Breakthrough Tracker record
A revised preprint claims all three de Bruijn–Erdős consecutive-gap conjectures
Samuel Korsky proves quantitative lower bounds for the largest and smallest r-spans formed by inserting points on a circle and a matching-order bound for their ratio, resolving the three asymptotic conjectures posed by de Bruijn and Erdős in 1949.
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- Stable ID
math-de-bruijn-erdos-consecutive-gap-resolution-2026- Revision
math-de-bruijn-erdos-consecutive-gap-resolution-2026.v1- Field
- Mathematics · Combinatorial discrepancy and uniform distribution
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Provisional · Provisional three-part resolution
- Last checked
AI role
No substantive AI role is disclosed in the inspected manuscript.
Record details
- Problem or result
- The three 1949 de Bruijn–Erdős asymptotic consecutive-gap conjectures
- Authors
- Samuel Korsky
- Institutions
- No affiliation stated in the manuscript
- Result date
- Version 2 submitted September 9, 2026
Why it matters
The revision expands a one-part result into a claimed resolution of the full 77-year-old problem and determines the ratio's order up to an absolute constant.
Limits
Version 1 resolved only one of the three limits; the broader version 2 is a fresh, non-peer-reviewed claim with no located external specialist assessment.
Sources
Correction and revision history
- 2026-09-10 — Added after primary-source, scope, status, AI-role and limitation review.
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