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

Finding bundle

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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.

id: vf_7273c1823848f6e3
frontier: Additive combinatorics: Sidon sets and N(h,k) bounds
version: 1
confidence: 0.85

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/frontier/sidon-sets/at/vev_4b72f36cba6fe4c0permalink · after_hash 4021aa2d29c2d2ea…

vf_7273c1823848f6e3 · sidon-sets · snapshot sha256:8badc78d64f9cdb5b9e9594b0e2855d9295d4b99abf972db104f3b417fa630af · https://vela-site-next.fly.dev/frontier/sidon-sets/at/vev_4b72f36cba6fe4c0

cite

raw json · vf_7273c1823848f6e3 (2.1 KB)

machine twin · index.json

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  "text": "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.",
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  "text": "Manually added finding; requires evidence review before scientific use."
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  "extraction_confidence": 1,
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  "evidence_spans": [
   {
    "section": "arXiv abstract",
    "text": "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."
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produced byagent:research-bot-2026-05-09finding.asserted · 2026-05-09vev_5e54fbcfde90e54f

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history · 2 events

e21/33finding.assertedagent:research-bot-2026-05-092026-05-09→f2b2072db3e25/33finding.span_repairedreviewer:solo-maintainer2026-05-21→0d936f1262

record state

frontier-owned

Review status

unreviewed

finding statement

finding type

theoretical

No entity list is declared.

evidence

source-bound

1 atoms

theoretical · manual state transition

proof impact

packet context

2 events

2 reviewable changes and 0 evaluation records are attached to this finding id.

evidence

method

manual state transition

evidence type

theoretical

evidence spans

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.
arXiv abstract

conditions

species_unverified
species_verified
text: Manually added finding; requires evidence review before scientific use.

provenance

source title

Croot-Lev-Pach 2017

authors

agent:research-bot-2026-05-09

Source records

source record

declared

Croot-Lev-Pach 2017

vs_b5e2d12c31e5aff7

title:Croot-Lev-Pach 2017

manual_curation

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.
vs_b5e2d12c31e5aff7 · section:arXiv abstract · manual_curation

Typed links

outgoing

No outgoing links.

incoming

No incoming links.

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 record targets this finding id.

Review status

theoretical

1 atoms

2 events

Source records

Croot-Lev-Pach 2017

Evidence atoms

Typed links

Review, event, and evaluation records

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