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 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 = 0. 477 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\% 2. 1\% reduction in memory usage, a 3. 8 0. 3 retrieval speedup, and a consolidation efficiency c = 2. 23 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.