Organic Curve Geometry (OCG): A Unified Framework for Generative Geometry, Physics, and Computation · Organic Curve Geometry: A Complete Mathematical Framework for Shape Generation and Analysis · Organic Curve Geometry (OCG): A Novel Geometric Framew

This record presents the complete framework of Organic Curve Geometry (OCG) , a non-Euclidean geometric system built from first principles. The framework replaces the straight line with the flowing curve as the fundamental building block of space and introduces the logarithmic gradient as a new fundamental measurement. It is generated from a single master wave equation and encompasses a full suite of mathematical tools, including organic trigonometry, calculus, topology, algebra, analysis, and a new invariant called Morphological Energy. The work is presented in four parts and includes over 90 rigorous mathematical proofs. It recovers Euclidean geometry as a distinguished equilibrium limit while exhibiting genuinely new phenomena in its general case.