SWhat changed
For each fixed dimension, a subset of a finite vector space containing a full affine line in every direction has size at least a positive dimension-dependent fraction of the entire space. A low-degree polynomial vanishing on a too-small candidate set would force incompatible vanishing of its homogeneous components.
Scientific scope
For each fixed dimension, a subset of a finite vector space containing a full affine line in every direction has size at least a positive dimension-dependent fraction of the entire space. A low-degree polynomial vanishing on a too-small candidate set would force incompatible vanishing of its homogeneous components. The field is finite and the contained objects are complete affine lines; this does not settle real Euclidean Kakeya dimension or maximal-function conjectures. The dimension-dependent constant is not asserted to be optimal. The revised text distinguishes Dvir's initial exponent improvement from the full-density sharpening credited to subsequent suggestions.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The field is finite and the contained objects are complete affine lines; this does not settle real Euclidean Kakeya dimension or maximal-function conjectures. The dimension-dependent constant is not asserted to be optimal. The revised text distinguishes Dvir's initial exponent improvement from the full-density sharpening credited to subsequent suggestions.
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.
- Noga Alon · SCIENCE: Credited in§1.1 with the observation sharpening the initial bound to a dimension-dependent full-density bound
- Terence Tao · SCIENCE: Credited in§1.1 with the full-density sharpening; acknowledgments print an extra-r spelling variant
- Richard Oberlin · SCIENCE: Acknowledged for pointing out improvements to Theorem1
Provisional WRS assessment, edition 2026-10-23.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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