The Topology of Aliasing

The Topology of Aliasing examines how apparent multiplicity emerges from temporal undersampling of continuous processes. When measurement resolution increases, discrete points collapse into continuous structure; when resolution decreases, continuous structure is reconstructed as discrete points. The paper shows that observed structure depends on sampling rate relative to process rate, a constraint imposed by measurement theory. The analysis proceeds from discrete sampling and Shannon-Nyquist constraints through resolution-dependent appearance and its logical consequences. Undersampling produces discontinuous appearances, while oversampling produces apparent stasis. These effects arise from measurement limits and form a continuous spectrum governed by sampling density.