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        "description": "This is an upper bound, not the exact largest cap size, and it does not transfer the same exponential saving to cyclic integer intervals. The joint paper states that the two authors developed essentially identical arguments independently. Predecessor polynomial methods retain their separate credit.",
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      "statement": "# Ellenberg and Gijswijt: exponential upper bounds for progression-free finite-field sets\n\nExtending the Croot–Lev–Pach polynomial method, the paper gives an exponentially smaller-than-q^n bound for three-term-progression-free subsets of finite-field vector spaces in the applicable odd-characteristic setting. In F_3^n it obtains a cap-set bound with exponential base below 2.756.\n\n## Scientific scope\n\nThis is an upper bound, not the exact largest cap size, and it does not transfer the same exponential saving to cyclic integer intervals. The joint paper states that the two authors developed essentially identical arguments independently. Predecessor polynomial methods retain their separate credit.\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\nJordan S. Ellenberg; Dion Gijswijt\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- [On large subsets of $F_q^n$ with no three-term arithmetic progression](https://arxiv.org/abs/1605.09223v1)\n",
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