SNT-LIFE: A Digital Learning Organism

SNT-LIFE: A Learning Digital Organism presents a unified operator framework for learning, memory, and behavior, demonstrating that seven fundamental operators—fluctuation ($\fleq$), cyclic reset ($\cyceq$), phase nexter ($\nexteq$), phase reverser ($\reveq$), liminal thresholding ($\liminfty$), irreversible loss ($\termop$), and subspace mapping ($\diveq$)—form a numerically closed operator algebra at machine precision ($4.82 \times 10^{-15}$).

Original Data: All results are validated against empirical datasets:

· C. elegans connectome (Cook et al. 2019, 300 neurons, 3,707 synapses)

· Whole-brain calcium imaging (Kato et al. 2015, 5 recordings, 60 s each)

· LongBench multi-document QA benchmark for LLM evaluation

Key Achievements:

· Biological validation: Variance spectrum correlation $r = 0.986$ with Kato data, PC1 = 42.3% (vs Kato 43.8%), using only 7 parameters—an 86× reduction vs Wilson-Cowan ($\sim$600 parameters)

· Generalization: $r > 0.95$ on all five Kato recordings without retuning

· Circuit validation: AVB-motor $r = +0.857$, AVA-motor $r = -0.700$ from connectome structure, not fitted

· Artificial validation: SNT-MEM achieves $63.3\% \pm 2.1\%$ memory reduction and $3.8\times \pm 0.3\times$ retrieval speedup on Llama-3-8B

· Soft-Clamp homeostatic mechanism: Stabilizes threshold at $\bar\theta = 0.477 \pm 0.095$, eliminating blackout instability ($\theta \to 0.874$ without Soft-Clamp)

· Necessity theorem: Learning requires consolidation ($\diveq$) or pruning ($\termop$); ablation shows $\diveq$ removal causes $78.3\%$ loss, Soft-Clamp removal causes $34.2\%$ loss

· Lie algebraic closure: 7-element basis $\{I,B,C,W,[W,B],[W,C],[B,C]\}$ closes at $4.82 \times 10^{-15}$; 4-element basis fails (residual $> 0.99$)

Impact: The framework provides a unified mathematical language for describing learning across scales—from a worm learning to avoid a toxin to a large language model consolidating knowledge—with potential applications in neuroscience, artificial intelligence, and quantum error correction.