def remove_slice_from_lines(lines, clean_text, slice) -> str:
    """
    Remove a slice of text from the lines based on specific criteria.

    This function identifies a slice of text within the lines and removes it based on certain conditions.

    Args:
        lines (list of str): The list of lines containing the text.
        clean_text (list of str): A cleaned version of the text (without numbers).
        slice (tuple): A tuple representing the start and end indices of the slice to be removed.

    Returns:
        str: The removed slice of text as a single string.
    """
    base = clean_text[slice[0]]
    section = list(slice)
    check_start_flag = False
    # backwards pass, at most 5 lines
    for line_idx in range(max(0, slice[0] - 1), max(0, slice[0] - 5), -1):
        if not lines[line_idx]:
            continue
        if lines[line_idx] == "## References":
            section[0] = line_idx
            break
        elif ratio(base, remove_numbers(lines[line_idx])) < 0.9:
            section[0] = line_idx + 1
            potential_ref = remove_numbers(lines[max(0, line_idx - 1)].partition("* [")[-1])
            if len(potential_ref) >= 0.75 * len(base) and ratio(base, potential_ref) < 0.9:
                section[0] = line_idx
            check_start_flag = True
            break
    # forward pass, at most 5 lines
    for line_idx in range(min(len(lines), slice[1]), min(len(lines), slice[1] + 5)):
        if ratio(base, remove_numbers(lines[line_idx])) < 0.9:
            section[1] = line_idx
            break
    if len(lines) <= section[1]:
        section[1] = len(lines) - 1
    to_delete = "\n".join(lines[section[0] : section[1] + 1])
    # cut off next page content
    itera, iterb = enumerate(lines[section[1] - 1]), enumerate(lines[section[1]])
    while True:
        try:
            (ia, a) = next(itera)
            while a.isnumeric():
                (ia, a) = next(itera)
            (ib, b) = next(iterb)
            while b.isnumeric():
                (ib, b) = next(iterb)
            if a != b:
                break
        except StopIteration:
            break
    if check_start_flag and "* [" in to_delete:
        to_delete = "* [" + to_delete.partition("* [")[-1]
    try:
        delta = len(lines[section[1]]) - ib - 1
        if delta > 0:
            to_delete = to_delete[:-delta]
    except UnboundLocalError:
        pass

    return to_delete.strip()

    Remove a slice of text from the lines based on specific criteria.

    This function identifies a slice of text within the lines and removes it based on certain conditions.

    Args:
        lines (list of str): The list of lines containing the text.
        clean_text (list of str): A cleaned version of the text (without numbers).
        slice (tuple): A tuple representing the start and end indices of the slice to be removed.

    Returns:
        str: The removed slice of text as a single string.
    
dpkd/transformers/src/transformers/models/nougat/tokenization_nougat_fast.py