Abstract
While world models learn compact representations of complex environments, they lack a physics-grounded metric to assess the structural fidelity of their latent spaces. We identify the wavelet scaling exponent α as a critical diagnostic, proposing optimal representations satisfy variance equipartition (α ≈ 1/2) -- mirroring Kolmogorov's inertial range. We establish α = 1/2 as a sharp transition boundary for the classical simulability of amplitude-encoded quantum kernels. Using tensor-network theory, we prove latents with α > 1/2 reside in an area-law phase admitting efficient classical emulation, while α < 1/2 triggers a volume-law phase where the Matrix Product State bond dimension χ grows exponentially with qubit count n. Analyzing pre-trained VideoMAE latents reveals a dichotomy: spatial tokens approach the equipartition limit (α ≈ 0.423), but permutation-invariant feature channels exhibit unstructured disorder (α ≈ -0.123). This forces real-world latents deep into the volume-law phase, providing a data-driven necessary condition for simulation hardness. Finally, we apply Weingarten calculus to derive the exact variance of the scrambled transition probability under a 2-design ensemble. We prove this variance scales strictly as [X] = Θ(d⁻²). We confirm this numerically with a log-log slope of -1.881 (R² = 0.999), identifying a formidable shot-noise wall demanding a measurement budget of M = Ω(d²) that constrains quantum machine learning scalability.