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_d9faa36c41106ee5"}

id: vea_216b15c926a9fc59
frontier: Erdős problems frontier
source: vs_9cc53e7115d29d9c
finding: vf_c773bca7c1b3fde3

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #128 has status 'falsifiable'. Statement: Let G be a graph with n vertices such that every subgraph on ≥ $n/2$ vertices has more than $n^2/50$ edges. Must G contain a triangle? Topics: graph theory. Erdős prize: $250. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

source binding

source-bound

cap_61973ee16b553d57 · vc_d9faa36c41106ee5

vs_9cc53e7115d29d9c

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_d9faa36c41106ee5"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_c81293f11f050d14

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_61a4e5a465f3d3b3finding.asserted
Candidate claim vc_d9faa36c41106ee5 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_34d7962a2dcde210finding.add
Candidate claim vc_d9faa36c41106ee5 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_49aa7a218d9e9ff3finding.note
SEMANTIC-EDGE DRAFT -> Erdos #566 (vf_80897a5c05f62d90) [related, confidence 0.6]: Both ask whether a local edge-density condition on every small/medium subgraph (n^2/50 edges on half-sets in 128; at most 2k-3 edges on k-sets in 566) forces or forbids a triangle/short cycle, the same extremal local-density-vs-triangle question. -- 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_d9faa36c41106ee5

1 events

Review, event, and evaluation records

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