Uniform power-law bounds for finite Jordan-block chains under the Aluthge transform

A fixed finite chain of Jordan blocks is joined by positive entries of maximum size mu. For ordinary half-Aluthge iteration in a specified moving triangular gauge, a calibrated positive bidiagonal reference gives a bound C[(m0+1)^(-rho)+mu^eta], uniform for all integer times m>=m0, for every rational 0<rho<1/2 and some eta>0. Constants depend on the fixed block sizes, with no lower bound on a joining entry or ratio and no merger waiting-time factor. An all-order consecutive-cut identity gives relative-coordinate entry; finite-order polynomial prefix bounds, exact adjacent-block calibration and logarithmic non-expansion control the whole future. Constants have terminating constructions; practical accuracy certificates and uniformity in growing dimension are not asserted. The principal theorem remains a provisional candidate.