proposed
reason
Candidate claim vc_9736a6d0475e83b9 imported from artifact packet cap_61973ee16b553d57
finding type
theoretical
proposed confidence
0.99
confidence basis
agent-imported candidate claim; reviewer acceptance required
frontiers / 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
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Reviewable change
back to reviewadd a finding
acceptedErdős 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.
- id
- vpr_73589f0a991a1bb8
- frontier
- Erdős problems frontier
- kind
- finding.add
- created
- 2026-05-30
- findings
- +1
- state
- null → 821ff02c
accept gate
1 of 4 on record- —
- signature
- reviewer:erdos-db-trust · no key registered on this bundle
- ✓
- chain
- null → 821ff02c
- —
- witness
- no verifier attachment on record for this target
- —
- grade
- in state · unreviewed
timeline
- 2026-05-30proposeproposed · finding.addagent:erdos-spine-ingest
vpr_73589f0a991a1bb8Candidate claim vc_9736a6d0475e83b9 imported from artifact packet cap_61973ee16b553d57 - 2026-05-30acceptfinding.assertedreviewer:erdos-db-trust
null→821ff02cvev_75208698eff785d2Candidate claim vc_9736a6d0475e83b9 imported from artifact packet cap_61973ee16b553d57
provenance
proposed by
agent:erdos-spine-ingest
actor type
agent
created at
2026-05-30
target type
finding
affected
inspect finding →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.
vf_d2a27270867e4632Diff
Read-only frontier; diff not recomputed.
Review chain
- 01requestopen review →
Change request
Erdős problems frontier receives a reviewable source, finding, caveat, replication, evaluation, or proof-affecting edit.
- 02packetopen the campaign →
Diff packet
The packet names affected record objects, evidence, rationale, reviewer-facing fields, and expected proof impact.
- 03checksinspect checks →
Check output
Schema, provenance, benchmark, contradiction, and proof checks decide whether the request is ready to read.
- 04reviewread queue →
Reviewer decision
A steward accepts, rejects, caveats, revises, or retracts the request under an inspectable identity.
- 05acceptedinspect events →
Accepted event
Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.