Spatial Organisation of Neural Oscillations as a Multi-Dimensional Marker of Phenomenal State: Metrics, Datasets, Limitations, and a Roadmap Toward a Universal Baseline

Abstract 1 The measurement of phenomenal consciousness from EEG signals remains an open methodological challenge. Existing scalar metrics — Lempel-Ziv Complexity, Perturbational Complexity Index, spectral entropy — capture the level of consciousness but lose information about the structure and organisation of phenomenal states. This paper presents a systematic empirical investigation of a family of metrics derived from the spatial pattern stability of neural oscillations across five canonical frequency bands (δ, θ, α, β, γ), validated across five independent EEG datasets spanning propofol sedation (N=21, N=20), polysomnographic sleep (N=7), rule reversal learning (N=22), and binocular rivalry (N=29). We evaluate seven metrics: spatial efficiency η, the angle between Effective Power and Dissipative Vectors angle (Ψ, Δ), inter-band synchrony of organisation CV-sync (Sγ), inter-band synchrony of dissipation CV-sync (1−Sγ), the dissipation gradient disgrad, the hierarchical decoupling gradient Δₕier, and shape-based metrics (profile slope, contrast, entropy). We identify three qualitatively distinct types of phenomenal trajectories in the two-dimensional (η, angle) state space, and demonstrate that the N2/N3 sleep distinction — a key test case — requires different metrics than the waking/sleeping distinction. We characterise in detail the central remaining obstacle: the absence of a cross-dataset-valid metric that simultaneously distinguishes N2 from N3 and is independent of dataset-specific baselines. We propose two concrete paths toward resolution: the construction of a population-level universal reference baseline, and the development of purely relational metrics based on profile shape. The paper concludes with a roadmap for future work including specific methodological proposals for establishing the universal baseline. Keywords: EEG; neural oscillations; spatial efficiency; inter-band synchrony; consciousness metrics; sleep staging; propofol sedation; binocular rivalry; cross-dataset validity; Negative Space Encoding; phenomenal state space Abstract 2 This paper presents a systematic empirical investigation of metrics derived from the spatial pattern stability of neural oscillations, with a focus on two problems identified in Version 1: (1) the absence of a cross-dataset-valid metric that simultaneously distinguishes N2 from N3 sleep and is independent of dataset-specific baselines; and (2) the construction of a universal reference baseline. Version 2 reports three new empirical findings. First, the temporal correlation structure of Sγ time series — Cfast-slow, the mean absolute correlation between fast-band (α, β, γ) and slow-band (δ, θ) Sγ — is validated across three independent datasets. Cfast-slow significantly distinguishes all sleep stages including N2 from N3 (d=2. 238, p=0. 016, N=7), is elevated during rule reversals (d=0. 793, p=0. 002, N=22), and is reduced pre-switch in binocular rivalry (d=−0. 228, p=0. 190, N=29). Critically, Cfast-slow does not require a reference baseline and is therefore inherently cross-dataset valid. Second, an attempt to construct a universal reference baseline from the LEMON resting-state EEG dataset (N=211/220 subjects) reveals that individual spatial amplitude patterns are essentially orthogonal to the population mean (mean r≈0), precluding direct cross-subject pattern comparison. This finding establishes that Path 1 (Universal Reference Baseline) in its naive form is not viable, and redirects attention to Path 2 (purely relational metrics). Third, we provide an updated metric summary table incorporating Cfast-slow alongside the original seven metrics. Keywords: EEG; spatial efficiency; Cfast-slow; hierarchical decoupling; sleep staging; N2/N3 distinction; cross-dataset validity; universal baseline; LEMON; Negative Space Encoding