...Which is to say that whenever there is (a physical arrangement with) a logical structure that matches (is transitive with) the logical structure of consciousness - then there would be consciousness. It gets more complicated. If you draw a line with a pencil on a piece of paper, so that it encodes a three dimensional trajectory over time of a sentient being's consciousness - you basically have created a "soulful" being. Except there's just a drawn line on a piece of paper.

Assuming this is possible, I would say the line on the paper is a "rendering" or "depiction" of a concious being at some point in time. In order for the rendering to in some way "be" a concious being, would it not require the ability to change itself somehow? At very least it must be able to accrue memories, meaning that over time some part or parts of the rendering must be updated to coincide with the new memories. If the rendering cannot physically update itself, it seems there must be at least one extra part required.

It's hard to discuss further without relying on my personal definition of conciousness. But now that I think about it, I probably came up with this definition by analyzing similar ideas. Perhaps in some way specifying precise boundary conditions is equivalent to having a precise definition?