Vela

frontiers / frontier

Erdős problems frontier

constellation seal · derived from vfr_37aec80d874a0239
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_27b47077dc2fe4d7"}

id
vea_14b52ec174dac874
frontier
Erdős problems frontier
source
vs_b8e140b0e98c3f49
finding
vf_8b85ef50f5aabb8d

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #645 has status 'proved (lean)'. Statement: If ℕ is $2$-coloured then there must exist a monochromatic three-term arithmetic progression $x,x+d,x+2d$ such that $d>x$. This was first proved by Brown and Landman [BrLa99], who in fact show that this is always possible with $d>f(x)$ for any increasing function $f$. This was formalized in Lean by Alexeev using Aristotle and ChatGPT. Topics: number theory, additive combinatorics, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

source binding

source-bound

cap_61973ee16b553d57 · vc_27b47077dc2fe4d7

vs_b8e140b0e98c3f49

review context

unverified

1 events

1 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_27b47077dc2fe4d7"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_d9125485157ea101

caveats

No caveats recorded.

Review, event, and evaluation records

2

events

  • vev_41767cc66c3e8153finding.asserted

    Candidate claim vc_27b47077dc2fe4d7 imported from artifact packet cap_61973ee16b553d57

    reviewer:erdos-db-trustreviewer:erdos-db-trust · 2026-05-30

reviewable changes

  • vpr_91d0db65cd458d2afinding.add

    Candidate claim vc_27b47077dc2fe4d7 imported from artifact packet cap_61973ee16b553d57

    agent — machine actor, no signing keyapplied · agent:erdos-spine-ingest · 2026-05-30

evaluations

No evaluation rows are attached.

finding.noted · reviewer:will-blair · 2 days

renders the record as of vev_d199cb2e · 1,338 events · hub

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