Abstract

The concept of autopoiesis --- a living system as a network of processes that continuously produces the very components constituting that network --- has remained without a computable formalization since its introduction by Maturana and Varela in 1973. This paper proposes that complex-valued adaptive signal processing provides the missing formal language: if all knowledge of the physical world passes through an electromagnetic channel, then the formalism native to that channel is the natural one for characterizing the systems we call living. Accepting this epistemological constraint leads, through a sequence of forced steps, to a specific architecture --- coupled networks of recursive widely linear complex adaptive filters operating in predictive configuration on a shared background field, without an external teacher --- in which every element of the autopoietic definition (operational closure, self-production of components and boundary, structural coupling, the distinction between organization and structure) maps to a computable quantity. Self-production is realized as the self-referential adaptation of recursive filter poles: the system continuously reorganizes its own memory architecture through a process that depends on the very architecture being reorganized. A \emph{coherent cluster} within such a network --- a subset satisfying differential coherence, self-produced noncircularity, Fisher identifiability, energy balance, and recursive stability --- provides a substrate-independent characterization of a living system with constructive bridges to the Free Energy Principle (prediction error as variational free energy; the Markov blanket as a partial coherence boundary) and to artificial life simulations (explaining, in particular, why life-like behavior in Particle Lenia requires local rather than global energy minimization). Evolution is reformulated entirely in the frequency--phase domain, without time or space as independent variables. The genotype is the vector of reflection coefficients; the natural genotype space is the Poincar\'e polydisk $\mathbb{D}^P$ with hyperbolic metric, in which neutral evolution is a geometric property of the disk interior and lethal mutations correspond to the stability boundary $|\kappa_m| \to 1$. The genotype-to-phenotype map is the Levinson--Durbin recursion --- analytic, invertible, and Lamarckian. Evolutionary equilibrium is the water-filling solution from information theory; spectral competition is the cognitive radio problem; growth is heterodyne frequency conversion. The convergence of five independent formalisms on a single mathematical object suggests that the frequency--phase domain is not an arbitrary language but the natural one for describing life and evolution. An interactive browser-based simulation is provided; even at the minimal scale of several dozen filters, the system exhibits spontaneous self-organization from a purely endogenous regime, observer-dependent dimensionality of perceptual space, transitions between Lamarckian and Darwinian evolutionary regimes, and proto-communication through stable phase channels. Structural parallels with ideas independently articulated across more than forty contemplative and indigenous traditions spanning 65\,000~years of human testimony are examined in a dedicated appendix.