```ts
export function splitCents(total: number, weights: number[]): number[] {
  if (!Number.isInteger(total)) throw new Error("total must be whole cents");
  if (total < 0) throw new Error("total may not be negative");
  if (!Array.isArray(weights) || weights.length === 0) throw new Error("weights must be a non-empty list");
  if (!weights.every((w) => Number.isInteger(w) && w > 0)) throw new Error("a weight is a positive whole number");

  const whole = weights.reduce((a, b) => a + b, 0);
  const parts = weights.map((w) => Math.floor((total * w) / whole));

  // Calculate the leftover cents
  const leftover = total % whole;

  // Sort partners by their discarded fraction in descending order
  const sortedParts = parts.slice().sort((a, b) => {
    const discA = leftover - (a * whole);
    const discB = leftover - (b * whole);
    return discB - discA;
  });

  // Distribute the leftover cents to the partners with the largest discarded fraction
  for (let i = 0; i < leftover; i++) {
    sortedParts[i]++;
  }

  return parts;
}
```