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_397e1406bc8b009f"}

id: vea_882adcd84aad5ccd
frontier: Erdős problems frontier
source: vs_d9ac00d707d0622f
finding: vf_61c6a46c0bd5227e

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #195 remains OPEN. Statement: What is the largest $k$ such that in any permutation of $\mathbb{Z}$ there must exist a monotone $k$-term arithmetic progression $x_1 < \cdots < x_k$? Topics: arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

source binding

source-bound

cap_61973ee16b553d57 · vc_397e1406bc8b009f

vs_d9ac00d707d0622f

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_397e1406bc8b009f"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_e0c122339ef68265

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_de6c6605a0fe9d6bfinding.asserted
Candidate claim vc_397e1406bc8b009f imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_697593037c051f90finding.add
Candidate claim vc_397e1406bc8b009f imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_80d83fa1d8e4821efinding.note
SEMANTIC-EDGE DRAFT -> Erdos #197 (vf_aff975922c8e0373) [related, confidence 0.7]: Both concern monotone arithmetic progressions inside permutations of the integers; 197's 2-colouring/permutation construction is exactly the kind of avoidance argument used to bound the k in 195. -- 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_95609b2dfdaabc07finding.note
SEMANTIC-EDGE DRAFT -> Erdos #196 (vf_f91e5876c643b8a0) [specializes, confidence 0.9]: 196 (must every permutation of N contain a monotone 4-term AP) is the k=4, ground-set-N special case of 195's question on the largest guaranteed monotone k-term AP in any permutation of Z. -- 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.

computational

open_question

cap_61973ee16b553d57 · vc_397e1406bc8b009f

1 events

Review, event, and evaluation records

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