This paper develops a root formalism for how distinguishability can arise without presupposing geometry, locality, carrier structure, calculus, or later physical machinery. By excluding isolated nullity and isolated undifferentiated totality as sterile primitive terminals, it derives a unique admissible origin as unresolved primitive opposition. Because discharge of this opposition would collapse into already excluded terminal states, any admitted articulation must bear the invariant internally. This yields non-flat distinguishability as the first live consequence. The paper then shows that articulation within a single admitted axis is exhaustively saturable but not terminal: once no genuinely new invariant-bearing articulation remains available in that same axis, continuation there is closed while discharge remains impossible. Orthogonal re-articulation is therefore forced. In this way the paper closes the primitive route from 0D to 1D to 2D and identifies the two-axis stage as the first point at which algebra becomes admissible. The result is a self-contained root formalism that prepares, but does not yet assume, the carrier and induced geometric machinery developed in the next paper.
Justin Lietz (Wed,) studied this question.