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_31964684fa99ab60"}

id: vea_63808c788d6b3809
frontier: Erdős problems frontier
source: vs_4c4a558cf98a404e
finding: vf_6b4ba8010dbbad76

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #91 remains OPEN. Statement: Suppose $A\subset \mathbb{R}^2$ has $\lvert A\rvert=n$ and minimises the number of distinct distances between points in $A$. Prove that for large $n$ there are at least two (and probably many) such $A$ which are non-similar. Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A186704, possible.

source binding

source-bound

cap_61973ee16b553d57 · vc_31964684fa99ab60

vs_4c4a558cf98a404e

review context

unverified

1 events

3 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_31964684fa99ab60"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_76b28488ff5ae552

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_4af268e8e302a49dfinding.asserted
Candidate claim vc_31964684fa99ab60 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_510517003bcf45cbfinding.note
SEMANTIC-EDGE DRAFT -> Erdos #89 (vf_9e0543dd7357caf2) [related, confidence 0.55]: Problem 91's notion of a distance-count-minimizing optimal configuration is the extremal object underlying the distinct-distances lower bound problem 89. -- 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
vpr_91365d0b0506c6cffinding.add
Candidate claim vc_31964684fa99ab60 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_f877dcb9fa6d6b8cfinding.note
SEMANTIC-EDGE DRAFT -> Erdos #98 (vf_ffd1943974b46af5) [depends_on, confidence 0.7]: An 'optimal' set in 91 is defined as one achieving the minimum distinct-distance count, which is exactly the function h(n) studied in 98, so 91's definition is parasitic on that minimum. -- 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_31964684fa99ab60

1 events

Review, event, and evaluation records

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