The Minary Primitive of Computational Autopoiesis

TL;DR

This paper introduces Minary, a novel probabilistic framework for autopoiesis that models interactions as superpositions, proving convergence to a stationary distribution and exploring implications for self-maintaining systems.

Contribution

Minary is the first formal primitive for autopoiesis using superposition of probabilistic events, with proven convergence and explicit formulas for consensus dynamics.

Findings

Converges to a unique stationary distribution.

Explicit formulas for mean and variance of consensus.

Consensus depends on competency structure, not raw inputs.

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.