计算自组织的Minary原始形式
The Minary Primitive of Computational Autopoiesis
AI总结：
Minary是一种计算框架，通过线性叠加处理随机事件，证明其收敛于唯一平稳分布，并揭示共识依赖于能力结构而非原始输入信号。
摘要：
我们介绍了Minary，一种计算框架，旨在作为第一个形式可证明的自组织原始形式的候选者。Minary将相互作用的随机事件表示为多维向量，并通过线性叠加而不是乘法标量操作来结合它们，从而保持不确定性，并在范围内[-1,1]内允许构造性和破坏性干涉。一个固定的“视角”集根据隐藏能力评估“语义维度”，其相互作用驱动两个离散时间随机过程。我们将此系统建模为迭代随机仿射映射，并利用迭代随机函数的理论证明其收敛于唯一的平稳分布；我们还获得极限期望的显式闭式表达式，该表达式以能力矩阵的行、列和全局平均值形式给出。然后我们推导出归一化共识的均值和方差的精确公式，条件是激活了给定的语义维度，揭示了共识如何依赖于能力结构而不是原始输入信号。最后，我们论证Minary在Maturana和Varela的意义下是组织上封闭但操作上开放的，并讨论了构建具有唯一主观身份观念的自维持、分布式和并行化计算系统的影响。
英文摘要：
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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