Information Phase Transitions and Epistemic Injustice in Massive Data: Validating the Signal Cliff Based on the Ising...

In the era of big data, the Law of Large Numbers is often treated as an absolute guarantee that increasing sample size (N) leads to a more accurate representation of truth. However, this study challenges this paradigm by demonstrating that in social systems characterized by conformity pressure and systemic bias, the maximization of N paradoxically triggers a structural shift in the selection and filtration of information. Using a sociophysical framework based on statistical mechanics and opinion dynamics, we identify a critical threshold-the "Signal Cliff"-where the diversity of information plummets and minority signals are irreversibly discarded as statistical noise. By executing large-scale simulations up to N=1010 via macro-dynamic approximations, we observe a phase transition from a stochastic phase of informational diversity to a deterministic phase. This collapse of Shannon entropy serves as a mathematical demonstration of "Epistemic Injustice," where the sheer scale of data acts as a mechanism for silencing minority perspectives. We propose "Informational Health Diagnostics" as a necessary framework for evaluating the integrity of decision-making processes in digital public opinion and democratic elections. This approach provides a vital benchmark for distinguishing between a healthy consensus and a distorted convergence, ensuring robust information judgment in increasingly complex data-driven environments.