AlphaProof Nexus
The source does not provide a sufficiently specific role description.
Provider: Google DeepMind · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Erdős Problem #12
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
Let $A \subset \mathbb{N}$ be infinite with no distinct $a, b, c \in A$ such that $a \mid (b + c)$ with $b, c > a$. Can $|A \cap [1, N]|/\sqrt{N}$ have positive lower limit? Must every such $A$ fall below $N^{1-c}$ infinitely often?
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
Lean-checked; formal proofs published with the AlphaProof Nexus report (arXiv:2605.22763).
Correctness: supported · statement fidelity: audited · peer review: none
Timeline
-
erdosproblems.com/12
parts (i) and (ii) resolved - a near-linear-density construction exists, refuting the N^{1-c} decay; the reciprocal-sum part 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.