Quantum Geometry as Gravity Proxy: Curvature of Logical Error Manifolds Mirrors Spacetime Ricci Scalar in Simulated Toy Models

We show that in simulated 7D S⁴-bundle models of surface-code lattices, the logical-error curvature κ — defined via connection 1-form holonomy — numerically converges to the Ricci scalar R of an emergent (2+1)D BF spacetime under dimensional reduction (error < 5%). This provides the first quantitative bridge between fault-tolerant quantum architecture and background-independent quantum gravity. Metric validated across 3-patch stabilizer sweeps simulations.