D3 Optical Probe v0.1: Minimal Optical Experiment for Torus Topology Detection via Commuting Phase Flows

This document defines a minimal experimental protocol for testing whether a photonic quantum-link platform can be constrained so that its output modes are organised by two independent commuting winding indices, rather than by externally programmed phase parameters. The protocol is designed for application to optical systems such as electro-optic transducer networks and programmable Mach–Zehnder interferometer meshes. It isolates two phase variables (θ1, θ2) ∈ S1 × S1 and applies three tests: (1) periodic closure on S1, (2) local commutation of infinitesimal phase flows, (3) spectral organisation as a Z x Z mode lattice with non-zero cross modes. The central condition is Test 2 v1.1, which measures the commutation residual C(θ1_0, θ2_0, δ) = ||Output_A − Output_B|| across the phase space. The maximum deviation C_max(δ) provides a quantitative measure of non-commutation. The protocol does not claim that existing optical link systems exhibit torus topology. It defines a testable constraint under which such topology would be detectable via the D3 spectral discriminator framework (Tuckwell, 2026). No experiment has been performed. C_max(δ) is unmeasured. The document is presented as an initial experimental design (v0.1) and is open to revision upon implementation. Structural analogy: PASS. D3 equivalence: FAIL. Experimental platform relevance: VERY HIGH. Keywords: torus topology spectral geometry quantum optics optical interferometry Mach-Zehnder interferometer phase space topology commuting generators winding indices D3 spectral discriminator experimental protocol electro-optic transduction quantum communication