Observer-Independent 3D Simulation and Topological Preservation Across Projection Boundaries

This paper presents a minimal engine architecture that enforces a hard separation between an observer-independent 3D simulation ("System 1") and an observation apparatus ("System 2") that exists as an object inside the simulation and queries it through a compile-time enforced API boundary. We construct a solid torus in a sparse voxel grid, verify d² = 0 on the cubical complex, confirm Betti number β₁ = 1, and measure whether this topological feature survives projection through the observation boundary into a depth map. A phase transition is detected: topology is preserved at dimensionless geometric ratio Γ = (R−r)/d > 0.10 and lost below Γ ≈ 0.08, independent of image resolution from 32² through 512². The critical threshold is distance-dependent and resolution-independent, demonstrating that topological preservation across a projection boundary is governed by geometric relationship, not observation fidelity. All results are reproducible from the companion Rust codebase in under five minutes on commodity hardware. 17 tests pass including explicit d² = 0 verification on the cubical complex.