```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]
    leftover = total * sum(weights) % whole
    if leftover == 0: return parts
    sorted_parts = sorted(parts)
    discarded = sorted_parts[-1]
    index = sorted_parts.index(discarded)
    parts[index] += leftover
    return parts
```