Semantic Tolerance Law Second Law of Information Axiomatic Manifesto

We present the axiomatic foundation of the Second Law of Information, deriving it from first principles without physical analogies. The law states that a classification problem is learnable if and only if there exists a representation ϕ where ρϕ < 1. We establish two fundamental thresholds: the universal mathematical threshold ρ = 1 (where local structure equals random), and the physical death threshold ρdeath ≈ 1.23 (derived from Ising 3D critical exponents).