AIProofWatch
← Explore interestsIndividual problem

Erdős’s reciprocal-sum progression conjecture

Positive density guarantees from Szemerédi’s theorem do not automatically cover every set with divergent reciprocal sum.

Progress records 1

Understand the problem ↓

1 record · How we rate progress

Understanding the problem

Read the background

Positive density guarantees from Szemerédi’s theorem do not automatically cover every set with divergent reciprocal sum. The needed quantitative bound addresses that stronger target.

Constants and the exponent depend on the fixed progression length and are not optimized. The claim does not provide a uniform bound as the length grows.

Why it matters

If correct, extends progression existence to the divergent-reciprocal-sum target through the stated quantitative bound.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • Constants and the exponent depend on the fixed progression length and are not optimized. The claim does not provide a uniform bound as the length grows.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

Website timeline

Publication dates and editorial changes.