The bulk-edge correspondence is one of the most important ingredients in the theory of topological phases of matter. While the bulk-edge correspondence is applicable for Hermitian junction systems where two subsystems with independent topological invariants are connected to each other, it has not been discussed for junction systems with non-Hermitian point-gap topological phases. In this Letter, based on analytical results obtained by the extension of non-Bloch band theory to junction systems, we establish the bulk-edge correspondence for point-gap topological phases in junction systems. We also confirm that almost all the eigenstates are localized near the interface which are called the “non-Hermitian proximity effects”. One of the unique properties is that the localization length becomes the same for both subsystems, nevertheless those model parameters are different.

Background: Digital exclusion is a validated risk factor for cognitive decline in older adults. Digital interventions exhibit high dropout rates due to low digital literacy, technology anxiety, and limited adaptation to individual states, resulting in limited real-world transfer. Objective: This protocol aims to present the CTC Framework (Coach–Teacher–Companion), a tri-agent generative AI system proposed for exploring the feasibility of adaptive cognitive interventions in older adults with existing digital access. The protocol provides technical architecture, feasibility-stage implementation procedures, and methodological and ethical guidelines to assist clinicians in safely applying AI-based cognitive interventions in clinical research settings. Methods: The framework integrates three AI agents (Coach, Teacher, and Companion) designed to provide behavioral, cognitive, and emotional support. The system is designed to embed cognitive exercises in daily activities, monitor emotional states, and incorporate accessibility features for age-related limitations. Implementation safeguards include digital literacy assessment (MDPQ-16), technology anxiety monitoring (CARS), emotional safety protocols, and data privacy protections. The protocol specifies a six-week feasibility study (n$=14$, MMSE 18–25) to evaluate usability (System Usability Scale, primary outcome), user experience (UEQ-S), psychological needs satisfaction (BPNS), emotional safety (PANAS), adherence, and preliminary cognitive outcomes (MMSE, TMT-A/B, Digit Span). Conclusions: The CTC Framework is designed to provide methodological and ethical safeguards for clinical implementation, including standardized procedures for digital literacy assessment, technology anxiety management, emotional safety monitoring, and data privacy protections. Empirical validation of the framework’s feasibility and efficacy is required through future studies.