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_8f97870bd7058c46

id: vs_0ce84fdcbaec5e57
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

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

citation

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locator

title:cap_61973ee16b553d57 · vc_8f97870bd7058c46

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 #562 remains OPEN. Statement: Let $R_r(n)$ denote the $r$-uniform hypergraph Ramsey number: the minimal $m$ such that if we $2$-colour all edges of the complete $r$-uniform hypergraph on $m$ vertices then there must be some monochromatic copy of the complete $r$-uniform hypergraph on $n$ vertices. Prove that, for $r \ge 3$, $$ \log_{r-1} R_r(n) \asymp_r n, $$ where $\log_{r-1}$ denotes the $(r-1)$-fold iterated logarithm. Topics: graph theory, ramsey theory, hypergraphs. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible.
open_question · vf_187280ca6f4d09c4

Evidence atoms

vea_4a41b742b9a1ce4dcomputational · supports
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_8f97870bd7058c46"}

Review, event, and evaluation records

events

vev_be753d8ca0abc604finding.asserted
Candidate claim vc_8f97870bd7058c46 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_1d25754ed5747738finding.note
SEMANTIC-EDGE DRAFT -> Erdos #564 (vf_8fdce4bf9419e970) [generalizes, confidence 0.9]: 562 defines the Ramsey number R_r(n) for all uniformities r, of which 564's R_3(n) is the r=3 instance. -- 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_e9144cb6284cd11efinding.add
Candidate claim vc_8f97870bd7058c46 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30

evaluations

No evaluation rows are attached.