Book 5: The Developmental Metric and the Cone

Book 5 develops the continuous core of developmental geometry from first principles. Starting from three axioms—stability, coherence curvature, and the minimal path principle—the book derives the balance law, developmental density, geometric time, finite propagation, mass divergence, the developmental metric, curvature, geodesics, the developmental cone, and the axis field. The theory is presented as a closed variational system: the balance law arises as an Euler–Lagrange equation, geometric time normalizes developmental motion, finite propagation imposes a universal speed bound, and mass divergence forces maximal‑velocity paths to converge to geodesics of the developmental metric. The axis field is…