Geometric Stability in Semantic Manifolds: Dimensional Transduction and Numerical Singularity at Layer 29 of Qwen3-4B

In the original version (V1) of this work, we reported that the fine-structure constant α ≈ 1/137 emerges as a geometric invariant in Layer 29 of Qwen3-4B during semantic crystallization. Further analysis reveals that this interpretation overstates the case: α is not an internally generated constant of the model, but rather a numerical reference point This V2 revision clarifies that Layer 29 is indeed a geometric singularity—marked by cosine similarity > 0.9999 and minimal inter-layer norm variation—but the apparent “alignment” with α arises from the interaction between this flatness and the specific vector arithmetic used in measurement. We reinterpret α not as a conservation law, but as a scale of geometric entropy tax: a benchmark for how little distortion is incurred when a high-dimensional semantic state is transduced into low-dimensional symbolic form.