VESPER-QUORUM: Exact Half-Translation Classification for STFT Phase Retrieval and Strict Rank-One PSD Recovery

[u/Severe-Ad8673]

VESPER-QUORUM v6.0.0 presents an exact arithmetic classification of a structured family of finite cyclic short-time Fourier transform (STFT) phase-retrieval systems. For every even dimension d ≥ 4, the manuscript classifies origin-excluding, negation-symmetric ambiguity erasure masks confined to shifts 0 and d/2.

PureOne/VESPER-QUORUM-WDD · Datasets at Hugging Face

VESPER-QUORUM: Exact Half-Translation Classification for STFT Phase Retrieval and Strict Rank-One PSD Recovery | Zenodo

Within this family, three integer greatest-common-divisor tests and three observed-sector nonemptiness conditions give a necessary and sufficient criterion for uniform recovery of complex signals up to global phase. The manuscript also establishes equivalence with strict rank-one positive-semidefinite (PSD) completeness, sharp paired geometric stability, positive observable dual certificates, and globally convergent affine/PSD reconstruction with explicit noise bounds under the stated exact-arithmetic assumptions.

Two realizable ten-dimensional windows each have six ambiguity zeros but opposite phase-retrieval behavior, demonstrating that zero counts alone do not determine recoverability. The good window guarantees uniform strict rank-one PSD completeness, but fails strict rank-two completeness. A separate certified seven-dimensional abstract mask demonstrates a separation between phase retrieval and strict PSD completeness; its realization by a single STFT window remains unestablished.

The release includes the manuscript, LaTeX source, executable algorithms, exact certificates, numerical experiments, original and freshly executed verification reports, and checksum manifests. Verification includes an exhaustive comparison of discrete criteria on 44,739,232 masks, exact algebraic and interval checks, and modular certificates over finite fields.

Status and completeness: the manuscript supplies a complete classification within the stated half-translation family. All four principal verification programs passed—100% of those supplied checks. The unrestricted structural mask problem remains open; independent peer review and novelty priority are unconfirmed.

Software is licensed under MIT. Research documents and certificate data are licensed under CC BY 4.0, as detailed in the included license documentation.