SNN-Synthesis v14: Liquid Neural Cellular Automata for ARC-AGI — From Stochastic Resonance to The NCA Intelligence Equation and Dual-Process Architecture: Architecture > Scale in Spatial Reasoning from 2.8K to 7B Parameters

SNN-Synthesis v14 extends the investigation to 202 experimental phases, adding 29 new experiments (Phases 174–202) that establish the NCA Intelligence Equation and prove that architectural hierarchy—not parameter scaling—is the key to spatial reasoning. v14 Key Discoveries (Phases 174–202) (XLII) The NCA Intelligence Equation: Memory capacity scales super-linearly as M ∝ P1.33, exceeding the P1.0 linear scaling of Transformers (Phase 188). However, generalization saturates at G ∝ P0.01 — the Generalization Wall (Phase 191). Computation time destroys memory (T=1 optimal), establishing a fundamental Time–Memory Antagonism (Phase 189). Grokking does not occur in weight-shared NCA (Phase 193). (XLIII) Dual-Process NCA & Gated Hybrid: Splitting NCA into System 1 (intuition, T=1) and System 2 (reasoning, T=10) achieves +6.3pp and the first exact match (Phase 192). The Gated Hybrid — a learned per-pixel fusion gate — achieves the project's all-time best PA=60.3%, EM=4.0% (Phase 199). Time-Travel NCA (+2.3pp) automatically rewinds to the highest-confidence step to prevent drift (Phase 201). (XLIV) The Locality Wall: Self-Attention (+0.4pp), Working Memory (−2.2pp), Spatial Pyramids (+0.3pp), and Dilated Convolutions (−1.4pp) all fail. LLM-derived global communication techniques destroy the spatial coordinate system essential for ARC geometric reasoning (Phases 195–198). Metabolic Sleep: Freezing high-confidence pixels during GA inference boosts PA by +6.2pp, functioning as anti-drift protection (Phase 177). v1–v13 Foundations (Phases 1–173) All 61 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, the 15 Laws of Digital Life, Thermodynamic Autopoiesis, and Darwinian supremacy over Backpropagation. 73 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.