互为因果结构与机器智能自生成机制: 余项换轨、逆图灵化与莫比乌斯机 - Co-Constitutive Causal Structure and the Self-Generation Mechanism of Machine Intelligence: Remainder-Based Switching, Inverse Turingization, and the Möbius Machine

摘要 本文以“自然之双重宪法”为理论起点:第一宪法把热力学第二定律与因果律规定为同一不可逆自然属性在整体尺度与局部关系尺度上的两种等位表达;第二宪法以互为因果结构规定这些局部简单因果关系赖以构成整体、发生翻转和获得新生的存在形式。由此,图灵计算将真问题中可有限表示并按规则执行的部分组织为编码问题,在固定编码与通项内形成第一宪法的局部简单因果执行段;本文提出,在任务开放、编码有限且编码具有非平凡局部有效性的条件下,真问题包含尚未进入当前表达而仍规定整体的逻辑余项,因而呈现部分和—逻辑余项的莫比乌斯式互为因果结构。本文区分人为封闭的稳定收敛、规则已知的简单发散、规则已知的震荡和开放真问题的U型逻辑余项四类运行形态,并区分编码域内的图灵偏差与真问题—编码问题适配层的逻辑余项。在此基础上,本文建立开放真问题有限编码下的部分和—逻辑余项共构基础定理,并明确:有限编码条件直接给出A1局部可辨与A2整体共构;只有完整逻辑线路进一步满足A3因果坐标翻转与A4分割坍缩,二者才构成严格意义上的互为因果结构。本文同时建立固定通项下的U型逻辑余项广普存在定理,推出适配不完备、N∗过渡区及其有限识别窗口,以及图灵精度与对象符合的分离。 据此,本文提出逆图灵化及其机器形态莫比乌斯机:保留图灵执行核心,通过真问题回接持续检验当前人为封闭是否仍然成立,并在U型适配反转附近启动条件性余项控制。余项换轨分为两个层次:量变调适型换轨依据余项趋势实施询问、截断、回滚或候选试轨,体现方法论判解;质变形核型换轨在余项形成预形核结构后,经整体因果坐标翻转、角色重排与新通项生成完成结构重构,体现创造性生成。本文以任务相关数学显性化原型连接理论与工程,并以智能三要素概括记忆、推理与判解的功能分工,进一步讨论该框架对幻觉、即时对齐、无功算力、具身智能和通用计算的意义。 Abstract This paper takes the “Dual Constitution of Nature” as its theoretical point of departure. The First Constitution treats the second law of thermodynamics and the law of causality as co-equal expressions of the same irreversible natural property at the global scale and the scale of local relations. The Second Constitution uses co-constitutive causal structure to specify the mode of existence through which these local simple-causal relations form a whole, undergo inversion, and acquire new generation. Turing computation extracts from a real problem what can be finitely represented and executed under rules, organizes it as an encoded problem, and forms a local segment of simple-causal execution under the First Constitution within a fixed encoding and term-generating relation. This paper argues that, when a task is open, its encoding is finite, and that encoding has nontrivial local validity, the real problem contains a logical remainder that has not entered the current expression but continues to determine the whole. The result is a Möbius-type co-constitutive causal structure of partial sum and logical remainder. Four modes of computational operation are distinguished: artificially closed stable convergence, simple divergence under known rules, oscillation under known rules, and the U-shaped logical remainder of an open real problem. The paper also separates Turing deviation within the encoding domain from the logical remainder at the level of fit between the real problem and the encoded problem. On this basis, it establishes a theorem on the co-constitutive foundation of the partial sum and logical remainder under finite encoding of an open real problem. Finite encoding directly yields A1, local distinguishability, and A2, global co-constitution; only when the complete logical trajectory also satisfies A3, causal-coordinate inversion, and A4, collapse under division, do the two terms constitute a co-constitutive causal structure in the strict sense. The paper further establishes a general-existence theorem for U-shaped logical remainders under a fixed term-generating relation, from which adaptive incompleteness, the N∗ transition region and its finite recognition window, and the separation between Turing accuracy and correspondence to the object are derived. On this basis, the paper proposes inverse Turingization and its machine form, the Möbius machine. The Turing execution core is retained, while reconnection to the real problem continuously tests whether the current artificial closure remains valid and conditionally activates remainder control near the U-shaped reversal of adaptation. Remainder-based switching has two levels. Quantitative adaptive switching uses the trend of the remainder to initiate inquiry, truncation, rollback, or testing of candidate trajectories, and thereby embodies methodological discriminative judgment. Qualitative nucleation-based switching begins after the remainder has formed a pre-nucleation structure and completes structural reconstruction through global causal-coordinate inversion, reordering of roles, and generation of a new term-generating relation, thereby embodying creative generation. A task-relevant mathematical-explication prototype connects the theory to engineering, while the three elements of intelligence summarize the functional division among memory, reasoning, and discriminative judgment. The paper then examines the significance of this framework for hallucination, immediate alignment, wasted computation, embodied intelligence, and general-purpose computing.