Reproduction and proof composition for an all-time Aluthge bound

Separate numerical reproduction and proof composition are provided for an existing candidate all-time Aluthge bound. The fixed problem begins with an unjoined three-block seed of sizes (1,1,2), with two positive joins varying independently in [255/32768,257/32768]. An integer/dyadic implementation encloses every center comparison at the 65,409 integer times from 128 through 65,536 and the shifted tail entry. Exact coefficient and interval-series calculations reproduce the local remainder bounds on 512 closed chart boxes. Rational consumers check the numerical composition. A coarse first-exit induction establishes chart membership before refinement; positive-definite order and reference non-expansion transfer the center estimate to the complete rectangle in a specified moving triangular gauge. The conclusion remains the previously published provisional conditional allowance 526607/2125000 < 1/4 at every integer time m >= 128. The contribution is additional reproducible evidence and an explicit account of the proof interfaces, with numerical enclosure implementations and stated analytic arguments remaining assumptions.