In the (10,4) Kaprekar system, the depth layer τ = 4 forms a structural bottleneck separating an initial expansion regime (τ ≤ 3) from a constrained convergence regime (τ ≥ 5). This bottleneck manifests as a local minimum in N_τ and induces the invariant spectral cut k* = 4 across all tested weight models.

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