ChatGPT-6 Astra
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Provider: OpenAI · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
The Erdos-Borwein Constant is 2-Dense
VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Is the Erdos-Borwein Constant 2-Dense?
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
The Lean development proves disjunctivity of the binary expansion conditional on two hypotheses supplied as theorem arguments, not as axioms: AGP, the Alford-Granville-Pomerance estimate in the form of Vandehey's Proposition 2.1, and PrimeIntervalSupply, a standard prime number theorem consequence bounding the primes in (L, 2L) below by L/(3 log L). Both are published theorems rather than conjectures, so the mathematics is conditional only on known results; neither is formalized here. Read directly from lean/ErdosBorwein/PrimeInputs.lean on 8 September 2026. The audited endpoints depend on propext, Classical.choice and Quot.sound only. Because the statement is the author's own rather than anchored to a canonical tracker, and because what the kernel certifies is the implication, this takes the statement-unaudited tier. No specialist in analytic number theory has read the argument.
Correctness: supported · statement fidelity: unaudited · peer review: none
Timeline
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GitHub repository with Lean proof
This work proves that the Erdős–Borwein constant's binary expansion contains every finite binary sequence as a consecutive block, each occurring infinitely often. This implies that the Erdős–Borwein constant is 2-dense.
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.
- The source status is candidate and must not be represented as solved.
- 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.