def merge_intervals(intervals):
    """Merge overlapping or touching intervals into the minimal covering set.

    Args:
        intervals: list of [start, end] pairs with start <= end, in any order,
            possibly overlapping or nested.

    Returns:
        A new list of non-overlapping [start, end] lists, sorted by start.
        Intervals that overlap or merely touch are merged.
    """
    if not intervals:
        return []

    # Copy each interval so the caller's input is never mutated, then sort by
    # start (and end as a tiebreaker) without disturbing the original list.
    ordered = sorted(([start, end] for start, end in intervals),
                     key=lambda pair: (pair[0], pair[1]))

    merged = [ordered[0]]
    for start, end in ordered[1:]:
        last = merged[-1]
        # Overlap or touch: the next start is at or before the current end.
        if start <= last[1]:
            if end > last[1]:
                last[1] = end
        else:
            merged.append([start, end])

    return merged