Temporal Alias Bound

The Temporal Alias Bound is the stability limit that the highest modal frequency times the Pulse Rhythm must not exceed π, so that the fastest modes on the minimal torus stay below the aliasing threshold and evolve stably. It caps how fast recursive processes can evolve within the minimal torus: frequency cannot rise without limit but must stay within the coherence window set by the Pulse Rhythm and the Nyquist constraint. Together with the modal spectrum, it leads the book to conclude that the Zinf torus defines not only the smallest possible geometry but also the fastest possible clock, the ultimate temporal sampling rate for reality. ω⥣ × ①⥂⧖ ≤ π, where ω⥣ is the maximum modal frequency for alias-free stepping [𝕋⁻¹], ①⥂⧖ is the half-cycle time quantum, the Pulse Rhythm [𝕋], and π is [∅]. The book's Where-list also reads κ_z, a safety factor for stable discretization, and N⥥, the minimum number of cells per loop for a stable sinusoidal mode, with the values 2, 4 and 0.5. The product is [∅] ≤ [∅]. It connects to the Nyquist Constraint, Maximum Modal Frequency, Pulse Rhythm Definition, Local Rhythm Quantum, Instantaneous Modal Frequency and the Zinf-Limit Universe.