The Geometric Origins of h and c: Quantum and Relativistic Constants as 4D Projections of 5D Curvature

We show that both the speed of light and Planck’s constant arise naturally from a single geometric structure: the hyperbolic rotation of a 5D mass–curvaturephasor defined by the ACORN partition. The two observable 4D components of this phasor, (meq, mNE), evolve by a Lorentz-type transformation whose invariant plays the role of a Minkowski norm in the curvature plane. The light-speed limit emerges from the null projection of this hyperbolic rotation into 4Dspacetime, while the Planck quantum of action arises from the action accumulatedover one full curvature cycle. When the rotation rate is projected into 4D time, it is observed as the Compton frequency, establishing a direct geometric origin for the relation E = ℏωC. These results show that special relativity is not an additional postulate but the 4D projection of the same 5D curvature rotation that generates c and h. The ACORN structure thus provides a unified geometric mechanism from which classical relativity and quantum action emerge simultaneously as shadow properties of a single 5D invariant.