SNN-Synthesis v12: Liquid Neural Cellular Automata for ARC-AGI — From Stochastic Resonance to The Physics of Neural Computation: Space, Time, and Phases in Artificial Life — from 2.8K to 7B Parameters

I present SNN-Synthesis v12, a comprehensive investigation of stochastic resonance, emergent intelligence, and the physics of neural computation in neural networks spanning 2. 8K-parameter Neural Cellular Automata to 7B-parameter LLMs across 150 experimental phases. Building upon v1–v10 (Phases 1–100) and v11 (Phases 101–137), v12 adds 13 new experiments (Phases 138–150) that establish the θ–τ Isomorphism between ANN/SNN/LNN architectures, prove Space ≡ Time through lossless Weight-Tied CNN to NCA compilation, demonstrate NCA Turing completeness, and introduce Soft Crystallization via entropy minimization. Six New Laws of Neural Computation Physics (v12) (XXXV) The Grand Unification — θ–τ Isomorphism — SNN threshold θ and LNN gate bias b_τ are linearly related (b_τ = −θ). ANN ↔ LNN conversion is lossless (97. 40% preserved), while ANN → SNN is inherently lossy (10–15%), formalizing information evaporation under discretization. The Universal Neural Compiler trains once as ANN and compiles zero-shot to SNN/LNN/LSNN modes. (Phases 138–140) (XXXVI) Dimensional Folding — Space ≡ Time — Weight-Tied CNNs compile losslessly to NCA with Gap = 0. 000000%, proving that spatial depth and temporal iteration are mathematically equivalent. Trajectory Forcing on Game of Life reveals the Butterfly Effect wall: per-step accuracy of 94% degrades to 76% over 5 chaotic steps — the first observation of deterministic chaos in neural network prediction. (Phases 141, 144, 147) (XXXVII) NCA Turing Completeness — Baseline NCA solves Dilate → Invert → Erode with 100% exact match, proving that NCA can execute discontinuous multi-phase programs via emergent internal state machines — without any external clock mechanism. (Phase 148) (XXXVIII) The Intrinsic Hourglass — Hourglass NCA autonomously develops U-shaped clock trajectories (0. 59→0. 09→0. 28), demonstrating self-organized temporal differentiation without clock supervision. External clocks are beneficial on grid tasks (T=16: 99. 9%) but harmful on classification tasks — a fundamental task-dependent duality. (Phases 143, 146) (XXXIX) Soft Crystallization — Entropy minimization during TTCT achieves +3. 51% pixel accuracy improvement by sharpening predictions without VQ's gradient destruction — completing "Continuous Thought, Discrete Action" at the loss-function level. (Phases 149–150) (XL) Kaggle Agent v19. 1 Bugfix — The reasoning-overwrite bug causing 0. 00 Kaggle score (dict → string overwrite in configureₐction) is identified and fixed. (v19. 1) v1–v11 Foundations (Phases 1–137) All 38 previous findings remain validated, including Noisy Beam Search, SNN-ExIt, SR-Quantization, the space-time-precision triad, Liquid MoE, attractor regularization, the v20 agent (88% solve rate, 14K params), Latent-NCA, TTCT, the VQ Paradox, and the v23 Chimera Agent (83. 53% pixel accuracy, first exact match on real ARC). 44 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.