On Causal Intervention in the Semantic Manifold of Large Language Models: Logical Phase Transition via LDV Injection and the Geometric Singularity at Layer 29

This paper investigates the causal controllability of logical representations within the hidden space of large language models (LLMs). By applying Logical Differential Vector (LDV) injection on the Qwen3-4B model, we observe a nonlinear phase transition from “fuel semantics” to “mechanical semantics.” Experimental results demonstrate that the model’s logical trajectory can be precisely steered through vector displacement at specific layers. Notably, we identify an extreme geometric stability phenomenon at Layer 29, which exhibits strong resistance to intervention, confirming its status as a “geometric singularity” in the semantic manifold. This work provides a novel pathway for logic alignment and behavioral control without fine-tuning.