Indeed, your Cuilian Squint Theory may hold a means of perceiving answers. I add to it my own understanding.
In my understanding of your theory, the funnels around Zero Cuil (>.<) expand outward at a possibly exponential rate to the point at which we cease to be able to imagine a possibility as a permutation of 'reality' (represented by zero cuil.) I propose that they then funnel back in to both the positive infinity point and the reddye number, where experience becomes either so logical (reddye) or so illogical (+infinite cuil) that it is completely unimaginable. Thus the squinting diagram would appear such (+)-< >.< >+(-), with both -infinite and +infinite cuil occuring at the same singularity on this cyclical line.
I rationalize this thusly;
When an experience is experienced completely logically (reddye), it ceases to be truthful to 'reality' (0 cuil) and becomes completely theoretical. The example of the circle above works here; when a circle is expressed as 'real-ly' as possible, you have mathematical formula 2 pi r2. If we take this as the definition for 'circle', anything that can be defined as a singular, numerical value can be applied to this equation, since 'r' no longer means 'radius' but rather is a part of the definition of 'circle'. At this point 'circle' becomes completely meaningless despite being a singular definition for all things, since one can enter the value for circle into the calculation for the value of circle. Thus 'circle' refers to nothing and everything within the True, and is perfectly defined as 2 pi r2.
On the positive end of the spectrum, an experience is experienced completely illogically. This experience is also false to 'reality' (0 cuil) and completely theoretical. To completely understand how our circle fits into positive infinite cuil, I wish to take you down the spectrum. Immediately, the circle is a 'circle' instead of a formula. At one cuil, where most of us live, the circle is a hamburger bun, or a patty, or perhaps a knot on a tree trunk. There is an infinite number of things that fit this definition of 'circle,' but there are also an infinite number of things that do not. Just as there is an infinity between 0 and 1, but 0<x<1 does not describe all numbers. All of these things are circles by the 1 cuil definition, but none of them are 'a circle.' As we branch along the spectrum the number of things that are defined as a 'circle' increase exponentially, until we can no longer count them. At the outer extremes of the positive spectrum, our experience of 'circle' has expanded so far that all things are contained within the definition. We have a situation of total entropy where all things are the same and we have a singular definition of everything that is a circle.
Does this singular definition sound familiar? Both reddye and positive infinite cuil end with a definition of 'circle' that is so untrue to the 'real' that they are nearly completely hypothetical, and only applicable to our attempts to comprehend the truth of 'circle' at zero cuil. By this logic, the band of possible experiences would be completely cyclical although not closed, such that there is an infinite number of possibilities between zero cuil and +/-infinite cuil. Seems fitting, since there is an infinite number of possibilities between 0 and +/- infinity.
Expanding upon this theoretical circle of cuil, where we picture a funnel system between 0 cuil and +-infinite cuil along the + and - axis, imaginary cuil fits in the space between the + and -. Where + and - values of cuil are found as locations within the dimensional plane of the axes, imaginary cuil is found in non-dimensional experience. This is the connection between the incomprehensive 0 cuil and unTrue infinite cuil. If we see 0 cuil as the Truth, and infinite cuil as the abstract understanding of the Truth, then imaginary cuil is the application of the abstract understanding within the singularity of Truth. It is the bridge between every opposing possibility in this cyclical linear explanation of experiential possibility. Imaginary cuil is the measuring unit for distances between non-linear cuils. At 0i cuil, the circle is completely True (0 cuil), completely unTrue (-+infinite cuil) and both perfectly defined and undefined, thus the circle is both at the 0 cuil and +/-infinite cuil levels of experience. There is 0 distance between 0 cuil and +-infinite cuil. At +-infinitei cuil, the experience is neither True nor defined. There is infinite distance between experiences.
At 2i cuil, our 'circle' is defined as both 2 pi r2 and the abstract "circle" of all things, as defined above in my explanation of -infinite and +infinite cuil. However, these definitions are no longer completely hypothetical. The definition does not completely describe the thing named 'circle' as it is at 0 cuil. There is
I hypothesize that we have an innate understanding of how to bridge the distance measured by imaginary cuil, and that is why we can use 2 pi r2 to describe a circle and everyone knows roughly what we mean. I believe that a part of understanding the imaginary cuil is in the application of every definition together at once, the definition of 'radius' and 'shape' and 'distance' all factoring in to what the definition of 'circle' means so that 'circle' fits in the True, where 'radius' and 'shape' and distance' exist. The imaginary is the logicalization of the abstract and the abstraction of the logical. It is the connection between 'rose' and 'flower,' and perhaps 'red' and even 'love.'
I see this theory as compatible with GMT, and this is how. Visualize the mesh of GMT as a 3 dimensional (or more) mesh. Every experience exists within this mesh, and the center of it is -/+infinite cuil and zero cuil. Within this mesh is contained a coloured area, sort of shaped like a multi-dimensional infinity symbol. It is singular at the point where it crosses itself, and each limb expands out from that singularity in thickness. As you travel toward the outer end of each loop the colour fades gradually until you can hardly tell it is there at all. the point where it fades completely is infinite cuil/2. The colour is the essence of our comprehension, and the width of the band is the infinite possible experiences of 'True' and 'Definition' at that number of cuil. However, there is more mesh than that which is contained within the positive, negative and zero cuil. This is the imaginary cuil, which we can pretend to experience. Positive imaginary cuil surrounds the positive cuil loop, -i cuil surrounds the - cuil loop. Through our attempts to experience through the imaginary cuil, that which is neither quite defined nor True, we can change our own experience and our perception of Truth and definition, so that perhaps, for a while, we are able to experience at 7 or 8 cuil, or -5, or -12. The less true and defined we are willing to get (the closer to +/- infinite i cuil), the farther we are able to jump in experience. If we equal +/- infinite i cuil, we can shift from +infinite cuil/2 to -infinite cuil/2, theoretically the farthest distance possible within the Cuil Mesh.
… In terms of the colour wheel example for GMT, imagine that + cuil is on the top of the page the wheel is printed on and - cuil is on the bottom, + imaginary cuil is the length of the pencil above the page and - imaginary cuil is the length below the page. This would make the outer edge of the page +/- infinite cuil and the inner edge (touching the pencil) zero cuil. The distance between the outer edge of the paper and the inner edge would have an imaginary cuil measurement of 0i. (This is much the same as how a horizontal line along the x axis of a cartesian plane has y=0, regardless of x.) +/-infinite i cuil is the ends of the pencil where you're holding it. You are +/-infinite i cuil. You connect understanding in the strangest ways possible, and you can comprehend every distance between experiences. To measure (and possibly traverse) a distance between experiences on opposite sides of the page, one must use imaginary cuil or zero/+/-infinite cuil, and since we can't comprehend zero/+/-infinite cuil, we must be imaginary.
Non-imaginary cuil is not a distance from True. From zero cuil. It is a distance between zero cuil and infinite cuil, with such numbers as +infinite cuil -4 cuil being to definition experience what +4 cuil is to Truth experience. The numbers go both ways. Every step away from zero is toward infinity, and vice versa. The midpoint is +/-infinite cuil/2
I must stop and return another day. It grows late, and my mind strays further into abstraction than I intend. It interests me that always we seek to define instead of understand, that we seek logical explanation instead of experience itself. Perhaps it is because so many of us live at one cuil, and, in reaching for the negative side of the spectrum, we hope to comprehend the Truth that lies between. To truly understand the nature of what the cuil measures, I believe that we must understand the immense scope of possibility and perception in every experience. We speak in infinities and zeros and imaginaries as though they mean something beyond the meaning we give them. The cuil is a measure of our experience relative to each other and the eternal truth that ties every experience together. To exist, we must exist within cuil's scale. And yet we seem to have the power to jump through the imaginary from logical experience to illogical and back, without ever experiencing the Truth of zero cuil or the definition of infinite cuil.