J-Emergence in Semantic Systems: Empirical Evidence for Complex Structure from Stability Dynamics
Year: 2025
Type: article
Abstract: 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.
Author: Gebendorfer, Jonas Jakob
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7107855301
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