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      "statement": "# Kelley and Meka: stretched-exponential density bounds for integer three-term progressions\n\nNew analytic structural and density-increment methods give a stretched-exponential-in-logN upper bound on the density of three-term-progression-free subsets of {1,…,N}. The paper develops related finite-field structural results as a route to the integer theorem.\n\n## Scientific scope\n\nThis is an upper bound with unspecified absolute constants here, not the exact extremal function or a matching Behrend exponent. The finite-field estimate is explicitly weaker than then-known algebraic bounds; analytic transfer, rather than a new best finite-field cap-set bound, is the relevant distinction.\n\n## Reading status\n\nThis 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.\n\n## People and systems\n\nZander Kelley; Raghu Meka\n\nSource-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.\n\n\n\n## Original sources\n\n- [Strong Bounds for 3-Progressions](https://arxiv.org/abs/2302.05537v1)\n",
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