Calibrated simultaneous mergers of three Jordan blocks under the Aluthge transform

Three fixed Jordan blocks are joined by two positive links tending to zero. A candidate joint limit is given for ordinary half Aluthge iteration when the two initial crossover exponents coincide. For block sizes p, q, r and links a ε^α and b ε^β, the balance relation is κ = 4α/(p+q) = 4β/(q+r). At times m = floor(x ε^(−κ)), the rescaled triangular representative converges on compact positive x windows to a positive bidiagonal cubic-flow profile with entrances a C_pq and b C_qr, where C_uv = [2^(u+v−2)(u−1)!(v−1)!]^(−1/2). The profile retains one shape parameter after time translation. A graded ancient-uniqueness argument selects it from full triangular trajectories, including cases in which an outer rectangular mode has a larger linear growth rate than either joining mode. The constants are calibrated after every fixed discrete prefix, and a uniform comparison transfers the cubic passage to the discrete iteration. Dimensions, positive coefficients and powers are fixed; parameter-uniform limits, complex phases and quantitative error rates are outside the claim. The theorem retains candidate status; the established-status verification threshold has not been met.