Binary Endpoints

Binary Endpoints are the two discrete states, 0 and 1, between which every pulse transition runs; the endpoints stay fixed while the transition between them carries a rich structure of information. The book's point is that although the endpoints are discrete, the transition phases are not empty: they hold information that follows Information Conservation, I⊚ = I▱ + Iℜ, and that can be used for navigation and computation, which is what makes synchronized phase manipulation possible within causal limits. Each cycle is timed on two scales: the Pulse Rhythm ①⥂⧖, the half-cycle binary transition from one endpoint to the other, and the Pulse Tempo T⥂, the full 0 → 1 → 0 computation, with T⥂ = 2 × ①⥂⧖. The book writes the Rhythm as ①⥂⧖⌂ = α × ①⥂⧗⌂ [𝕋] with α = ½ exactly, anchoring the timing in the Local Pulse Tempo (the Planck time); inherited resolution enters through the child's Tempo ①⥂⧗'⌂, not through α. The Pulse Phase Function describes the path between the endpoints within each Pulse Tempo. It connects to Pulse Rhythm Definition, Pulse Tempo Definition, Pulse Phase Function, Phase Coupling Equation, Information Conservation, State |0⟩ and State |1⟩.