What is recorded here?
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.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
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.
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People and systems
OpenAI organizational byline; individual human preparation and verification roles incompletely disclosed The recorded author list is incomplete.
OpenAI research model · OpenAI · Unreleased internal frontier model; exact identifier not disclosed
Source-reported mathematical argument generation. Source-reported attribution; provider attestation is unavailable.
Research locations and affiliations
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English catalogue narrative
OpenAI: Arithmetic progressions from divergent reciprocal sums
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.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
OpenAI organizational byline; individual human preparation and verification roles incompletely disclosed
OpenAI research model / OpenAI / Unreleased internal frontier model; exact identifier not disclosed: Source-reported mathematical argument generation (source reported).