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

Source record

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cap_61973ee16b553d57 · vc_96f84be927cb3894

id: vs_dcec0ebdd0e76d5d
frontier: Erdős problems frontier
type: synthetic_report

source boundary

frontier-owned

synthetic

finding bindings

record context

1 findings

evidence atoms

materialized

1 atoms

review context

inspectable

1 events

4 reviewable changes and 0 evaluations are attached through this source or its findings.

citation

external source

locator

title:cap_61973ee16b553d57 · vc_96f84be927cb3894

imported

2026-05-30T00:42:06.826507+00:00

extraction mode

artifact_to_state_import

authors

Erdős Open-Problem spine ingest

caveats

source requires human review before being treated as evidence

Bound findings

Erdős Problem #98 remains OPEN. Statement: Let $h(n)$ be such that any $n$ points in $\mathbb{R}^2$, with no three on a line and no four on a circle, determine at least $h(n)$ distinct distances. Does $h(n)/n\to \infty$? Topics: geometry, distances. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible.
open_question · vf_ffd1943974b46af5

Evidence atoms

vea_b09e62193033a9d8computational · supports
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_96f84be927cb3894"}

Review, event, and evaluation records

events

vev_80a37ab375987e46finding.asserted
Candidate claim vc_96f84be927cb3894 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_3151d5846e2a266efinding.add
Candidate claim vc_96f84be927cb3894 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_4594c3547a681d67finding.note
SEMANTIC-EDGE DRAFT -> Erdos #1082 (vf_c7f890d876accf7d) [related, confidence 0.7]: Both ask for a lower bound on the number of distinct distances determined by n points under a general-position-type hypothesis (no three collinear), with 1082 conjecturing the explicit bound floor(n/2). -- 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_7ef037714e22c815finding.note
SEMANTIC-EDGE DRAFT -> Erdos #982 (vf_ede0b0cddd2bbaab) [related, confidence 0.6]: Problem 982's claim that some vertex of a convex n-gon realizes at least floor(n/2) distinct distances is a convex-position instance of the general-position distinct-distance question quantified in 98's h(n). -- 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_ac7fde84f928fc70finding.note
SEMANTIC-EDGE DRAFT -> Erdos #89 (vf_9e0543dd7357caf2) [specializes, confidence 0.75]: Problem 98's h(n) is the minimum number of distinct distances under the general-position (no three collinear) restriction, a special case of the unrestricted distinct-distances lower bound asked in 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

evaluations

No evaluation rows are attached.