```ts
export function mergeIntervals(intervals: [number, number][]): [number, number][] {
  // 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 must not be greater than end");
    }
  }

  // Handle empty input
  if (intervals.length === 0) {
    return [];
  }

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

  // Merge overlapping intervals
  const result: [number, number][] = [sorted[0]];
  
  for (let i = 1; i < sorted.length; i++) {
    const current = sorted[i];
    const lastMerged = result[result.length - 1];
    
    // Check if current interval overlaps or touches the last merged interval
    if (current[0] <= lastMerged[1]) {
      // Merge intervals by extending the end time
      lastMerged[1] = Math.max(lastMerged[1], current[1]);
    } else {
      // No overlap, add current interval to result
      result.push(current);
    }
  }

  return result;
}
```