Governance Contraction Proof Tools

3 Python tools providing formal and empirical verification of governance convergence properties. These prove the mathematical foundation of Morphism's κ (kappa) metric — specifically that the governance operator is a contraction mapping (κ < 1), which guarantees convergence of agent compliance toward the ideal state.

Files:

proofs_gamma_contraction_sympy.py (50 lines, ⭐⭐⭐⭐) — Symbolic proof using SymPy. Proves the gamma contraction property of the governance operator analytically. Establishes that applying the governance functor repeatedly drives κ toward 0.

tools_empirical_estimate_k_and_report.py (77 lines, ⭐⭐⭐⭐) — Empirical estimation of the κ contraction constant from real execution traces. Measures actual convergence rate and generates a report. Bridges the formal proof with observed behavior.

tools_symbolic_prove_governance_contraction.py (21 lines, ⭐⭐⭐) — Symbolic verification of the governance contraction property. Compact verifier; likely used as a fast-check before running the full empirical estimator.

Mathematical context: In Morphism, κ = 0 means full compliance; κ < 1 means the governance operator is a contraction. By the Banach Fixed-Point Theorem, a contraction on a complete metric space has a unique fixed point — meaning repeated governance application converges to a unique compliant state. These tools prove that guarantee holds for Morphism's specific operator definitions.

Dependencies: sympy (symbolic math), no other runtime dependencies.

Source of truth: hosted in alawein/governance-proofs.