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_632fc78f576f2aa3"}

id: vea_975362f71a58eb92
frontier: Erdős problems frontier
source: vs_39705be50e022f60
finding: vf_b66b7c5d84d7554e

evidence boundary

supports

computational

finding binding

bound

open_question

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.

source binding

source-bound

cap_61973ee16b553d57 · vc_632fc78f576f2aa3

vs_39705be50e022f60

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_632fc78f576f2aa3"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_e48cc00d58703f0f

caveats

No caveats recorded.

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.

computational

open_question

cap_61973ee16b553d57 · vc_632fc78f576f2aa3

1 events

Review, event, and evaluation records

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