The next question after Turing's question: Introducing the Grow-AI test

Abstract: This study aims to extend the framework for assessing artificial intelligence, called GROW-AI (Growth and Realization of Autonomous Wisdom), designed to answer the question "Can machines grow up?" -- a natural successor to the Turing Test. The methodology applied is based on a system of six primary criteria (C1-C6), each assessed through a specific "game", divided into four arenas that explore both the human dimension and its transposition into AI. All decisions and actions of the entity are recorded in a standardized AI Journal, the primary source for calculating composite scores. The assessment uses the prior expert method to establish initial weights, and the global score -- Grow Up Index -- is calculated as the arithmetic mean of the six scores, with interpretation on maturity thresholds. The results show that the methodology allows for a coherent and comparable assessment of the level of "growth" of AI entities, regardless of their type (robots, software agents, LLMs). The multi-game structure highlights strengths and vulnerable areas, and the use of a unified journal guarantees traceability and replicability in the evaluation. The originality of the work lies in the conceptual transposition of the process of "growing" from the human world to that of artificial intelligence, in an integrated testing format that combines perspectives from psychology, robotics, computer science, and ethics. Through this approach, GROW-AI not only measures performance but also captures the evolutionary path of an AI entity towards maturity.