What Weight Stabilisation Would Require: A Finite-Window Audit of Admissibility Weights

Version 1 claimed to prove common positive convergence of the admissibility weights from spectral universality. That proof imported a relative profile estimate never supplied by U1, identified the weights with shell-capacity sums without a bridge to Q5a's fingerprint-response averages, and sent the calibrated fitting-window endpoint to infinity although the established five-block protocol has endpoint at most 22 for large primes. We retain the exact conditional summation inequality, but it concerns a separately defined partial-sum proxy. For a fixed nonnegative profile and the published window protocol, that proxy's target is the sum through depth 22, provided the necessary convergence input is supplied; it is not the infinite series asserted in version 1. Neither the proxy inequality nor fibre constancy proves convergence of Q5a's actual weights, whose horizontal-generator limits may differ. The finite O25 pair exponents do not establish a global pointwise profile bound or identify a Born–Infeld normalisation. Thus [H-w] remains open on these inputs. Interpretive outlook. The audit isolates a testable bridge: construct the measured response weights from the block-sampled rank observable and control them uniformly on the calibrated finite window before assigning an effective kinetic coefficient.