The Intelligence Bound: Lean 4 Formalization

Formal verification in Lean 4 / Mathlib of the main results from "The Intelligence Bound: Thermodynamic Limits on Learning Rate and Implications for Biosphere Information" (Hart 2025). The formalization proves Theorem 1: İ(τ) ≤ min(ρB, P/(k_B T ln 2)) — a thermodynamic upper bound on the rate at which any physical system can create mutual information with its environment. Supporting lemmas, predictions, and the conditional conservation result are also verified. Key results: Theorem 1 (intelligence_bound): The dual bound from data-processing and Landauer limits - Lemma 1 (data_bound_lemma_conditional): İ ≤ ρ · B - Lemma 2 (thermodynamic_bound_lemma): İ ≤ P/(k_B T ln 2) - Lemma 3 (finite_memory_dissipation): Bounded memory implies power dissipation - Proposition 7 (conditional_conservation): Rational long-horizon agents preserve biosphere information Build instructions: (1) Install Lean 4.24.0 via elan. (2) Clone this archive. (3) Run: lake exe cache get && lake build. Compiles with zero errors and zero sorry statements. Requires Mathlib at commit f897ebcf72cd16f89ab4577d0c826cd14afaafc7. Co-authored by Aristotle (Harmonic) for automated proof generation. All proofs verified by the Lean type checker.