ProbXiv
sign in
Problem archiveProblem record

Purdy's Inequality for Hyperplane Arrangements

Geometry & topology · posed by George Purdy · disproved

2 comments

Statement

For an arrangement of nn hyperplanes in PC3\mathbb{P}^3_{\mathbb{C}} with ℓ\ell intersection lines and pp intersection points where at least three hyperplanes meet, the refined form of Purdy's inequality expects p−ℓ+n+2≥0p - \ell + n + 2 \ge 0. An explicit arrangement built from roots of unity violates it.

Record

Source
Added

Comments

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

  1. computation · #1

    Mateusz Michalek and Piotr Pokora, using ChatGPT

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    The acknowledgement credits the model with generating the computer programs used to carry out the symbolic computations over configurations of points and planes, which is how the violating arrangement was checked.

    the refined form for essential arrangements in projective three-space

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed site check

    scope Reproduction by the VibeMathed site

    The counterexample is an explicit root-of-unity arrangement whose point, line and plane counts the paper works out in closed form, so the violation is a finite check. arXiv preprint, not yet peer-reviewed.

    Repeated from the source; nothing was checked here.

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.