Reflecting on the Möbius Phenomenon: Theoretical Foundations and Mathematical Models for Question-Jumper AI

With the rapid advance of large language models and the growing complexity of AI applications, the need for open-ended, question-evolving AI systems—capable of reframing their own inquiry space—is more urgent than ever.
This paper proposes and formalizes the Möbius Phenomenon as a theoretical and mathematical framework for the next generation of artificial intelligence: the Question-Jumper AI.
Unlike conventional answer-optimizing systems, Möbius-based AI is designed to evolve its own question space through recursive self-reference, multi-persona architectures, and the explicit modeling of question dynamics.
Drawing on philosophical traditions of self-negation and historical paradigms of cognitive leap, this work introduces a formal sequence model for question circulation, persona emergence, and dimensional leaps in reasoning.
The Möbius Phenomenon is positioned as a paradigm for building open-ended, explainable, and resilient AI, with a roadmap from theory to implementation and social embedding.
All mathematical formulations, model flowcharts, and core concepts are included for academic critique and further development.