frontiers / frontier

Additive combinatorics: Sidon sets and N(h,k) bounds

id: vfr_496956067dc5ad79
license: CC-BY-4.0
findings: 22
accepted core: 1
contested: 1
links: 0
sources: 22
evidence: 22
avg conf: 0.83

used by 1 · replayed by 1 producer · second seat open

e33/33 · finding.asserted · reviewer:will · 2026-06-03 · null→e123

Evidence atom

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arXiv:1605.09223 states that the Croot-Lev-Pach method bounds progression-free subsets of F_q^n by c^n with c < q; for q = 3 this is the cap-set problem.

id: vea_da5823dd5a21022c
frontier: Additive combinatorics: Sidon sets and N(h,k) bounds
source: vs_3d86039e17bccee8
finding: vf_eee5b19763f3c625

evidence boundary

supports

theoretical

finding binding

bound

theoretical

Ellenberg-Gijswijt extend Croot-Lev-Pach to prove a 3-AP-free subset of F_3^n has size at most 2.756^n, settling the cap-set problem up to a constant in the exponent.

source binding

source-bound

Ellenberg-Gijswijt 2017

vs_3d86039e17bccee8

review context

unverified

2 events

2 reviewable changes and 0 evaluation records target this atom or its bound objects.

statement

arXiv:1605.09223 states that the Croot-Lev-Pach method bounds progression-free subsets of F_q^n by c^n with c < q; for q = 3 this is the cap-set problem.

locator

section:arXiv abstract

extraction method

manual_curation

support relation

supports

condition refs

vcnd_37930dc72168271c

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_3b8bca3bf09d4358finding.span_repaired
Attach source-backed abstract span for the Ellenberg-Gijswijt cap-set result; leaves the numeric constant as methodology context rather than new accepted evidence.
reviewer:solo-maintainer · 2026-05-21
vev_82306caefdf8aedbfinding.asserted
Manual finding added to frontier state
agent:research-bot-2026-05-09 · 2026-05-09

reviewable changes

vpr_11afa6e155380c7ffinding.span_repair
Attach source-backed abstract span for the Ellenberg-Gijswijt cap-set result; leaves the numeric constant as methodology context rather than new accepted evidence.
applied · reviewer:solo-maintainer · 2026-05-21
vpr_d56eb9bd0cb6b9fbfinding.add
Manual finding added to frontier state
applied · agent:research-bot-2026-05-09 · 2026-05-09

evaluations

No evaluation rows are attached.

theoretical

theoretical

Ellenberg-Gijswijt 2017

2 events

Review, event, and evaluation records

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