The Σ-Semantic Normal Form for Skeleton-Factorized Markov Dynamics

We study semantic projections for adaptive dynamics represented as controlled Markov kernels on an extended state space Z = X x H x G x P. Assuming a fixed Skeleton factorization (DAG decomposition) together with Prime admissibility, we introduce a measurable semantic map Sigma_Z: Z -> S and formalize when the induced semantic process S_t = Sigma_Z(Z_t) closes as a controlled Markov process. We separate closure (weak Sigma / Sigma-W, i.e., Sigma-lumpability) from quality axes (Sigma+) that diagnose non-vacuity, temporal coherence, and reusability. Under Sigma-W, we state a Sigma-semantic normal form as a kernel-level existence result (version-equivalence representation), explicitly separated from any algorithmic convergence guarantee. We introduce an effective neural-network degradation rate D_Sigma^NN that extends the degradation prediction from softmax parameterizations to arbitrary differentiable mappings w -> P(w), and validate it empirically on softmax Markov chains, MLP classifiers, and ResNet-18 (CIFAR-10). Semantic conjugacy formalizes when two Sigma-specifications represent the same theory, and adapter layers relate heterogeneous semantic structures via iterated lumpability. A computational supplement provides full reproducible experiments.