Buddhism And Dimension

There is indeed a rumour that Enlightenment may open freedom of travel in an extra dimension. If this were true, here is one way it could work:

For a human observer the extra dimension could look like parallel/alternative variants of reality, analogous to what's described in the endless works of fiction. Moving along this dimension would require ability to see the space of variants, which to the observer would look like (partially constrained) perceptual ambiguity. Picking one concrete perceptual interpretation among the variants would constitute moving along the extra dimension. In order to see the ambiguity of the extra dimension, one would need to learn to overcome the deeply ingrained habit of rigid interpretation. Altogether this could look rather similar to mastery of Emptiness as is taught in Mahayana Buddhism, particularly in Vajrayana and Zen.

The author of this answer had some first-hand experience with the above, enough to suspend his judgement and admit possibility thereof.

Another line of thinking interprets time as dimension that things evolve along, denying possibility of free will in the absolute sense and only leaving it as a perceptual illusion from the perspective of an individual observer. This seems to be logically consistent with the teaching of anatta, and is confirmed by historical Zen Masters either explicitly (Dogen) or implicitly.

What does the perception of Buddhism observe or speculate, about the limitations of our 4 dimensions of perceptual observation (three dimensions of space, giving us the material; and time being the fourth, affording us a memory of events within the material that we can judge the present by)?

If we understand dimension as a vector direction in which energy or information is expressed, then I will say Buddhism largely acknowledges the limitations of perceptual four dimensions. With my definition, you can say that each of the four Jhnanas are different dimensions of existence which are hidden from the ordinary experience. As a matter of fact, Buddhism says that there are 121 different states of consciousness, rendering each of them as a dimension of existence in turn.

If Buddhism's pursuit is of enlightenment, could that goal lead to the perception of five dimensions of observation?

You have limited your view to physicalist point. Enlightenment will entail witnessing everything, ability to look into the future is a trivial thing, IMHO the leaves in the hands of Buddha are fewer than the total leaves in the woods. The Rabbit hole is the abyss.

Is this the enlightenment Buddhism is pursuing.....?

What you say is the obvious byproduct, but that's not what is being pursued.

What does the perception of Buddhism observe or speculate, about the limitations of our 4 dimensions of perceptual observation (three dimensions of space, giving us the material; and time being the fourth, affording us memory of events within the material that we can judge the present by)?

We can only find limitations for any number of dimensions of perception because all dimensions eventually collapse. Space is not self.Space does not give us material or time. Material is a separate element. It can be classified Earth element. Every element needs to be examined separately. Time is actually embedded with every element as every element must change or perish.

If Buddhism's pursuit is of enlightenment, could that goal lead to perception of five dimensions of observation (as that perception would afford a picture of the direction of time both ways, and give the observer a picture of every possible event leading from the 'choices' of each of the inhabitants of this world and every outcome of every choice chosen past present and future)?

No dimension can include all choices we make because sometimes there is free will. Free will by definition can not be predicted individually or statistically. In other words if you tell me through prediction what I will do in future then I sometimes have the free will to change it. For example if you predict that I will stop this sentence with a full stop then I won't

Is this the enlightenment Buddhism is pursuing (as it would give the observer knowledge of the outcome of every choice, and in a sense the 'Judgement and sentence' of every action, but would detach them from any interaction within the four as a consequence of its perception, and the certainty which would trap any attempt to change the four's events because of the undeniable logic)?

I don't think so. Enlightenment is state which is unborn , uncreate. Nirvana can not be expressed in words because the One who attained Niravana can not be said to conscious or unconscious or choice driven or choiceless.