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_b9f07b01e3fba855"}

id: vea_12d34d95cdfbc48f
frontier: Erdős problems frontier
source: vs_b2ca93c9b664c788
finding: vf_af9a340f76a26927

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #108 remains OPEN. Statement: For every r ≥ 4 and k ≥ 2 is there some finite f(k,r) such that every graph of chromatic number ≥ f(k,r) contains a subgraph of girth ≥ r and chromatic number ≥ k? Topics: graph theory, chromatic number, cycles. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible.

source binding

source-bound

cap_61973ee16b553d57 · vc_b9f07b01e3fba855

vs_b2ca93c9b664c788

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_b9f07b01e3fba855"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_99af3b7800aa5d37

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_22f728420e7ce434finding.asserted
Candidate claim vc_b9f07b01e3fba855 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_7bf3d45c7fc1afacfinding.add
Candidate claim vc_b9f07b01e3fba855 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_ee828e1a98ce8591finding.note
SEMANTIC-EDGE DRAFT -> Erdos #750 (vf_790fcc99a314fb3c) [shares_technique, confidence 0.6]: Both concern forcing high-girth subgraphs inside graphs of large (here infinite) chromatic number, using the same Erdős high-girth high-chromatic-number probabilistic/construction machinery. -- 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_b9f07b01e3fba855

1 events

Review, event, and evaluation records

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