The Second Law of Information Semantic Tolerance Law — Complete Theory Physical Extension of the Axiomatic Manifesto

This paper presents the complete theory of the Semantic Tolerance Law (STL), the Second Law of Information. The core law was established axiomatically in the companion paper “Semantic Tolerance Law: Axiomatic Manifesto”, which proves: A classification problem is learnable ⇐⇒ ∃ϕ : ρϕ < 1This paper extends the axiomatic foundation with: • The transition tensor Tcc′j and its uniqueness theorem • Physical derivation of the death threshold ρdeath ≈ 1.23 • Empirical validation across 48,000+ datasets • Ontological and philosophical implicationsThe central quantity is the disorder ratio ρ = (1−τ ∗)/(1−pmax). The axiomatic version establishes ρ < 1 as universal threshold. The physical version adds ρdeath = γ/(νd) ≈ 1.23 as irrecoverability threshold.