A Gram-Spectral Autopsy of the BNBD Inversion Problem

The Nyman–Beurling–Báez–Duarte framework converts the Riemann Hypothesis into a Hilbert-space closure problem. This note isolates two distinct components of the finite inversion problem: a rigid Blaschke skeleton associated with hypothetical right-half off-critical zeros, and an arithmetic Gram projection defect arising from the finite fractional-part basis. We prove an orthogonal splitting identity showing that these two components interact with zero cross-term, record the spectral whitening formula for Tikhonov regularization, and present a finite-dimensional audit up to M=60. The diagnostics show that the tested projection is dominated by a low-divisor channel, while high-divisor indices provide only weak correction at substantial conditioning cost. No proof of the Riemann Hypothesis is claimed.