The Minary Primitive of Computational Autopoiesis

2026-01-08

AI Summary

This work proposes the Minary framework, the first formally verifiable autopoietic computational primitive designed to support self-sustaining, distributed parallel systems endowed with a sense of subjective identity. The approach models interaction events as multidimensional probability vectors and integrates information through linear superposition—rather than scalar multiplication—preserving uncertainty within the interval [−1,1] and enabling interference effects. Semantic dimensions are evaluated from a fixed “perspective,” driving two discrete-time stochastic processes formalized as iterated random affine maps. Theoretical analysis demonstrates that the system converges to a unique stationary distribution, for which the authors derive a closed-form expression of the limiting expectation and exact formulas for the mean and variance of normalized consensus along any given semantic dimension. Crucially, consensus formation is shown to depend on the structure of the capability matrix rather than the original input signals, thereby realizing an autopoietic architecture that is organizationally closed yet operationally open.

Technology Category

• Multiagent Systems: Other Foundations of Multi Agent Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Web Mining and Content Analysis: Models for Web evolution
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

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.

Problem

• autopoiesis
• computational primitive
• organizational closure
• subjective identity
• self-maintaining systems

Innovation

• computational autopoiesis
• linear superposition
• iterated random affine map
• organizational closure
• semantic consensus