proposed
reason
Candidate claim vc_d11ea0453b020966 imported from artifact packet cap_61973ee16b553d57
finding type
open_question
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 #501 remains OPEN. Statement: For every $x \in \mathbb{R}$ let $A_x \subset \mathbb{R}$ be a bounded set with outer measure $< 1$. Must there exist an infinite independent set, that is, some infinite $X \subseteq \mathbb{R}$ such that $x \notin A_y$ for all $x \neq y \in X$? If the sets $A_x$ are closed and have measure $< 1$, then must there exist an independent set of size $3$? Known results: Erdős–Hajnal [ErHa60] proved the existence of arbitrarily large finite independent sets. Hechler [He72] showed the answer is **no** assuming the continuum hypothesis. Topics: combinatorics, set theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
- id
- vpr_2183116a1007e07b
- frontier
- Erdős problems frontier
- kind
- finding.add
- created
- 2026-05-30
- findings
- +1
- state
- null → 4e571011
accept gate
1 of 4 on record- —
- signature
- reviewer:erdos-db-trust · no key registered on this bundle
- ✓
- chain
- null → 4e571011
- —
- witness
- no verifier attachment on record for this target
- —
- grade
- in state · unreviewed
timeline
- 2026-05-30proposeproposed · finding.addagent:erdos-spine-ingest
vpr_2183116a1007e07bCandidate claim vc_d11ea0453b020966 imported from artifact packet cap_61973ee16b553d57 - 2026-05-30acceptfinding.assertedreviewer:erdos-db-trust
null→4e571011vev_576fcd8062db0145Candidate claim vc_d11ea0453b020966 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 #501 remains OPEN. Statement: For every $x \in \mathbb{R}$ let $A_x \subset \mathbb{R}$ be a bounded set with outer measure $< 1$. Must there exist an infinite independent set, that is, some infinite $X \subseteq \mathbb{R}$ such that $x \notin A_y$ for all $x \neq y \in X$? If the sets $A_x$ are closed and have measure $< 1$, then must there exist an independent set of size $3$? Known results: Erdős–Hajnal [ErHa60] proved the existence of arbitrarily large finite independent sets. Hechler [He72] showed the answer is **no** assuming the continuum hypothesis. Topics: combinatorics, set theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
vf_fccad3dc897074b9Diff
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
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- 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.