The CARD framework models spacetime as a causal medium with finite geometric response, regulated by a maximum proper acceleration and a packetized correction mechanism. In this medium, radial distortions generate gravitational and electric response, while angular distortions generate magnetic interactions and intrinsic spin. CARD-III develops the rotational sector of the framework, showing that spin corresponds to the minimum stable vortex permitted by the causal structure of the medium and that the magnetic moment is the external imprint of this vortex on surrounding worldlines. The fine-structure constant emerges as a dimensionless ratio of the medium’s radial and angular kinematic taxes, and Maxwell’s equations arise as the continuum limit of the medium’s response to curvature and vorticity. A central result of this installment is the use of hydrogen as a probe of the medium’s discrete sector. Because both radial curvature and angular vorticity are regulated by the same minimum action K, the equilibrium geometry of the ground state yields a direct relation between observable hydrogenic quantities and the fundamental geometric constant K. Solving this relation with measured hydrogenic observables produces a value of K that agrees with the reduced Planck constant h-bar to experimental precision. In CARD, this agreement is not an assumption but a prediction: the quantum of action arises from the causal structure of the medium itself. Together with the results of CARD and CARD-II, this work completes a unified geometric picture in which curvature, action, and vorticity are manifestations of a single causal substrate.
Gary A. Marszalek (Sat,) studied this question.