J-Emergence in Semantic Systems: Empirical Evidence for Complex Structure from Stability Dynamics

We present the first empirical evidence for the emergence of complex structure J in large language model (LLM) semantic dynamics. Analyzing N = 10,000 conversations from the LMSYS-Chat-1M dataset, we identify 521 perturbation events and track post-perturbation relaxation trajectories in embedding space. Our central finding: 77.2% of perturbation events (402/521) exhibit oscillatory rather than monotonic relaxation, with mean rotation 0.944 rad (σ = 0.308 rad), far exceeding the J-emergence threshold of 0.1 rad. This confirms the theoretical prediction that when antisymmetric coupling ω exceeds symmetric coupling λ, the relaxation dynamics acquire a rotational component—the empirical signature of an emergent complex structure J. The result establishes that semantic systems are not merely gradient-descent optimizers but exhibit Kähler-like geometry with phase degrees of freedom. We provide falsification criteria, discuss implications for AI alignment theory, and outline the connection to the Proto-Kähler Gradient System (PKGS) framework linking semantic stability to string-theoretic moduli stabilization.