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Theorem W2 demonstrates KL divergence in hierarchical processes, implying exponential growth in divergence with depth.
We prove Theorem W2: D_KL(P_D||PD-1) = K·2D-1, derived via Transfer Matrix method (Mistral §6) and confirmed numerically (ratio→0.5000 for D≥6). The sum D_KL(P_D||Q_d) = K·2^d·(2D-d-1) closes the open question from Beyer 2026v. KL divergence scales exponentially with depth separation — each level is informationally twice as far from its neighbour as the previous pair.
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Beyer et al. (2026) studied this question.
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