```ts
export function mergeIntervals(intervals: [number, number][]): [number, number][] {
  if (intervals.length === 0) {
    return [];
  }

  // Validate input
  for (const interval of intervals) {
    if (!Array.isArray(interval) || interval.length !== 2) {
      throw new Error("Each element must be a two-number pair");
    }
    const [start, end] = interval;
    if (!Number.isFinite(start) || !Number.isFinite(end)) {
      throw new Error("Both start and end must be finite numbers");
    }
    if (start > end) {
      throw new Error("Start cannot be greater than end");
    }
  }

  // Sort intervals by start time
  const sorted = [...intervals].sort((a, b) => a[0] - b[0]);

  const result: [number, number][] = [sorted[0]];

  for (let i = 1; i < sorted.length; i++) {
    const currentStart = sorted[i][0];
    const currentEnd = sorted[i][1];
    const lastEnd = result[result.length - 1][1];

    // If current interval overlaps or touches the last merged interval
    if (currentStart <= lastEnd) {
      // Merge intervals by extending the end time
      result[result.length - 1][1] = Math.max(lastEnd, currentEnd);
    } else {
      // No overlap, add the current interval
      result.push(sorted[i]);
    }
  }

  return result;
}
```