, prefix = stack.pop()
        check_node(node)
        path = prefix + node["name"]
        if "bytes" in node:
            paths.append(path)
        else:
            for child in reversed(node["children"]):
                stack.append((child, path + "/"))
    return paths


def tree_bytes(root: dict) -> int:
    total = 0
    stack = [root]
    while stack:
        node = stack.pop()
        check_node(node)
        if "bytes" in node:
            total += node["bytes"]
        else:
            stack.extend(node["children"])
    return total


def heavy_folders(root: dict, min_bytes: int) -> list:
    if not isinstance(min_bytes, int) or min_bytes < 0:
        raise ValueError("min_bytes must be a non-negative whole number")

    paths = file_paths(root)
    heavy_folders = []

    stack = [(root, "")]
    while stack:
        node, prefix = stack.pop()
        check_node(node)
        path = prefix + node["name"]
        if "bytes" in node:
            continue  # Skip files
        else:
            total = tree_bytes(node)
            if total >= min_bytes:
                heavy_folders.append([path, total])
            for child in reversed(node["children"]):
                stack.append((child, path + "/"))
    return heavy_folders
```