Time most certainly is not a dimension (or even very dimension-like, in general) in my opinion. It structures the orderings of events, more like some ultimate p

Time most certainly is not a dimension (or even very dimension-like, in general) in my opinion. It structures the orderings of events, more like some ultimate process that all other processes are hanging off (are a part of). The complexity in the ordering could be irreducible at any given point, depending what is happening there, and that includes fully non-reversible processes. To me, this is time's arrow.