The Minary Primitive of Computational Autopoiesis

TL;DR

The paper introduces Minary, a vector-based autopoietic primitive that preserves uncertainty by representing interacting probabilistic events as multi-dimensional vectors and combining them through linear superposition. It formalizes the model as an iterated random affine map driven by random active dimensions and a fixed competency matrix, proving convergence to a unique stationary distribution and providing explicit limits for the learning memory and consensus statistics. The authors derive exact mean and variance expressions for the normalized consensus conditioned on active dimensions, revealing a strong dependence on competency structure rather than raw inputs. They also present worked and alternative examples illustrating emergent properties such as signal cancellation, the promotion of generalists, and halo effects, and discuss implications for self-maintaining, distributed computation with a uniquely subjective identity, framed within Maturana and Varela's autopoiesis. Overall, Minary is positioned as the first formally provable autopoietic computational primitive with potential for robust, parallelizable, and self-referential computation in uncertain environments.

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.

Figures (2)

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Theorems & Definitions (6)

• Theorem 5.1
• Lemma 5.2
• proof
• proof : Proof of \ref{['thm:convergence']}
• Theorem 6.1
• proof