Observer Horizon Limits and the Non-Measurability of Cosmic Finitude: An Information-Theoretic Boundary in Minkowski Spacetime

This paper establishes a formal epistemological limit on observational cosmology derived from the proper time constraint of physical observers ($\Delta\tau > 0$). By examining the signal processing bounds imposed by the speed of light $c$, we demonstrate that any physical entity capable of recording data or executing cognitive state transitions is strictly confined within a local causal horizon. Consequently, empirical verification of whether the global spacetime metric is spatially finite or infinite remains fundamentally inaccessible. We show that attributing finite boundaries to the universe based on observational limits is a category error that projects observer-dependent temporal architecture ($\Delta\tau > 0$) onto absolute cosmic geometry.