Probability is Lack of Information: Part II -The Binary Entropy Function as a Formal Proof of Universal Determinism

Following the axiomatic declaration that Probability is lack of information, this second installment provides the formal information-theoretic validation of this motto through the lens of the Binary Entropy Function (H(p)). We demonstrate that the characteristic "horse-shoe" geometry of H(p) is not merely a measure of uncertainty, but a rigorous benchmark quantifying the informational deficit between the observer and the deterministic signal source. By mapping the Hendeca-Tier Cosmic Signal Architecture (HCSA) onto the entropy curve, we establish that the peak at p = 0.5 represents the point of maximum informational gap, while the convergence toward H(p) → 0 at the boundaries signifies the emergence of objective reality as the informational resolution reaches the Cevher-i Ferd (singular information unit) limit. Through a differential analysis of the entropy gradient, we prove that even the slightest probabilistic deviation is a direct function of missing data within the 121-unit universal mizan. This paper establishes the Binary Entropy Function as the ultimate benchmark for Universal Determinism, transforming probability from an inherent physical property into a measurable indicator of human observational limitations.