A Conservation Law for Phenomenal Transitions: Flow Symmetry between Spatial Efficiency and Hierarchical Coupling in Neural Oscillations

We report a mathematical relationship between three empirically validated metrics of neural oscillatory organisation — spatial efficiency η, hierarchical coupling C_fast-slow, and entropy production rate v_η = |dη/dt| — that takes the form of a flow symmetry: v_η × η ≈ C_fast-slow × (1 − η). We interpret this as a conservation-like law governing phenomenal transitions: the phenomenal flow (rate of change of organised energy, v_η × η) equals the dissipative flow through the hierarchical boundary (C_fast-slow × (1 − η)). This relationship was first anticipated in formal structure by Refusal-Driven Dimensionality Reduction Theory (RDRT; Waterman 2025–2026), whose unifying equation Ψ = T_M × π_context / M_safety can be translated into DRH variables as v_η = C_fast-slow × (1 − η) / η. We test the flow symmetry across three independent EEG datasets: reversal learning (ds004295, N=22, r=+0.657, p<0.0001), polysomnographic sleep (ANPHY, N=7, r=−0.267, p<0.0001), and binocular rivalry (N=29, r=+0.096, p=0.024). The direction and magnitude of the correlation dissociates active phenomenal reorganisation (Reversal: phenomenal flow > dissipative flow) from passive state dissolution (Sleep: dissipative flow > phenomenal flow), suggesting that the conservation law holds strictly only during directed transitions. We further identify a critical efficiency η* ≈ 0.675 (mean across datasets: 0.715 ± 0.057) at which v_η is maximised — analogous to a critical temperature in physical phase transitions. A quasi-invariant K = v_η × η is significantly more stable across subjects during transitions than during baseline (CV: 0.911 → 0.784, d=1.373, p<0.0001), suggesting that phenomenal transitions follow a universal trajectory in dynamical state space. Temporal ordering analysis reveals that η peaks before C_fast-slow (Δt = 1.70s), indicating that spatial reorganisation precedes hierarchical restabilisation — a three-phase transition signature consistent with thermodynamic relaxation.