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.
Authors
- T.A. Ziad (ORCID: https://orcid.org/0009-0001-7304-3533)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-05-19
- DOI
- https://doi.org/10.5281/zenodo.20277867
- Primary Topic
- Mathematical Analysis and Transform Methods
- Type
- preprint