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…