Something just occurred to me: the if test may not actually function properly as written. It is intuitively reasonable, but it might be that the comparison logic works differently. I haven't found a solid answer to this yet... will keep looking.

Meanwhile, limiting the test to one 'cPath=3' will avoid this possible problem. If that works, we can reformulate the test statement.
PHP Code:
  if (($box_categories_array[$i]['path'] == 'cPath=3') or ($box_categories_array[$i]['path'] == 'cPath=7') or ($box_categories_array[$i]['path'] == 'cPath=7_25')) { 
will definitely work, but is unbelievably cumbersome for a long list. There will be a more elegant way of stating it.

I suppose the first space-saver would be to substitute a simple variable for the $box expression.
PHP Code:
    $cPTest = $box_categories_array[$i]['path'];
    if (($cPTest == 'cPath=3') or ($cPTest == 'cPath=7') or($cPTest == 'cPath=7_25')) } 
is not so bad.

Hope this will do it.