Calibrated sequential mergers of three Jordan blocks under the Aluthge transform

Three fixed Jordan blocks are joined by two positive links that vanish as positive powers of a small parameter. A candidate joint limit is given for ordinary half Aluthge iteration when the two initial crossover exponents are strictly ordered. The first merger changes the background seen by the remaining link and accelerates the second merger. For blocks of sizes p, q and r, when the last two merge first, links aε^α and bε^β give late exponent 4[α+βr/(q+r)]/(p+q+r) and matrix entrance amplitude a b^(r/(q+r)) [2^(p+q+r−2)(p−1)!(q+r−1)!]^(−1/2). Both discrete profile limits are uniform on compact positive crossover windows in a specified moving triangular gauge. The proposed proof combines a graded early passage, a uniform estimate through the interval between mergers and an exact weighted-product identity, which calibrates the late entrance without a normalized matrix-variation assumption through the first merger. Block sizes, positive coefficients, powers and the strict ordering gap are fixed. The balanced simultaneous case, shrinking separation gaps, complex phases and quantitative error rates are outside the result. The theorem retains candidate status; the established-status verification threshold has not been met.