SWhat changed
Extending 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.
Scientific scope
Extending 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. 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.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. 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.
Contributors
- The named authors in the research record · SCIENCE: Source-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.
Provisional WRS assessment, edition 2026-10-23.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
Full scientific record · Browse contribution grades · Request a correction