A Bidirectional Criticality TAC Model of Conscious Emergence: A Phase-Transition Framework under Temporal Integration and Resource Constraints

Abstract

Consciousness research has largely been framed in static, binary terms, lacking a dynamical description of how conscious states switch, exit, and rebuild over time. Starting from three minimal physical constraints—finite resources, non-equilibrium maintenance, and discrete input—this paper develops a temporal-dynamics model under an Information Capacity Frame (ICF) and proposes the TAC framework, in which temporal span (T) and reconstruction activity (A) act as two orthogonal control parameters and closed-loop completeness (C) serves as the order parameter. We argue that conscious emergence is a critical phase transition in this two-parameter temporal–reconstructive space. On the temporal side, we separate the existence of a finite window bound, an Ω(m²) worst-case lower bound for open-ended reassociation, and a linear average-cost operating point under sparse priors; a single sufficient summary (USVI) shows how the self-referential closed loop converges. On the critical side, a cusp normal form unifies three signatures—discontinuous jump, hysteresis, and critical slowing—within one dynamical form. The model yields the critical condition for the L2→L3 transition, a T–A zero-sum budget identity, and the scaling T_max ≈ θ·√(P/u), and connects four quantitative predictions and five falsifiable hypotheses to age-related degradation, anesthetic hysteresis, θ-power scaling, and supercritical oscillations. All results are constraint-driven convergence claims rather than uniqueness proofs, and are substrate-neutral. Independent calibration of the unit-link cost and the allocated power defines the empirical agenda ahead.