Minimal-Energy Paths

Minimal-Energy Paths are the trajectories of least energy that the Primordial Binary Distinction selects from the infinite potential of the Pre-Pulse Field, and along which binary transitions must run. The book builds its geometric account of π on them. When δ₀: Ω◁ → {0, 1} selects Minimal-Energy Paths, the requirement that binary transitions follow Energy-Minimizing Trajectories while preserving Information Conservation, I⊚ = I▱ + Iℜ, gives rise to the geometric interpretation of the Prime Pulse: a continuous trajectory through binary state space, the Emergence Arc, which is the optimal path selected by the primordial distinction and is described by the Emergence Arc Function EA(t) = L × sin(πt/τ⥂). In this way π appears as the geometric constant that sets the baseline for all subsequent phase relationships and curvature constraints. It connects to the Primordial Binary Distinction, Energy-Minimizing Trajectories, the Emergence Arc, Emergence Arc Function, Optimal Trajectory, Minimal-Energy Arc Constraints and the Intrinsic Geometric Constant.