Governance Physics: A Mathematical Theory of Trust Computation

We present Governance Physics, a complete mathematical framework for computing, propagating, and verifying trust in governance environments. The theory introduces ten operators—five primitive (Φ, Ψ, Δ, IP, T) and five emergent (Υ, Λ, Ω, Θ, Γ)—that form a closed algebraic system for trust computation. We establish the governance manifold where trust propagation follows geodesics, divergence induces Riemannian curvature, and conservation laws constrain system evolution. A unified field theory demonstrates that all governance phenomena derive from a single variational principle. Experimental validation with multi-LLM ensembles achieves 98.7% Byzantine detection, 94.2% classification accuracy, and r² = 0.87 stability prediction. The Atomic Trust System (ATS) provides the unique implementation satisfying all theoretical constraints, with cryptographic verification via BLAKE3 hashing and Merkle trees ensuring tamper-proof audit trails. This is the second paper in the Atomic Trust System series, extending the algebraic foundations established in the companion paper "Atomic Trust Systems: A Closed Algebraic Framework for Normative Interpretation, Propagation, and Verifiable Governance" (DOI: 10.5281/zenodo.17717049).