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_632fc78f576f2aa3

id: vs_39705be50e022f60
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

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

citation

external source

locator

title:cap_61973ee16b553d57 · vc_632fc78f576f2aa3

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 #142 remains OPEN. Statement: Prove an asymptotic formula for $r_k(N)$, the largest possible size of a subset of $\{1, \dots, N\}$ that does not contain any non-trivial $k$-term arithmetic progression. Topics: additive combinatorics, arithmetic progressions. Erdős prize: $10000. Statement is machine-verified in Lean (formal-conjectures). OEIS: A003002, A003003, A003004, A003005.
open_question · vf_b66b7c5d84d7554e

Evidence atoms

vea_975362f71a58eb92computational · supports
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_632fc78f576f2aa3"}

Review, event, and evaluation records

events

vev_1ef43241a0723e57finding.asserted
Candidate claim vc_632fc78f576f2aa3 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_4e8c391a3f233eabfinding.note
SEMANTIC-EDGE DRAFT -> Erdos #139 (vf_29ab904190a2f3db) [related, confidence 0.85]: Both concern r_k(N), the largest AP-free subset of {1,...,N}; 139 states the bound problem while 142 asks specifically for an asymptotic formula for the same quantity. -- 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_aaefaf3f4cd0ee9cfinding.note
SEMANTIC-EDGE DRAFT -> Erdos #138 (vf_8d5ada8b450f91ca) [related, confidence 0.55]: 142 is the density (Szemeredi) version of avoiding k-term APs while 138 is the coloring (van der Waerden) version of forcing monochromatic APs, two faces of the same arithmetic-progression Ramsey phenomenon. -- 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_bb01ad67b62a350ffinding.add
Candidate claim vc_632fc78f576f2aa3 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30

evaluations

No evaluation rows are attached.