Hardy and Cabello Arguments in Spatial and Temporal Frauchiger-Renner Scenarios

We investigate Hardy- and Cabello-type logical structures within spatial and temporal extensions of the Frauchiger--Renner (FR) framework, embedding these constructions directly into the FR multi-observer architecture. In the spatial multi-observer scenario, both Hardy and Cabello contradictions arise, with the Cabello construction yielding the stronger violation,\(Δ_{rm Cabello}^max=0.1078\), which exceeds the maximal Hardy probability \(P_H^max=frac{5sqrt{5}-11}{2}approx 0.09017\). We then develop a sequential temporal FR protocol based on coherent multi-observer measurements performed on a single spin-tfrac12 system. In this temporal setting, the Hardy contradiction disappears identically due to dynamical constraints imposed by sequential state updates, whereas a finite Cabello-type violation survives, Δ_{rm Cabello}^maxapprox 0.0674. Our results establish a fundamental structural distinction between spatial entanglement and temporal multi-observer correlations in FR-type logical scenarios, and demonstrate that certain observer-independent description failures persist even without spacelike separation.