After spending time studying a number of personality theories, I have a better sense of what Ti both is and isn't - and I've come to the realization that, in socionics, Ti is often confused with Te ('ll talk more about this later). With respect to the first point, I spent a lot of time researching MBTI, cognitive processes and other theories. Some of these theories talk a lot about "Ti." I have the sense that Ti in socionics is not about being neat, organized or regimented, but essentially being a "systems thinker." What this means is that Ti egos understand long chains of reasoning better than other types. This translates into an understanding of computer systems, mathematical systems, even philosophical logic. Ti-egos understand the principles and logic behind most any conceptual system, and they can either design such systems or apply these systems to the real world; this is connected with socionics notions of Ti egos as the builders of models, formulas, and blueprints, and is also correlated with the notion of Ti egos as those who understand the structure of any system or idea. When this gets taken too far is when this notion of interpreting the structure or logic of an idea becomes translated into notions of being a "structured individual" who likes organizing closets and rooms; Ti cannot be removed from some of its abstract roots, and, when it is, it becomes closer to the list-making, status-checking nature of its Te counterparts, who are good at organizing what is laid out before them, but do not have a deep understanding of the logic behind such organization. In fact, I've seen both descriptions of clear Ti egos and real life Ti egos who are far from organized.
In any event, these are my findings. I would like to hear anyone's input, insofar as it is constructive.