An all-time Aluthge bound uniform in two joining entries

Using retained finite and whole-chart center premises, we give a candidate Frobenius error bound for ordinary Aluthge iteration (weight 1/2) on Jordan blocks of sizes (1,1,2) when two joining entries vary independently in [255/32768,257/32768]. In a specified moving triangular gauge, the scaled discrete orbit stays within 1/4 of its own entrance-normalized bidiagonal reference at every integer time m >= 128. A positive-definite lift preserves the initial order comparison without accumulating error in time; a Cholesky estimate converts it to the required gauge bound. Logarithmic non-expansion controls the input-dependent references. Reusing the center receipts with a sharper tail composition gives a total allowance 526607/2125000 < 1/4. A rational checker verifies the numerical composition conditional on the written analytic arguments and inherited enclosure contracts. The claim remains a provisional candidate. The result is restricted to this closed independent input rectangle, these block sizes and the stated gauge.