Two Attractors and Five Layers: A Phenomenal State Space Defined by Spatial Efficiency and Inter-Layer Tension of Neural Oscillations

Abstract We propose that the phenomenal state of a conscious system can be characterised by two independent dimensions derived from the spatial organisation of neural oscillations across five canonical frequency bands (δ, θ, α, β, γ): (1) η — the spatial efficiency, measuring the overall fraction of oscillatory energy organised into coherent spatial patterns, and (2) angle(Ψ,Δ) — the angle between the Effective Power Vector and the Dissipative Vector in five-dimensional frequency space, measuring the degree of inter-layer tension across the oscillatory hierarchy. Theoretically, these dimensions correspond to two fundamental aspects of phenomenal experience: η tracks the overall level of consciousness — the degree to which the phenomenal field is maintained — while angle(Ψ,Δ) tracks the structural complexity of that field — the number of active boundaries between phenomenal layers, each constituting what we term a "local hard problem." This framework is grounded in the theory of Negative Space Encoding (NSE), which proposes that the oscillatory hierarchy implements progressive constraint-based encoding, with slow bands (δ,θ) serving as a global scaffold for local processing in fast bands (α,β,γ). We validate the two-dimensional framework across five independent EEG datasets spanning propofol sedation (Bajwa et al. 2024, N=21; Chennu et al. 2016, N=20), polysomnographic sleep (Wei et al. 2024, N=7), rule reversal learning (ds004295, N=22), and binocular rivalry (Torralba Cuello et al. 2025, N=29). Three qualitatively distinct trajectory types are identified in the (η, angle) space: horizontal (η changes, angle stable — sedation and reversal), diagonal ascending (η falls, angle rises — sleep onset), and vertical descending (angle collapses at low η — deep sleep). These trajectory types correspond to three distinct mechanisms of phenomenal transition: quantitative reduction, structural complexification, and structural collapse. The two-dimensional framework resolves a key limitation of scalar consciousness metrics: it distinguishes between states with different phenomenal structures at similar consciousness levels, and identifies the N2 sleep stage as the state of maximum inter-layer tension — the state with the most active boundaries between phenomenal layers — even though its overall consciousness level is low. Part of the NSE/RDRT preprint seriesKeywords: consciousness; neural oscillations; spatial efficiency; inter-layer tension; phenomenal state space; sleep; propofol sedation; binocular rivalry; Negative Space Encoding; RDRT; two attractors; frequency bands; EEG