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

e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null

Evidence atom

back to sources

{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_33d7e7704dc86004"}

id: vea_f8d8a2d12be2e2ab
frontier: Erdős problems frontier
source: vs_132b024e395d8b6d
finding: vf_9e0543dd7357caf2

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #89 remains OPEN. Statement: Does every set of $n$ distinct points in $\mathbb{R}^2$ determine $\gg \frac{n}{\sqrt{\log n}}$ many distinct distances? Topics: geometry, distances. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: A186704, A131628.

source binding

source-bound

cap_61973ee16b553d57 · vc_33d7e7704dc86004

vs_132b024e395d8b6d

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_33d7e7704dc86004"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_bd6a49f7d58e8eff

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_01d2f4cc97fc986bfinding.asserted
Candidate claim vc_33d7e7704dc86004 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_022eb3671041aa98finding.add
Candidate claim vc_33d7e7704dc86004 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_907b11f9c1385f29finding.note
SEMANTIC-EDGE DRAFT -> Erdos #1082 (vf_c7f890d876accf7d) [related, confidence 0.6]: Both are distinct-distance lower-bound problems for n planar points; 1082 strengthens the bound to floor(n/2) under the no-three-collinear hypothesis whereas 89 asks the unrestricted n/sqrt(log n) bound. -- 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_33d7e7704dc86004

1 events

Review, event, and evaluation records

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