Aletheia (Gemini Deep Think)
The source does not provide a sufficiently specific role description.
Provider: Google DeepMind · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Erdős Problem #654
VibeMathed reports this item as open. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
If $n$ planar points have no four concyclic, must some point determine $(1 - o(1))n$ distinct distances? Failing that, can one always force more than $(1/3 + c)n$?
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
Expert-reviewed within the Aletheia project, with public report and transcripts; no journal review.
Correctness: supported · statement fidelity: unaudited · peer review: none
Timeline
-
Aletheia project report (Feng et al.)
the strongest form is disproved via configurations where every point sees at most about 3n/4 distinct distances; the weaker improvement remains open
Known method families
construction (source-reported)
Source-reported tools: construction.
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.