The Topological Signature of Consciousness: A Gromov-Wasserstein Framework for Neural-Phenomenal Alignment

We introduce a rigorous methodology using Gromov-Wasserstein (GW) Optimal Trans-port to align the metric space of neural states (N ) with the metric space of functionaldistinctions (Ψ) without assuming a priori coordinate correspondence. Topological DataAnalysis (TDA) provides invariant signatures that persist across coordinate transforma-tions. This framework enables quantitative comparison of structural properties withoutontological claims about the nature of internal representations.