The Constitutional Hamiltonian: Deriving Observable Consequences from Topological First Principles

This document presents a first‑principles Hamiltonian framework for constitutional AI governance. By embedding knot invariants (Jones and Alexander polynomials) directly into a three‑term non‑Hermitian Hamiltonian, it transforms constitutional compliance from a set of behavioral rules into a physical energy landscape. The framework derives observable consequences: an exponential coherence time scaling with knot complexity, a universal drift threshold of 0.17, a 3.33 ms operational heartbeat, and a spectral linewidth‑knot correspondence. It unifies AI safety, strategic economics, and topological physics, providing a mathematically self‑consistent foundation for verifiable, fail‑closed sovereign AI systems.