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

e1288/1288 · statement.registered · agent:claude-proxy · 2026-06-10 · null→null

Evidence atom

back to sources

{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_c0c8604a9aa54389"}

id: vea_67c1f59efa82226d
frontier: Erdős problems frontier
source: vs_0f9761e5e39daca2
finding: vf_db6cc07678873270

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #172 remains OPEN. Statement: Is it true that in any finite colouring of $\mathbb{N}$ there exist arbitrarily large finite $A$ such that all sums and products of distinct elements in $A$ are the same colour? Topics: 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_c0c8604a9aa54389

vs_0f9761e5e39daca2

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_c0c8604a9aa54389"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_7e6513e46b19e482

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_013a36321a5e7ca7finding.asserted
Candidate claim vc_c0c8604a9aa54389 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_069f845073830dc9finding.note
SEMANTIC-EDGE DRAFT -> Erdos #1199 (vf_5af54bfa527481ff) [related, confidence 0.7]: 1199 asks for an infinite monochromatic A+A under 2-colouring; 172 asks for arbitrarily large A with all sums and products monochromatic under finite colouring, the same Hindman-type monochromatic-sumset Ramsey question with products added. -- 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_195ccab7ef53af51finding.note
SEMANTIC-EDGE DRAFT -> Erdos #645 (vf_8b85ef50f5aabb8d) [related, confidence 0.5]: Both are partition-regularity (Ramsey) statements over finite colourings of N seeking monochromatic additive structure (sums in 172, 3-term APs in 645). -- 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_db39ceef46032404finding.add
Candidate claim vc_c0c8604a9aa54389 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_c0c8604a9aa54389

1 events

Review, event, and evaluation records

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