The Architecture of Adaptation: Algebraic Foundations of Signal Weighting Theory

This paper introduces the algebraic foundations of Signal Weighting Theory (SWT), a unifying framework for understanding adaptation as the recursive optimization of signal relevance. Moving beyond gene-centric models of evolution, SWT formalizes how biological and artificial systems adapt by dynamically adjusting the weights they assign to incoming signals. We derive a substrate-neutral algebra applicable across immune systems, neural networks, microbiomes, and AI architectures. Special attention is given to mutualism as an emergent attractor state — a signature of co-adaptive entanglement in both natural and technological ecosystems. By framing evolution as relevance optimization, SWT offers a testable, generative model of learning and adaptation across scales, with implications for evolutionary theory, AI alignment, and the future of human–machine coevolution.