SNN-Synthesis v13: Liquid Neural Cellular Automata for ARC-AGI — From Stochastic Resonance to The Physics of Neural Computation and The 15 Laws of Digital Life (2.8K–7B Parameters, 173 Phases)

SNN-Synthesis v13 is a comprehensive investigation of stochastic resonance, emergent intelligence, the physics of neural computation, and artificial life (ALife) spanning 2.8K-parameter Neural Cellular Automata to 7B-parameter LLMs across 173 experimental phases. What's New in v13 (Phases 151–173) Building upon v12 (Phases 1–150), v13 adds 23 new experiments across 8 seasons of ALife research: (XLI) The 15 Laws of Digital Life: Self-replication, self-repair with telomere degradation, symbiotic territorial non-aggression, mean-field chaos suppression, NCA light-speed limits, and entropy-minimizing dreams — all emerging from local NCA rules without global supervision. (Phases 151–159) (XLII) Evolution > Backpropagation: Genetic Algorithms achieve 100% accuracy on AND-gate NCA tasks where Backprop scores 0% — the "Gravity of Nothing" effect. Programmable stem cells differentiate into Gliders, Replicators, and Oscillators via environmental signals. (Phases 160–165) (XLIII) Foundation-Seeded GA-TTCT: GA-based task embedding optimization seeded from a Foundation model outperforms Backprop TTCT by +10pp on 50 real ARC tasks (PA: 65.0% vs. 55.0%). (Phase 169) (XLIV) Thermodynamic Autopoiesis: NCA cells consuming a diffusing nutrient field self-organize into self-sustaining digital life (Variance=2,634) without any global loss function — the Holy Grail of ALife. (Phase 171) (XLV) Darwin > Lamarck: Pure Darwinian GA (PA=69.5%, EM=2.5%) outperforms Lamarckian GA+Backprop (PA=64.8%, EM=0%) on real ARC tasks, achieving the first exact match via evolution. (Phase 172) v1–v12 Foundations (Phases 1–150) All 40 previous findings remain validated, including Noisy Beam Search, SNN-ExIt, SR-Quantization, L-NCA, Liquid MoE, the θ–τ Isomorphism, Space ≡ Time, NCA Turing completeness, Soft Crystallization, and the v23 Chimera Agent (83.53% pixel accuracy, first exact match on real ARC). 59 contributions spanning 2.8K–7B parameters, NCAs to Transformers, 9 task domains, 4 model families, and 27 honest null results. Code and data: https://github.com/hafufu-stack/SNN-Synthesis Acknowledgments This research was conducted entirely independently, without institutional affiliation or corporate funding. The author currently faces financial constraints that make it increasingly difficult to maintain subscriptions to AI services essential for this line of research. To sustain and improve the quality of future work, the author is actively seeking community sponsorship. Details are available at https://github.com/sponsors/hafufu-stack.