evidence boundary
supportsfrontiers / frontier
Erdős problems frontier
- id
- vfr_37aec80d874a0239
- license
- CC-BY-4.0
- findings
- 1,256
- accepted core
- 6
- contested
- 0
- links
- 17
- sources
- 1,234
- evidence
- 1,256
- avg conf
- 0.98
e1288/1288 · statement.registered · agent:claude-proxy · 2026-06-10 · null→null
Evidence atom
back to sources{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_9736a6d0475e83b9"}
- id
- vea_d625b775fe29f472
- frontier
- Erdős problems frontier
- source
- vs_6347ef02a4f57233
- finding
- vf_d2a27270867e4632
finding binding
boundtheoretical
Erdős Problem #847 has been DISPROVED (a counterexample is known). Statement: Let $A \subset \mathbb{N}$ be an infinite set for which there exists some $\epsilon > 0$ such that in any subset of $A$ of size $n$ there is a subset of size at least $\epsilon n$ which contains no three-term arithmetic progression. Is it true that $A$ is the union of a finite number of sets which contain no three-term arithmetic progression? A negative answer was given by Reiher, Rödl, and Sales [RRS24], who proved that, for any $0<\mu<1/2$, there exists $A\subseteq \mathbb{N}$ such that every finite colouring of $A$ contains a three-term arithmetic progression, and yet every subset of $A$ of size $n$ contains a subset of size $\geq \mu n$ without a three-term arithmetic progression. Topics: additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
source binding
source-boundcap_61973ee16b553d57 · vc_9736a6d0475e83b9
vs_6347ef02a4f57233
review context
unverified1 events
1 reviewable changes and 0 evaluation records target this atom or its bound objects.
statement
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_9736a6d0475e83b9"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_137220c786379cdd
caveats
No caveats recorded.
Review, event, and evaluation records
2events
vev_75208698eff785d2finding.assertedCandidate claim vc_9736a6d0475e83b9 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_73589f0a991a1bb8finding.addCandidate claim vc_9736a6d0475e83b9 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.