What is the alternative hypothesis? The first candidate for an encompassing Grand Unified Theory of representation faces a logical paradox worthy of Goedel. On the one hand, being a theory of how information is processed, it must scrupulously respect the Bayesian formalism that one must choose among hypotheses. In other words, claiming to debunk one hypothesis without offering an alternative is beyond cheating, it's conceptually inconsistent (i.e. "not even wrong"). On the other hand, any first candidate theory by definition has no competitors, so it automatically becomes the default hypothesis until a newer, better theory explains more with less (in the usual Kuhnian/Occam sense). Therefore, this theory must proclaim it's own (provisional) status as the reigning explanation of brains, merely due to the accidents of its subject matter and time of appearance.
So this theory's primary intellectual challenge, logically prior to any evaluation of its claims or predictions, is a simple one: what other coherent and complete explanations of brains are on offer, and what are their merits?
What are the resolution upper bounds of nervous sub-systems? Experiments are difficult, so their first incarnations are optimized around effects which are easy to measure. Those effects do not necessarily represent the system operating at its optimal capacity. But because brains have presumably been optimized by evolution, they are much better characterize by the extremes of their performance, so the most informative experiments will test the absolute limits of the circuitry under ideal conditions.
At what temporal resolution can a volley of spikes be reconstituted: milliseconds or microseconds? What kind of multi-scale or chaotic patterns can a cortical column (or a whole brain) resonate with and/or stabilize: how many simultaneous parameters, at what frequency, with what latency, how effectively? With what spatial and temporal scales do mechanical vibrations propagate in body tissue, whether as tensile waves within myofascial tissue, or as capillary waves on the skin?
What are the resolution upper bounds of the entire nervous system? Twenty years ago, James Simmons showed the echo-locating "big brown bat" (Eptesicus fuscus) could resolve acoustic signals with 30 nanosecond accuracy. What are comparable figures for humans? In particular, how sensitively, and with what net bandwidth, can vibrations from one person be detected by another when passing directly from skin to skin? How do those vibrations affect sensation and emotions?
What informational insults does civilized life inflict on us? Our bodies evolved for a very different way of life, one of "natural statistics": barefoot on rocky ground, cold nights outdoors, fellows constantly nearby, and no words or rules. Life now involves frequent, well-tuned interruptions, informationally impoverished inputs (e.g. screens), low-entropy physical environments, and a low range of physical discomfort. The highest bandwidth and most personally salient channels (e.g. touch) have been shut down disproportionately. How does this environment affect a brain?
Do miracle workers exist? Traditions have always spoken of healers, sages, and shamans whose touch and presence create happiness, understanding, and success. Such healing vibrations are absolutely possible in this theory, and could easily be concentrated by skilled people. But the vibrations themselves are likely too subtle to be detected by any instrument except another human, and not reproducible in laboratories or under duress. How can we learn about these effects, and how powerful are they?
What are the topological origins of consciousness? If representation theory underlies control theory, control theory underliess spinal theory, spinal theory underlies skeletal theory, skeletal theory underlies brain theory, then ultimately the topological constraints of representation and 3-D space underlie "consciousness." How?
What does cloaking look like? At every scale in this theory, a model's defects are "cloaked" from self-discovery. What would an actual cloaking effect look like in 3-D space? Imagine a mini-"Death Star" cloaked and hovering in the middle of a room. Would it shimmer like a mirage? Would images passing through it have lower resolution? Would light beams scanned across it show the sort of tugging or snapping which would happen if a string were pulled across/through it in the same way? How might one detect discontinuities or defects in spite of the cloaking? (These answers matter for discovering and correcting sensorimotor darkspace in one's own body).
How should one apply signal-processing and information theory to life decisions? Humans are informational beings. We operate in regimes of perpetual data-insufficiency. We are buffeted by circumstances, urges, and thought-patterns far beyond conscious control, forced to use barely-tested assumptions, fooled as to the accuracy of our perceptions. Our processors are approximate and our lives are glitchy. But such signal-processing and informational constraints apply to robots as well, and are thus easily solved.
We can thus have mathematically-informed life strategies: