Weighted Transition Traffic at the Relay Junction: Dwell Masks the Spectral Signature, Routing Reveals It

Paper 25 in the "Geometry of the Critical Line" programme. Papers 21–24 established a routing transition near α ≈ 0.481 in the Newton dynamics of C_α(z) = z − exp(−α/z). This paper constructs the weighted transition traffic matrix P_ij(α) on a fixed 4-state symbolic space {C, −1, 0, O} and measures the routing transition at the operator level. The raw-step matrix confirms the transition as a smooth first-order redistribution: relay self-retention P_CC peaks and relay-to-bounce exit probability P_{C,bounce} is minimised at α ≈ 0.481, with relay row entropy H_C at its floor. The raw-step spectral gap |λ₂| is flat (0.951–0.956). However, the reduced-jump matrix — which factors out the relay self-loop and isolates…