Selection and Interaction: Why Incompatible Projections Force Interference-Like Structure

Incompatible projections force context, history, and interference-like combination. This paper derives the next forced structures that follow once plural, incompatible closure criteria induce projection-like stabilization maps. Building on prior results establishing ordered asymmetry, thresholded measure, and non-commuting stabilizations, we show that any nontrivial use of multiple projections requires (i) an explicit selector indicating which stabilization regime is enforced and (ii) a representation of route-dependence under sequences of stabilizations. Non-commutation implies the existence of distinct admissible routes yielding distinct stabilized outcomes, so a state-only description becomes lossy. To…