I will disagree. State is true, but only as a snapshot in a linear array. It is still a time line.
However, what you say can be said of each, respectively, with the exception of the first dimension in it's discrete state (a dot) - Each is 'aware if itself, and each of the lesser dimensions contained within itself (proven, provable)... with the next step or dimension only conceptually represented...
Until time, which is where the whole thing ceases to be logically extended. Or our perception thereof is limited, even as the concept of each progressive dimension can only be theorized from the one beneath it.
No, I don't think you understand what I am describing. There is a reason it is called "space-time." Time is a representation of the sequential changes in the space's state.
For example, if I lived in a universe with one physical dimension (a line), along which I traveled, time would be a representation of me being at state 0, 1, 2, 3, etc. When talking about the universe, in all it's 3-dimensional glory, time is a just a representation of state changes within the three dimensions.
This is a generally accepted physics principle whether or think so or not.