The General Theory of Curvature: A Unified 5D Curvature Framework for Matter, Fields, and Quantisation

We present the General Theory of Curvature, a unified geometric framework in which all physical phenomena arise from the curvature of a five-dimensional manifold, SpaceTime+. The theory is defined by two identities:1. The Master Curvature Equation:a 5D curvature operator acting on the full Einstein-like tensor GAB. No stress–energytensor is required; matter is encoded directly in curvature. 2. The Boundary Loop Conditions (the heartbeat law):which quantise the internal curvature modes of matter through dip–twist cycle synchronisation. From these two principles we recover, without postulates: Einstein gravitation, Maxwellelectromagnetism, quantum energy quantisation, inertial mass, charge, spin, probability as projected phase density, and the internal structure of matter as curvature phasor modes. All 4D physics is the projection of a deeper, deterministic 5D geometry.