```ts
export function runThermostat(start: number, low: number, high: number, power: number, drifts: number[]): { temp: number; heated: number; switches: number; coldest: number } {
  if (!Number.isInteger(start) || !Number.isInteger(low) || !Number.isInteger(high)) throw new Error('Start, low, and high must be integers');
  if (low >= high) throw new Error('Low must be strictly below high');
  if (!Number.isInteger(power) || power <= 0) throw new Error('Power must be a positive integer');
  if (!Array.isArray(drifts)) throw new Error('Drifts must be an array');
  if (drifts.some(d => !Number.isInteger(d))) throw new Error('All drift values must be integers');

  let temp = start;
  let heated = 0;
  let switches = 0;
  let coldest = start;

  for (const drift of drifts) {
    const heaterOn = temp < low || temp >= high;
    if (heaterOn && !drift) continue; // Skip no-op ticks

    if (heaterOn) {
      heated++;
      switches += temp > coldest ? 1 : 0;
      coldest = Math.min(coldest, temp);
      temp += power + drift;
    } else {
      switches += temp < coldest ? 1 : 0;
      coldest = Math.min(coldest, temp);
      temp += drift;
    }
  }

  return { temp, heated, switches, coldest };
}
```