Quantum Amplitudes on Causal Sets as a Structured Framework for Propagation and Realization

This paper proposes an operational interpretation of quantum amplitudes in causal set theory by relating them to unresolved radiative relations prior to physical realization. While standard causal set theory provides a discrete kinematical structure for spacetime, the role of quantum amplitudes within such a framework remains an open question. Building on existing approaches to quantum dynamics on causal sets, including quantum measure theory and discrete path integrals, the present work introduces a physically grounded perspective in which amplitudes correspond to lawful but unrealized connections that may become fixed through radiative closure events. This interpretation distinguishes between realized causal structure and generative relations, offering a bridge between discrete spacetime models and quantum theory. The framework is compatible with Lorentz invariance at the level of realized structure while providing a novel account of how probabilistic features arise in a fundamentally discrete setting.