Problem detail · source-aware
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For an arrangement of $n$ hyperplanes in $\mathbb{P}^3_{\mathbb{C}}$ with $\ell$ intersection lines and $p$ intersection points where at least three hyperplanes meet, the refined form of Purdy's inequality expects $p - \ell + n + 2 \ge 0$. An explicit arrangement built from roots of unity violates it.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
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.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
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 arXiv preprint, not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
the refined form for essential arrangements in projective three-space
Source-reported tools: computation.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.