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frontiers / frontier

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

constellation seal · derived from vfr_496956067dc5ad79
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

back to sources

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.

id
vea_aa70162760bbe7f4
frontier
Additive combinatorics: Sidon sets and N(h,k) bounds
source
vs_b5e2d12c31e5aff7
finding
vf_7273c1823848f6e3

evidence boundary

supports

theoretical

finding binding

bound

theoretical

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.

source binding

source-bound

Croot-Lev-Pach 2017

vs_b5e2d12c31e5aff7

review context

unverified

2 events

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

statement

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.

locator

section:arXiv abstract

extraction method

manual_curation

support relation

supports

condition refs

vcnd_92b21bbab19aa796

caveats

No caveats recorded.

Review, event, and evaluation records

4

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-maintainerreviewer:solo-maintainer · 2026-05-21

  • vev_5e54fbcfde90e54ffinding.asserted

    Manual finding added to frontier state

    agent — machine actor, no signing keyagent:research-bot-2026-05-09 · 2026-05-09

reviewable changes

  • vpr_a3f3e64fc4888fc0finding.add

    Manual finding added to frontier state

    agent — machine actor, no signing keyapplied · 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.

    reviewer:solo-maintainerapplied · reviewer:solo-maintainer · 2026-05-21

evaluations

No evaluation rows are attached.

statement.registered · agent:claude-proxy · 4 days

renders the record as of vev_e73c9b6c · 1,355 events · hub

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