Challenge: Onwards with Detail #11

I went and edited a really old post recently, because I realized I had never visualized the idea in it well enough.

I realized while looking at it, that maybe a few quirks could make it even better. Right now it's fairly rigid - two or three words are resolved to their roles, and no way of changing how they are resolved. Every adverbial and other argument basically requires its own VP, so that's a bit unwieldy, but not all that impossible ultimately. The language probably needs a bunch of subordinating conjunctions for that kind of thing, but let's not get our hands in that deep just yet.

Let's consider the illustration of the words' "distributions" along the SOV circle:

life as a graphical artist is not in my future

Now, what operations would give us full control over this? How many possible elements do we have in the first place? An element is an n-tuplet of the form [S, O, V, d, z]. S, O and V ∈ {1, 0}, d ∈ {clockwise, counterclockwise}, z ∈ {s,v,o}.

Interpretation of this tuplet works like this: if S,V or O is 0, it is not close to that point along the circumference, if S,V or O is 1, it is close to the corresponding point along the circumference. d gives the direction along the perimeter as shown, and z (for 'zero') is the starting point, the most preferred element out of the elements.

Thus there are 2⁴*3 possible configurations for the words, a total of 48 possibilities. A three-word clause can be 48³ combinations of configurations. Meanwhile, three words can map onto subject, object and verb in six ways. We have a bit of a gap of orders of magnitude here. 48³ = 110592.

We have more than one hierarchy here: for each word, there's an internal hierarchy. [1, 1, 0, clockwise, s] prefers being Subject, over Verb, over Object. However, when resolving which out of a = [1,1,0,clockwise, s] and b = [1,0,0,clockwise,s] gets to be the subject, we find that b is more likely of the two to be the object, and a ends up our subject. 

Challenge: come up with a small set of markers that operate on this system in a way that does not reduce to directly marking role, but that operate on the tuplet-level of the representation, yet provides us a full way of getting any of the six possible SVO-assignments out of any of the 48³ possible configurations.