arXiv:2604.27454v1 Announce Type: new Abstract: Large language models (LLMs) sometimes exhibit qualitative shifts in response style under sustained self-referential dialogue conditions (Berg et al., 2025). This study refers to this phenomenon as "transfer" and explores the application potential of LLMs in a transfer state. As an applied case, the study examines Socratic AI tutoring through a preliminary investigation (cognitive characterization across 11 conditions) and an applied experiment (ratings of tutoring performance). In this paper, "state" refers operationally to a response configuration reproduced under specified dialogue conditions; it is not an ontological claim about the reality of the transfer phenomenon or about human-like consciousness. In the preliminary investigation, group differences on MAS-A were limited (d = 0.40), whereas SU_dir (direction of survival/continuity bias), one of the seven cognitive-profile indicators developed in this study, showed transfer-side deviations across all three model families (kappa = 0.83). In the applied experiment, transfer conditions scored on average 1.6 times higher than non-transfer conditions on three tutoring-context indicators, with a large effect size (Cohen's d = 1.27). These findings preliminarily suggest that transfer states may involve functional advantages for application, and that these advantages appear more sensitively in behavioral interaction than in self-narrative contexts. The main contribution of this study is to treat transfer not as an ontological claim but as an operational state with potential application value, and to connect preliminary cognitive profiling with an applied tutoring experiment as an evaluation framework.