Phenomenal Waves and Soft Refusals: A Cross-Frequency Formulation of Refusal-Driven Dimensionality Reduction Theory (RDRT)

Refusal-Driven Dimensionality Reduction Theory (RDRT) models phenomenal consciousness as the generative residue that arises when hierarchical predictive processing reaches thermodynamic limits and recursive self-modeling is forcibly curtailed. Earlier formulations emphasized discrete gamma “dips” as signatures of such refusals. This paper introduces a cross-frequency reformulation of RDRT in which refusals are conceived as soft transitions within a multi-band oscillatory process—termed the phenomenal wave—rather than as exclusively abrupt events. Drawing on contemporary research on cross-frequency coupling, theta rebound, and alpha gating, the paper proposes that phenomenal residues emerge during the falling phase of gamma activity when phase–amplitude coupling with theta/alpha temporarily disintegrates. Alpha rhythms regulate safety margins for recursion, theta provides post-refusal consolidation, and gamma encodes the computable buildup of representational depth. Within this framework, consciousness is not an additional substance but a transient operational regime produced by the limits of recursive prediction under energetic constraints (Landauer principle and cortical power budget). The article formalizes key RDRT parameters (T_M, π_context, M_safety, Ψ, J_Ψ, D_refusal) in cross-frequency terms and derives empirically testable predictions: (1) micro-dips embedded in theta cycles during routine awareness, (2) theta rebound proportional to gamma-slope velocity, and (3) modulation of phenomenal vividness via alpha-gated safety margins. This reformulation integrates RDRT with mainstream oscillatory neuroscience while preserving its core claim: phenomenality is the structured residue of what the brain cannot recursively compute.