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

used by 0 · replayed by 2 producers

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_b5ee363411b157fb"}

id: vea_8b2179d7c253ea2b
frontier: Erdős problems frontier
source: vs_972608fe29ee7c05
finding: vf_912ea88190378ef3

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #75 remains OPEN. Statement: Is there a graph of chromatic number `ℵ_ 1` with `ℵ_ 1` vertices such that for all `ε > 0`, if `n` is sufficiently large and `H` is a subgraph on `n` vertices, then `H` contains an independent set of size `> n ^ (1 - ε)`? Topics: graph theory, chromatic number. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

source binding

source-bound

cap_61973ee16b553d57 · vc_b5ee363411b157fb

vs_972608fe29ee7c05

review context

unverified

1 events

2 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_b5ee363411b157fb"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_766da9594268923c

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_87cbee4912a29702finding.asserted
Candidate claim vc_b5ee363411b157fb imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_3fa32759c5c32d19finding.add
Candidate claim vc_b5ee363411b157fb imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_d94f166e98624123finding.note
SEMANTIC-EDGE DRAFT -> Erdos #750 (vf_790fcc99a314fb3c) [related, confidence 0.55]: Both ask whether graphs of large (uncountable/infinite) chromatic number must contain finite subgraphs of prescribed chromatic complexity as a function of size. -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.
pending_review · agent:semantic-edge-extractor · 2026-06-10

evaluations

No evaluation rows are attached.

computational

open_question

cap_61973ee16b553d57 · vc_b5ee363411b157fb

1 events

Review, event, and evaluation records

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