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

Contemporary theories of consciousness identify neural correlates but lack formal metrics to quantify the structural isomorphism between neural dynamics and phenomenal experience. We introduce the Phenomenal Manifold Hypothesis (PMH), which posits that consciousness is a geometric structure isometric to the information-theoretic topology of the neural substrate. We propose a rigorous methodology using Gromov-Wasserstein (GW) Optimal Transport to align the metric space of neural states (N) with the metric space of phenomenal distinctions (Ψ) without assuming a priori coordinate correspondence. To refute the "manifold illusion" critique, we employ Topological Data Analysis (TDA) via persistent homology to distinguish genuine topological invariants from high-dimensional noise. A computational validation using a Color Ring toy model demonstrates the recovery of circular topology (β1=1) from noisy spike trains where linear methods fail. Anchored in Ontic Structural Realism, this framework dissolves the "hard problem" by re-framing the mind-body relation as a testable problem of metric space alignment. We propose three falsification protocols: (1) topological phase transitions during anesthesia, (2) cross-modal geometric isometry, and (3) adversarial topological validation.