I know this is too late to be useful, but it only takes 1b per nesting level to track the nesting depth in O(1) time, or just a 64b integer to track the nesting

I know this is too late to be useful, but it only takes 1b per nesting level to track the nesting depth in O(1) time, or just a 64b integer to track the nesting depth in O(n) time. I wonder if there a sublinear algorithm? At best to me, right now, it could made to look like bitstream compression.