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Vinzant's Conjecture on Phase Retrieval Injectivity

Analysis · posed by Cynthia Vinzant; restated by Afonso S. Bandeira · partial

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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.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Rethlas, with Zhangsong Li

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    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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