arXiv:2606.17922 · v2

Resolution of Vinzant's Conjecture on Phase Retrieval Injectivity

首次提交 2026-06-16 21:36

版本更新 2026-11-10 20:09

雷达观测 2026-11-11 13:08

摘要

Let $A\in\mathbb C^{N\times M}$ with $N=4M-5$ has independent standard complex Gaussian entries. We prove that the probability that the phase retrieval map generated by $A$ is injective is strictly smaller than $1$, and is $O(M^{-1})$ as $M\to \infty$. This proves a conjecture of Cynthia Vinzant, which was later restated by Afonso S. Bandeira in \cite{bandeira2026randomstrasse101}. The main result of this paper was obtained using generative AI, in particular GPT6-Astra, GPT 5.6-sol, and the Rethlas system.

作者备注：13 pages; AI generated, human verified