SWhat changed
New 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.
Scientific scope
New 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. This 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.
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 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.
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