Empirical Information Geometry on an Embedded Adaptive Lighting System: Multi-Chart Manifold Transitions Under Signal Collapse

LUCES is a 4-node ESP32 mesh network that learns the transmission of outdoor sunlight into an indoor space by tracking three coordinates on a transmission manifold: solar elevation θ, intensity observability ρ, and spectral ratio χ =log((cold+ε)/(warm+ε)). At sunset, when ρ collapses to zero, the system transitions from the intensity chart U₁ = (θ, ρ) to the spectral chart U₂ = (θ, χ). The spectral coordinate continues to evolve non-monotonically while τ remains frozen with zero drift. From the empirical data, we extract a strongly anisotropic diagonal Fisher metric (g_ρρ/g_θθ ≈ 1500), Christoffel symbols, and a regularized Levi-Civita connection that exhibits clear hysteresis between sunset and sunrise trajectories. All results were obtained on physical hardware (ESP32-S3, <2 W total consumption) with no simulation and no cloud computation. To our knowledge, this is the first empirical demonstration of signal-dependent multi-chart Riemannian geometry on resource-constrained embedded hardware.