ProbXiv
sign in
unchecked

Predicting Diagonalizability of a Mean Matrix

Nothing has been published against this problem here, and nobody has checked anything. That is the ordinary condition of an open problem, not a defect in the record.

wu-santhanam-diagonalizability-predictionProbability & statisticsposed by Yuheng Wu, Narayana Santhanam, 2024recorded: solved

1 attempt · no person has looked

Statement

Wu and Santhanam asked whether one can determine, from an increasing i.i.d. sample of binary random matrices, whether the unknown mean matrix is diagonalizable, while making only finitely many errors almost surely. Answered affirmatively over both R and C.

Context

The general principle is the interesting part: every semialgebraic property of a bounded fixed-dimensional mean parameter is eventually almost surely predictable. Against merely integrable matrix laws it fails from dimension two.

A recent question from a single specialist paper on eventually-almost-sure prediction, with a real but small audience.

People

no project yet · nobody looking

Projects

none yet

Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.

begin a project on this problem →

Interest

nobody looking

Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.

Attempts

1 attempt

No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

review this attempt

  • #1

    Attempt 1

    proof attemptGPT-5.6 Sol Ultra with Jinze Zhao ·
    AI involvement
    ai discovered
    the result was found by a model.
    models
    GPT-5.6 Sol Ultra
    people
    Jinze Zhao

    A disclosure section of its own: "The proof strategy and counterexample were produced by OpenAI's GPT-5.6 Sol Ultra through Codex in response to prompts from the author. Codex was also used to revise the exposition and prepare the LaTeX manuscript. The author selected the problem, directed the interactions and revisions, and is the sole named author."

    Reviews

    0 human reviews · 0 machine checks

    No person has reviewed this attempt. It has not been checked at all.

    Endorsements

    0 endorsements

    No one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.

    Discussion of this attempt

    no comments

Discussion

no comments

Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.

Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.