What was already known
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.
What changed and why it matters
Extends progression existence to the divergent-reciprocal-sum target through the stated quantitative bound.
The AI contribution
OpenAI attributes these manuscripts to its internal model. The entry does not infer individual human contributions beyond that publisher attribution.
Limitations
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. Preprint. This is a source-statement and significance assessment, not a proof audit. No independent checking or successful formal compilation is asserted by this entry.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
The publisher reports the scoped result. AIProofWatch has not independently validated its correctness.
Accessible artifact / proof
The original written argument is accessible. Availability does not establish a successful proof check or Lean verification.
Correction and publication history
Historical report added after statement, scope, and importance review. No proof audit or formal checking asserted; subscriber alerts disabled.
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