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Vinzant's Conjecture on Phase Retrieval Injectivity

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vinzant-phase-retrieval-injectivityAnalysisposed by Cynthia Vinzant; restated by Afonso S. Bandeirarecorded: partial

1 attempt · no person has looked

Statement

Vinzant conjectured, in a form later restated by Bandeira, that the 4M−44M-4 threshold for injective complex phase retrieval is sharp. Part (1) holds: for A∈CN×MA \in \mathbb{C}^{N \times M} with N=4M−5N = 4M-5 and i.i.d. standard complex Gaussian entries, the phase retrieval map generated by AA fails to be injective with positive probability.

Context

part (1) of the conjecture

A named conjecture on the sharp measurement count for complex phase retrieval, a central constant in frame theory that Bandeira put back into circulation.

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1 attempt

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  • #1

    Attempt 1

    proof attemptRethlas with Zhangsong Li ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    Rethlas
    people
    Zhangsong Li

    The paper states that the main result was obtained using generative AI, in particular the Rethlas system.

    part (1) of the conjecture

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