```python
"""A storage report over a tree of named folders and byte-sized files."""
from typing import Dict, List


def check_node(node: Dict[str, any]) -> None:
    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[str, any]) -> List[str]:
    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[str, any]) -> 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[str, any], min_bytes: int) -> List[List[str]]:
    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)
    folder_totals = {}
    for path in paths:
        parts = path.split("/")
        current_total = 0
        for part in parts:
            if part in folder_totals:
                current_total += folder_totals[part]
            else:
                current_total += tree_bytes({part: {"name": part}})
                folder_totals[part] = current_total
        if current_total >= min_bytes:
            heavy_folders.append([path, current_total])
    return heavy_folders
```