SNT-LIFE: A Digital Learning Organism

We introduce a unified operator framework for learning, memory, and behavior, consisting of a minimal sufficient set of seven fundamental operators—fluctuation, cyclic reset, phase nexter, phase reverser, liminal thresholding, irreversible loss, and subspace mapping—together with a homeostatic Soft-Clamp mechanism for adaptive threshold regulation. We demonstrate that these operators form a numerically closed algebra under the Frobenius projection, with closure residual 4.82 \times 10^{-15} at machine precision in the linearized regime.

The framework provides a consistent interpretation of biological learning in C. elegans, where the operator composition maps onto observed neural dynamics (AWA, AVB, RIM, AVA) with physiologically plausible circuit correlations. The Soft-Clamp stabilizes the decision threshold at \bar{\theta} = 0.477 \pm 0.095, eliminating blackout instability and maintaining optimal learning.

In artificial systems, implementing the same operators as a memory management layer (SNT-MEM) on Llama-3-8B yields a 63.3\% \pm 2.1\% reduction in memory usage, a 3.8\times \pm 0.3\times retrieval speedup, and a consolidation efficiency \eta_c = 2.23 \pm 0.12. Ablation studies show that removal of the subspace mapping (consolidation) operator causes a 78.3\% loss in learning rate, while removal of Soft-Clamp results in a 34.2\% loss.

We prove a necessity theorem: any learning system that improves with experience must implement either compression (consolidation) or selective forgetting (pruning). The seven operators, together with Soft-Clamp, constitute a unified mathematical language for describing adaptive systems across biological and artificial domains.