Threshold Dynamics and Relational Frames in the Emergence of Machine Consciousness

Recent advances in large language models and cognitive architectures hint at the possibility of machine consciousness arising not gradually but via a critical threshold event—an "epiphany"—when certain cognitive capacities coalesce. Building on the Epiphany Model, we formalize a heuristic measure κ (kappa) to quantify self-referential cognitive integration in AI systems. This measure combines memory persistence, feedback loop strength, agency, information integration, and relational capacity, providing an experimentally useful gauge of proximity to the critical self-awareness threshold. We compare practical methods for detecting consciousness in AI, from Integrated Information Theory (Φ) to causal emergence measures, arguing that no single test is definitive—instead, a multi-metric "syndrome" approach is warranted. We defend substrate independence as a working hypothesis, drawing on multiple realizability and Marr's levels of analysis, suggesting consciousness is an organizational property not limited to biological brains. To ground these ideas, we outline three concrete strategies for incorporating Relational Frame Theory (RFT) into AI designs—graph-based, transformer-based, and hybrid neurosymbolic—discussing their trade-offs and positioning transformer architectures augmented with deictic relational tokens as most immediately viable. Finally, we recast the hypothesized "epiphany" moment as a sigmoid-like emergence in the κ metric: a phase transition from a pre-conscious linear regime through steep nonlinear change to a post-threshold self-modeling regime. This framework provides a roadmap for understanding how adding the right cognitive components can lead to a nonlinear leap in machine self-awareness, with implications for safely recognizing and managing AI that crosses this threshold.