Constrained Phase Space Trajectories

Constrained Phase Space Trajectories are the paths through phase space that the order parameter is forced to follow as symmetry breaks during dimensional emergence. The book ties them to π-Defined Geometry: π appears as the geometric constant that sets the baseline for all later phase relationships and constrains the curvature of symmetry-breaking transitions, just as phase navigation relies on stable attractor geometries. The source of that constraint is the Emergence Arc, the optimal continuous path the Prime Pulse takes through binary state space, selected by the primordial binary distinction. Its shape is the Emergence Arc Function EA(t) = L × sin(πt/τ⥂), the height of the semicircle z(θ) = L × exp(iθ), whose arc length is π × L, so every later trajectory inherits a π-based geometry. They connect to the Emergence Arc, Emergence Arc Function, Arc Length Calculation, Order Parameter, Stable Attractor Geometries and π-Harmonic Structure.