Gemini
"For the proof of Theorem 9 we used some back and forth interaction with Google's Large Language Model Gemini." One theorem of the paper, attributed plainly.
Provider: Google DeepMind · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Pach's Tangency Conjecture: Improved Bounds
VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Pach conjectured that $n$ Jordan arcs, pairwise crossing exactly once with no triple points, have $O(n)$ tangent pairs. The best known bound stood at $O(n^{7/4})$; the paper improves it to $O(n^{3/2})$ (and $O(n^{5/3})$ in the at-most-one-crossing relaxation), plus a tight $\Theta(n^{4/3})$ for a grounded x-monotone variant.
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.
What AI did
Verification boundary
No verification note supplied.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Timeline
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arXiv
Exponent improvements toward Pach's conjecture, which remains open.
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
- VibeMath has not independently verified the mathematical claim.
- AI-attempt independence and training-data exposure are unknown unless explicitly documented.
- VibeMath has not independently audited the mathematical statement, proof, or novelty claim.