Scene-Code-as-Topology: Overcoming 1D Token-Stride and Diagonal Blindness in Large Language Models via 3D/4D Procedural Scene Graph Compilation

While frontier Large Language Models (LLMs) and Vision-Language Models (VLMs) demonstrate strong proficiency in symbolic deduction and code synthesis, recent studies reveal a severe spatial perception bottleneck on discrete 2D grids. First, visual encoding via Vision Transformers (ViTs) operates as a lossy spatial compression that blurs discrete grid intersections. Second, while representing a 2D board as an ASCII text matrix provides lossless token input, serializing a 2D array row-by-row into a 1D token sequence shatters vertical and diagonal topological adjacency, inducing severe diagonal blindness and spatial occupancy hallucinations during Chain-of-Thought (CoT) reasoning. In this preliminary study, we propose Scene-Code-as-Topology, a training-free framework that dynamically compiles discrete 2D spatial states into executable Three.js 3D/4D procedural scene graph code augmented with 4D collinear diagonal invariants (udiag1 = x − z, vdiag2 = x + z) and contiguous 3D ray vectors. In an initial self-funded pilot benchmark of 30 controlled self-play Gomoku games (719 plies) starting from an empty 15×15 board across two flash-tier models (gemini-3.8-flash-high and DeepSeek-V4.1-Flash-1017 under both non-thinking and thinking-enabled regimes), Scene-Code-as-Topology outperforms the 2D ASCII matrix baseline by 23 Wins, 3 Draws, and 4 Losses (85.2% decisive win rate, two-tailed exact binomial p = 0.00031 < 0.001), achieving a 9–0 sweep on all diagonal victories and a 56.3% reduction in CoT spatial hallucinations. We explicitly discuss current limitations (preliminary empirical phenomenon observed vs. underlying neural mechanisms remaining a theoretical conjecture, limited sample size N = 30, and 2 models evaluated due to independent research budget constraints) to guide future large-scale replication.