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OpenAI: Arithmetic progressions from divergent reciprocal sums

Reported result · significance if the exact claim is established

If verified · conditional significanceClaim scope and evidenceReported result · not independently verified.
If verified · reference score500,000Editorial revision range 300,000–750,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.

Provisional assessment of the stated contribution scope. Scientific evidence and contributor attribution are separate.

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What is claimed?

The paper claims every set of positive integers with divergent reciprocal sum contains progressions of every finite length, via quantitative bounds r_k(N)<=C_k N exp(-c_k(log N)^epsilon_k) for each fixed k>=3. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.

Scientific scope

Constants depend on fixed progression length. The selected formal scope covers the reciprocal-sum consequence, not the quantitative bound. It does not relabel Szemeredi or the three-term predecessor as this new proof. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run.

Evidence state

The source reports this result. WRS has not independently reconstructed the complete argument or validated the reported evidence. The grade and score here express conditional significance; they do not certify correctness. The provisional value enters the main reference rankings with an unverified label, but not achieved-science progress totals.

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