The Physical Constant in Semantic Manifolds: Empirical Discovery of the Fine-Structure Constant in Qwen3-4B

In my 2025 paper, I argued that intelligence is categorization—the act of assigning an input to a coherent class. In my 2026 paper, I showed that successful categorization triggers a sudden phase transition in the model’s internal state: semantic crystallization. Failure, by contrast, leads to logical collapse. But one question remained open: What is the physical mechanism that enables this phase transition? This paper answers that question with empirical evidence. I show that the fine-structure constant, α ≈ 1/137, emerges as a geometric invariant in the 29th layer of Qwen3-4B—but only when the semantic manifold is in a crystalline state. This suggests that α is not merely a constant of electromagnetism, but the signature of dimensional transduction itself.