Source authenticated

Prime Gaps at Most 186

Assuming three explicit input statements, the project proves $\mathrm{DHL}[40,2]$ : every admissible $40$ -tuple contains at least two primes infinitely often after translation. An explicit admissible $40$ -tuple of diameter $186$ then gives $\liminf_{n\to\infty}(p_{n+1}-p_n)\le186.$ The Lean proof of the implication from the three inputs to the final theorem is kernel-checked. Two inputs are Kloosterman-type estimates cited to Katz/Deligne and Fouvry--Kowalski--Michel; the third consists of finitely many numerical integral and cap inequalities backed by a Python/FLINT certificate.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 3, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Prime Gaps at Most 186

Confidence: Not scored

Registry verification: lean checked · announcement · partial

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Attribution

VibeMathed
registry · event recorded by

GPT 6 Astra
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Prime Gaps at Most 186

specialist registry · passed

Lean-checked, not Lean-verified, and the distinction is the whole of it. The Lean development in openai/PrimeGaps186 reports zero sorry in its three main declarations, and Comparator and Lean's kernel accept them - but all three depend on three project-specific axioms: a rank-three hyper-Kloosterman bound, a rank-two Kloosterman correlation bound, and a package of 104 outer, 45 inner and 3 cap numerical inequalities. So the kernel has checked that those three statements imply DHL[40,2] and the bound; it has not checked them. The first two are tied to established literature and the third is recomputed by a Python and FLINT certificate that does not discharge its Lean axiom. No independent expert has read the paper on the record.

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Prime Gaps at Most 186

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Lean proof

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Lean proof

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.