Note...Regarding the PTRE-Integrated Alice Theory, Version 3: It is not so much a creation by myself and an AI, but rather an evolution of the Alice Theory that emerged from facilitating a discussion between the free versions of ChatGPT-5 and Gemini, with me acting as the mediator. Currently, we are in the phase of verifying its values by operating the conventional Alice Theory in conjunction with the \pm 0 Theory. I will report the results once the verification is complete. To continue the development trajectory: after reporting the results, if no significant need for improvement is found, we will move on to creating the full-scale mediation code for the LLMs.