```python
def parse_amount(text: str) -> int:
    """Parse a decimal amount string into integer cents."""
    if not isinstance(text, str):
        raise ValueError("Input must be a string")
    parts = text.split('.')
    if len(parts) == 1:
        return int(parts[0]) * 100
    elif len(parts) == 2 and parts[1].isdigit() and len(parts[1]) == 2:
        return int(parts[0]) * 100 + int(parts[1])
    else:
        raise ValueError("Invalid amount string format")

def format_amount(cents: int) -> str:
    """Render non-negative integer cents as a dotted decimal string."""
    if not isinstance(cents, int) or cents < 0:
        raise ValueError("Input must be a non-negative integer")
    return f"{cents // 100}.{cents % 100:02d}"

def allocate_cents(total_cents: int, weights: list) -> list:
    """Split total_cents across weights proportionally."""
    if not isinstance(weights, list) or len(weights) == 0:
        raise ValueError("Weights must be a non-empty list")
    if any(not isinstance(w, int) or w < 0 for w in weights):
        raise ValueError("Weights must be non-negative integers")
    if sum(weights) == 0:
        raise ValueError("Sum of weights must be greater than zero")
    if not isinstance(total_cents, int) or total_cents < 0:
        raise ValueError("Total cents must be a non-negative integer")

    proportion = [total_cents * w / sum(weights) for w in weights]
    shares = [int(p) for p in proportion]
    remainder = total_cents - sum(shares)

    for i in range(remainder):
        max_index = shares.index(max(shares))
        shares[max_index] += 1

    return shares
```