Energy-Minimizing Trajectories

Energy-Minimizing Trajectories are the optimal paths that binary transitions must follow, least in energy while preserving Information Conservation, and the requirement from which the book derives the geometry of binary computation. The primordial binary distinction, δ₀: Ω◁ → {0, 1}, selects minimal-energy paths from infinite potential. Requiring transitions to follow such paths gives the book's Geometric Interpretation: the optimal path through binary state space is the Emergence Arc, a half-sine in time, EA(t) = L × sin(πt/τ⥂), the height of the semicircle z(θ) = L × exp(iθ), whose arc length is π × L. This is how π becomes the first emergent constant and sets the baseline for all later phase relationships and curvature constraints, including the constrained paths the order parameter follows when symmetry breaks. They connect to Minimal-Energy Paths, Emergence Arc, Emergence Arc Function, Geometric Interpretation, Primordial Binary Distinction, Constrained Phase Space Trajectories and Dimensional Emergence Curvature.