Scene-Code-as-Topology: Bypassing the 2D Tokenizer Bottleneck in Large Language Models via Procedural 3D/4D Scene Graph Representations

Large Language Models (LLMs) struggle with 2D spatial grid reasoning—such as 15x15 Gomoku—due to a fundamental representation mismatch: autoregressive 1D BPE tokenizers shatter vertical and diagonal spatial adjacency into brittle multi-token strides. Rather than fine-tuning model weights or relying on lossy Vision-Language Model (VLM) pixel encoders, we introduce Scene-Code-as-Topology, a zero-shot representation paradigm that reformulates discrete 2D board states into executable Three.js 3D/4D procedural scene graph code with explicit kinematic ray-cast bindings and temporal history layers.Across a controlled 30-game (719-move) self-play benchmark spanning two frontier architectures—Gemini-3.8-Flash-High (Thinking ON) and DeepSeek-V4.1-Flash-1017 (evaluated under both non-reasoning and test-time reasoning modes)—our Agent B (3D/4D Scene-Code-as-Topology) achieves 23 Wins, 3 Draws, and only 4 Losses against the standard Agent A (2D ASCII Matrix Baseline), corresponding to an 85.2% decisive win rate (two-sided exact binomial p = 0.00031 < 0.001). Notably, Agent B achieves a 9 : 0 sweep across all diagonal victories, directly remedying the diagonal blindness of 1D tokenized grids.Open-Source Repository, Full 30-Game JSONL Trajectories & 1080p MP4 Replays: https://github.com/pathetic777/scene-code-as-topology-gomoku Primary Archival DOI (CERN Zenodo): https://doi.org/10.5281/zenodo.23691649