The Universal Form Principle (ULF): A Recurrent Principle of Morphogenetic Balance

This preprint introduces the Universal Form Principle (ULF), a third component that complements and extends the earlier USL (energetic stability) and LUDC (entropy–descent limit) principles, forming an informational triad that describes how patterns emerge and become regulated. ULF proposes that self-organization is constrained not only by energy and entropy, but also by a geometric regularization term (a curvature cost) that moderates form complexity through a dynamical equation for structured information Φ. The hypothesis is tested across seven domains: (E1) Gray–Scott reaction–diffusion, (E2) 3-SAT optimization (WalkSAT), (E3) neural learning (MLP), (E4) a discrete morphogenetic lattice (CPM proxy), (E5) the Game of Life cellular automaton, (E6) a genetic algorithm (One-Max), and (E7) biological patterning (zebrafish and angelfish). Results show robust quantitative agreement in continuous regimes (MRD < 10%, R² ≈ 0.9) and improved trends in discrete domains after physically motivated metric refinements. The document also provides falsifiable predictions and reproducibility details (metrics, protocols, and simulation parameters).