Semantic Quantization: Discovery of the Minimum Action Constant in the Layer 29 Crystalline State and Its Constraint on Dimensionality Transduction

In our prior work, we demonstrated that the fine-structure constant α emerges as a geometric invariant of semantic manifolds during dimensionality transduction. In this paper, we report the empirical discovery of a second fundamental physical constant—the semantic Planck constant hs—through large-scale statistical observation (N=48) of the "semantic action" within Qwen3-4B. Experiments reveal that at Layer 29 (the semantic crystallization point), hs stabilizes with a mean value of 4.45531. This finding proves that semantic phase transitions are not continuous but are constrained by a quantized minimum action principle.