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_d11ea0453b020966"}
- id
- vea_d4aee9ae62257a0a
- frontier
- Erdős problems frontier
- source
- vs_fc0b431668943c6a
- finding
- vf_fccad3dc897074b9
finding binding
boundopen_question
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.
source binding
source-boundcap_61973ee16b553d57 · vc_d11ea0453b020966
vs_fc0b431668943c6a
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_d11ea0453b020966"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_ed7e2abda58d1259
caveats
No caveats recorded.
Review, event, and evaluation records
2events
vev_576fcd8062db0145finding.assertedCandidate claim vc_d11ea0453b020966 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_2183116a1007e07bfinding.addCandidate claim vc_d11ea0453b020966 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.