From Geometric Control Manifolds to Toy Ψ-SLM: A Classical, Variational Implementation on Hyperbolic Manifolds

This paper presents a classical, discretized implementation of the Geometric ControlManifolds framework. The Toy Ψ-SLM is a variational architecture translating continuousgeometric principles into computable approximations for standard hardware. The imple-mentation preserves the Lorentzian substrate, the causal role of geometry as constraint, andstructural falsifiability, while substituting exact topological invariants with differentiableproxies and continuous flows with discrete Euler updates. No claims about consciousness, phenomenology, or cognition are made; all constructs are operational, approximate, and falsifiable.