```python
def split_cents(total: int, weights: list) -> list:
    if not isinstance(total, int) or isinstance(total, bool): raise ValueError("total must be whole cents")
    if total < 0: raise ValueError("total may not be negative")
    if not isinstance(weights, list) or not weights: raise ValueError("weights must be a non-empty list")
    if not all(isinstance(w, int) and not isinstance(w, bool) and w > 0 for w in weights): raise ValueError("a weight is a positive whole number")
    whole = sum(weights)
    parts = [total * w // whole for w in weights]
    leftovers = total - sum(parts)
    discards = [(w / whole - (parts[i] / whole), i) for i, w in enumerate(weights)]
    discards.sort(reverse=True)
    for _, idx in discards:
        if leftovers > 0:
            parts[idx] += 1
            leftovers -= 1
    return parts
```