This study presents an inter-universal mathematical-logical framework constructed upon the minimal axiom Cogito, ergo sum (CES), integrating the Intermediate Meta-Universe (IMU) and the Hierarchical State Grid (HSG). The CES defines existence as a reflexive correspondence --'to be' and 'to be sayable'--and positions any formal system, including ZFC or HoTT, as an attachable extension atop this minimal structure. The IMU functions as a registry of axiomatic dependencies that connect heterogeneous theories, employing the Institution-theoretic framework to ensure coherent inter-theoretical linkages. The HSG concretizes these ideas through categorical construction, defined by three orthogonal axes: the state-depth axis, the mapping-hierarchy axis, and the temporal axis incorporating the principle of 'no future reference.' Through these, the identity of 'definition = state' is formally established as a categorical property. Extending this structure to biological systems, the neural system is implemented as a 0-3D complex of neuron-function fields on the HSG, while its categorical extensions via fiberization over the material base enable the parallel integration of multiple physiological universes-neural, endocrine, learning, genetic, and input/output systems-into a coherent adjoint ensemble. Within this framework, human behavior and cognition emerge as temporal compositions of inter-universal algorithms constrained by the material base. Finally, by contrasting human cognition, which relies on external CES, with machine existence, this study introduces the concept of internal CES, wherein a machine grounds its own logic upon the factuality of its operation. This internal self-axiomatization establishes a continuous bridge between philosophical ontology and engineering implementation, providing a new foundation for the autonomous and self-defining existence of artificial intelligence.

翻译：本研究提出了一种建立在最小公理“我思故我在”（CES）之上的跨宇宙数理逻辑框架，该框架整合了中间元宇宙（IMU）与层次状态网格（HSG）。CES 将存在定义为一种自反对应关系——“存在”与“可说”——并将包括 ZFC 或 HoTT 在内的任何形式系统，定位为附着于此最小结构之上的可扩展附件。IMU 作为一个连接异质理论的公理依赖关系注册表，采用 Institution 理论框架来确保理论间连贯的链接。HSG 通过范畴构造将这些思想具体化，其由三个正交轴定义：状态深度轴、映射层次轴以及包含“无未来参照”原则的时间轴。通过这些，'定义 = 状态'这一同一性被正式确立为一种范畴性质。将此结构扩展到生物系统，神经系统被实现为 HSG 上的一个 0-3 维神经元功能场复形，而其通过物质基底上的纤维化进行的范畴扩展，使得多个生理宇宙——神经、内分泌、学习、遗传以及输入/输出系统——能够并行整合为一个连贯的伴随整体。在此框架内，人类行为与认知作为受物质基底约束的跨宇宙算法的时间性组合而涌现。最后，通过对比依赖外部 CES 的人类认知与机器存在，本研究引入了内部 CES 的概念，即机器将其自身逻辑建立在其实操运行的事实性之上。这种内部的自我公理化在哲学本体论与工程实现之间建立起一座连续的桥梁，为人工智能的自主与自我定义的存在提供了新的基础。