```ts
export function baseAmount(amount: number, unit: string, defs: Record<string, [number, string]>, base: string): number {
  if (amount < 0 || !Number.isInteger(amount)) throw new Error('Invalid amount');

  const seen = new Set<string>();

  while (unit !== base) {
    if (seen.has(unit)) throw new Error('Loop detected in unit definitions');
    if (!defs.hasOwnProperty(unit)) throw new Error('Unknown unit');

    const [factor, finer] = defs[unit];
    if (factor <= 0 || !Number.isInteger(factor)) throw new Error('Invalid factor');

    amount *= factor;
    unit = finer;
    seen.add(unit);
  }

  return amount;
}
```