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

back to sources

arXiv:2007.03528 states that if A in {1,...,N} has no non-trivial 3-term arithmetic progressions, then |A| is bounded by N/(log N)^(1+c) for some absolute c > 0.

id: vea_74798c142b62e1c4
frontier: Additive combinatorics: Sidon sets and N(h,k) bounds
source: vs_7d2d5a9a0f13bd38
finding: vf_f16e736879b4b42c

evidence boundary

supports

theoretical

finding binding

bound

theoretical

Bloom-Sisask break the 'log barrier' for Roth: density alpha > 1 / (log N)^{1+c} for an absolute c > 0 suffices for a 3-AP, the first sub-1/log N bound.

source binding

source-bound

Bloom-Sisask 2020

vs_7d2d5a9a0f13bd38

review context

unverified

2 events

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

statement

arXiv:2007.03528 states that if A in {1,...,N} has no non-trivial 3-term arithmetic progressions, then |A| is bounded by N/(log N)^(1+c) for some absolute c > 0.

locator

section:arXiv abstract

extraction method

manual_curation

support relation

supports

condition refs

vcnd_177ff115ffe93a32

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_5a5e570b6781367afinding.span_repaired
Attach source-backed abstract span for the Bloom-Sisask Roth log-barrier result; does not change the assertion.
reviewer:solo-maintainer · 2026-05-21
vev_9be516b6d864aa48finding.asserted
Manual finding added to frontier state
agent:research-bot-2026-05-09 · 2026-05-09

reviewable changes

vpr_206f9fda54ef0d0ffinding.span_repair
Attach source-backed abstract span for the Bloom-Sisask Roth log-barrier result; does not change the assertion.
applied · reviewer:solo-maintainer · 2026-05-21
vpr_2436bdba91b28491finding.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

Bloom-Sisask 2020

2 events

Review, event, and evaluation records

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