提出可形式证明的自产自足计算原语，实现主观身份与动态共识的数学建模。
The Minary Primitive of Computational Autopoiesis
- 用多维向量表示概率事件，线性叠加保留不确定性并支持干涉效应。
- 系统收敛到唯一稳态分布，共识均值与方差由能力矩阵的行列平均决定。
- 适用于构建自我维持、分布式且具有主观身份的智能计算系统。
我们提出Minary，一个作为首个可形式证明的自产自足计算原语的候选框架。Minary将交互的概率事件表示为多维向量，并通过线性叠加而非乘法标量运算进行组合，从而保留不确定性，并在区间[-1,1]内实现建设性与破坏性干涉。一组固定“视角”依据隐藏能力评估“语义维度”，其相互作用驱动两个离散时间随机过程。我们将该系统建模为迭代随机仿射映射，利用迭代随机函数理论证明其在分布上收敛至唯一稳态律；进一步获得极限期望的显式闭式表达，以能力矩阵的行、列及全局平均表示。随后推导出给定语义维度激活时归一化共识的均值与方差精确公式，揭示共识依赖于能力结构而非原始输入信号。最后，我们认为Minary在组织上封闭但操作上开放，符合马图拉纳与瓦雷拉的定义，并讨论其对构建自维持、分布式、可并行计算系统的意义，这些系统具备独特的主观身份观念。
原文摘要 · Abstract (English)
We introduce Minary, a computational framework designed as a candidate for the first formally provable autopoietic primitive. Minary represents interacting probabilistic events as multi-dimensional vectors and combines them via linear superposition rather than multiplicative scalar operations, thereby preserving uncertainty and enabling constructive and destructive interference in the range $[-1,1]$. A fixed set of ``perspectives'' evaluates ``semantic dimensions'' according to hidden competencies, and their interactions drive two discrete-time stochastic processes. We model this system as an iterated random affine map and use the theory of iterated random functions to prove that it converges in distribution to a unique stationary law; we moreover obtain an explicit closed form for the limiting expectation in terms of row, column, and global averages of the competency matrix. We then derive exact formulas for the mean and variance of the normalized consensus conditioned on the activation of a given semantic dimension, revealing how consensus depends on competency structure rather than raw input signals. Finally, we argue that Minary is organizationally closed yet operationally open in the sense of Maturana and Varela, and we discuss implications for building self-maintaining, distributed, and parallelizable computational systems that house a uniquely subjective notion of identity.
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