Why Conscious Gating Locks onto the Theta Frequency: A First-Principles Account

Recent intracranial evidence shows that high-order thalamic nuclei (intralaminar and medial) gate conscious perception through thalamofrontal loops, with information flowing from thalamus to prefrontal cortex; yet the necessity of θ-frequency dominance and the all-or-none discontinuity of gating failure remain unexplained at the first-principles level. Starting from three axioms—finite resources, non-equilibrium maintenance tendency, and discrete input—we derive a dual-configuration architecture under the Information Capacity Frame (ICF), and derive a bidirectional critical feasible domain for temporal span (T) and reconstruction activity (A). We show that the minimal temporal window T_min required for self-referential closure is logically determined by the minimal construction of tri-segment attribution; in carbon-based nervous systems, this value converges to the θ-cycle timescale. This explains, from physical boundary conditions, the rigid constraint of θ-rhythms on conscious gating, and redefines conscious perception as a critical transition of cross-moment temporal integration. The framework provides a constraint-convergence-based dynamical explanation for consciousness emergence and yields falsifiable morphological criteria for critical transitions, with a quantitative scaling law for the upper window bound.