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

Source record

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Croot-Lev-Pach 2017

id: vs_b5e2d12c31e5aff7
frontier: Additive combinatorics: Sidon sets and N(h,k) bounds
type: paper

source boundary

frontier-owned

declared

finding bindings

record context

1 findings

evidence atoms

materialized

1 atoms

review context

inspectable

2 events

2 reviewable changes and 0 evaluations are attached through this source or its findings.

citation

locator

title:Croot-Lev-Pach 2017

imported

2026-05-09T22:52:52.541144+00:00

extraction mode

manual_curation

authors

agent:research-bot-2026-05-09

caveats

No caveats recorded.

Bound findings

The polynomial method bounds 3-AP-free subsets of (Z/4Z)^n by 4^{0.926n}, far below the 4^n total, breaking the previous logarithmic-style bounds for cap-set-style problems.
theoretical · vf_7273c1823848f6e3

Evidence atoms

vea_aa70162760bbe7f4theoretical · supports
arXiv:1605.01506 states that for n > 0, any 3-term-progression-free subset of Z_4^n has size below 4^(c n) for c about 0.926.

Review, event, and evaluation records

events

vev_34883b43241d8c83finding.span_repaired
Attach source-backed abstract span for the Croot-Lev-Pach Z_4^n bound; does not change the assertion.
reviewer:solo-maintainer · 2026-05-21
vev_5e54fbcfde90e54ffinding.asserted
Manual finding added to frontier state
agent:research-bot-2026-05-09 · 2026-05-09

reviewable changes

vpr_a3f3e64fc4888fc0finding.add
Manual finding added to frontier state
applied · agent:research-bot-2026-05-09 · 2026-05-09
vpr_e3d8c0aa1f6869e5finding.span_repair
Attach source-backed abstract span for the Croot-Lev-Pach Z_4^n bound; does not change the assertion.
applied · reviewer:solo-maintainer · 2026-05-21

evaluations

No evaluation rows are attached.