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The Near-Quadratic Elekes-Ronyai Expander Conjecture

Combinatorics · posed by Gyorgy Elekes, Lajos Ronyai, 2000 · disproved

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Statement

The near-quadratic Elekes-Ronyai expander conjecture over R\mathbb{R} predicts that a nonspecial polynomial expands any finite set to near-quadratic size. False: a fixed nonspecial quadratic polynomial, together with arbitrarily large finite sets of real algebraic integers, has image with a fixed power saving from quadratic size.

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

  1. construction · #1

    ChatGPT 5.5 Pro, Rethlas, with Jihao Liu

    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 abstract states that the main result was obtained by generative AI, particularly ChatGPT 5.5 Pro and the Rethlas system. The proof builds on a recent OpenAI construction of an infinite tower, so this is an AI result standing on another AI result.

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